Home

MacSADIE 1.2 User`s Manual

1. BIL command is useful for composing three images into a color composite Note that the output image will appear to be a grayscale image if the three input images are identical however it is nonetheless a three band image Complex Real The Complex Real command converts an input image in complex format to two images in real format You need to indicate whether the complex values should be separated into their real and imaginary or magnitude and phase components Real Imaginary O Magnitude Phase Image Names EERE Cancel The graylevel of a pixel in the output images O and P are computed from the input image as l lijak 1f Real Imaginary is specified Oik ij a le ae ii 2 1 if Magnitude Phase is specified Lij2 k 1 if Real Imaginary is specified Pik 2 I ij2 k 1 tan a if Magnitude Phase is specified IT ij2 k where tan represents the trigonometric arc tangent function 87 The Complex Real command is useful for separating an image in complex format created by the Filter FFT or Filter FHT command into its components in real format for further processing Real gt Complex The Real Complex command converts two input images in real format to one image in complex format You need to indicate whether the input images represent the real and imaginary or magnitude and phase components of the complex image Both images default to the image in the frontmost window The two in
2. Image Name Pixels are assigned labels based on the proximity of their graylevel values to the graylevel means of the clusters Initially the class means are distributed uniformly across the m dimensional feature space Using the city block distance criterion each pixel is then assigned to the class with the closest mean New class means are computed from those clusters and the pixels are re assigned to the classes This process is repeated until the number of iterations specified in the dialog has been reached If during the iterative process the number of pixels in any given class falls below the minimum class size specified in the dialog that class is removed from subsequent iterations by allowing its pixels to be absorbed into other classes Similarly if two cluster means become in each feature dimension closer than the class merging threshold specified in the dialog the corresponding classes are merged Two classes c and d are merged if Vilsism Ptal y 6 64 where u a and uq are the graylevel means for classes c and d in band i Ge and Og are the graylevel standard deviations for classes c and d in band i and ty is the class merging threshold as specified in the dialog Recommended values for this parameter are between 0 0 no merging 92 and 1 0 If two classes are merged the resultant class is not permitted to be merged with any other class in the same iteration If the minimum class size and the cluster merging th
3. and the number of distinct graylevels The generated grayscale has the minimum graylevel on the left and the maximum graylevel on the right side Image Size Line s Pinel s Graylevels o o Minimum 299 0 Maximum Number BERGE The graylevel value of a pixel in the output image O is computed as k 1 f g Omax O min s 1 where n is the number of pixels line Omin and Omax are the minimum and maximum graylevels and g is the number of graylevels in the output image as specified in the dialog Oir z Omin You can use the Geometry Rotate command to reverse the order of graylevels in the output image or to rotate the grayscale from horizontal to vertical To append a grayscale to an existing image you can use the Geometry Horizontal Mosaic the Geometry Vertical Mosaic or the Geometry General Mosaic command When doing this you should keep in mind the automatic display stretch used by MacSADIE In order for the combined image to utilize the full dynamic 20 range of the display the grayscale being appended must have the same graylevel minimum and maximum as the original image Sinewave The Sinewave command creates a horizontal sinewave pattern Parameters are the size of the output image and the period and phase of the sinewave Image Size Line s Pinel s Period Pixel s Phase Pinel s Engari The graylevel value of a pixel in the output image O is computed as sin Oj 255 on y
4. reb Tix where rgb is the color space transformation function This function is described in detail in A R Smith Color Gamut Transform Pairs Computer Graphics Vol 12 No 3 August 1978 pp 12 19 The HSV RGB command is the functional inverse of the RGB HSV command which 1s described above 85 BIL gt BSQ The BIL gt BSQ band interleaved to band sequential command separates a three band color image into three single band images The graylevel of a pixel in the output image R G or B is computed from the graylevel of the corresponding pixel in the input image Z as Ex hy Gik hjk Bk hjk The BIL gt BSQ command is useful for separating individual bands for further processing BSQ BIL The BSQ BIL band sequential to band interleaved command combines three single band images into a three band color image Parameters are the three input images which all default to the image in the frontmost window The three input images which must all be single band and have the same number of lines band and pixels line are chosen from pop up menus of all images currently on the desktop with all menu choices permanently enabled Red Image Green Image Blue Image Engari Image Name 86 The graylevel of a pixel in the output image O is computed from the graylevels of the corresponding pixels in the input images R G and B as Re if i 1 Ox Ge if i 2 iB Geiss The BSQ
5. the absolute value of x if x is a set the number of elements in x Examples 1 2 1 2 1 2 1 2 1 2 3 3 Set containing x Example 1 2 3 the set containing the numbers one two and three Set membership Example Jj S Ij is an element of set All x for which y is true Example ijx lijk lt xj the set of all Jj that are less than or equal to x There exists an x such that y is true Example d i j k Lijk O there exist indices i j k such that ijk equals zero For all x y is true Example V i j k Ijk lt Tijk 1 Tix is less than x 1 for all indices i j k Logical conjunction of x and y true when both x and y are true false otherwise Example Iyk lt Iimn Tijk gt limn false Logical disjunction of x and y true when either x or y are true false otherwise Example Ijz lt Iimn V Lijk gt mn true Logical negation of x true when x is false false otherwise Example Ujx Imn V Tijk gt Imn false 99 Appendix B Keyboard Shortcuts Menus It is possible to select frequently used MacSADIE commands directly from the keyboard by holding down the Command key and typing a single letter The following is a complete list of those keyboard shortcuts ordered by menu About MacSADIE Fil Fil Fil Fil Fil Open Close Save Print Quit oO UVNnNaO A HS 00000 Edit Edi Edit Edi elete gt Edi Edit Undo Cut
6. 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column Like the Diversity Map command see below the Variance Map command generates an image representing the local contrast graylevel variation in the input image It is useful for creating a spatial texture or edge activity feature map from an image With a suitable graylevel threshold applied afterwards see the Contrast Threshold Graylevels command the variance operation can be a useful edge detector for some images Diversity Map The Diversity Map command computes a map of the input image where the graylevel of a pixel in the map represents the number of different graylevels within a window centered at the corresponding pixel of the input image Parameters are the vertical and horizontal window size which must both be odd Window Size Line s EJ Pixel s EERE 62 The graylevel of a pixel in the output image O is computed from the input image and a window of size m by n as Oijk 1 j m p neg l lt psmalsqs n 2 2 Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column The Diversity Map command generates an image representing the local contrast graylevel variation in the input image It is particularly useful for creating a map of local class heterogeneity from a clas
7. 53 Filter 54 Inverse Transform 55 FHT 56 Inverse Transform 56 File Format 102 File Menu 19 Filter Conditional Average 66 FFT 54 High Pass 54 Low Pass 54 Majority 63 Maximum 65 Median 64 Minimum 65 Parametric High Boost 54 55 Filter Menu 53 Fourier Transform 55 Frequency Domain Image 56 57 Full Color 13 97 Function 21 G General Mosaic 74 Generic Image 24 Geometry Menu 69 Gradient Library Mask 59 User Mask 60 Graylevels Requantize 47 Saturate 48 Threshold 49 Grayscale 11 20 Display 11 Image 11 Grid 88 H Hardware Requirements 7 Hartley Transform 56 Help Button 14 101 Hide Clipboard 32 Session Log 32 High Pass Filter 54 Histogram 34 Histogram Equalize Stretch 42 Horizontal Mosaic 71 HSV 84 85 RGB 85 Hue Saturation Value 84 85 l Image 9 BIL 25 86 BSQ 25 86 Color 11 Complex 56 57 87 88 File Format 102 Frequency Domain 56 57 Generic 24 Grayscale 11 MacSADIE 8 9 24 27 28 102 105 Multi Band 11 PICT 8 9 24 Single Band 11 Spatial Kernel 54 57 58 Synthetic 19 Text 32 TIFF 8 9 24 Image Information 33 Import 24 Insert 75 Installation 8 Interpolation Bi Linear 69 78 Nearest Neighbor 69 78 Parametric Cubic 69 78 Inverse Transform FFT 55 FHT 56 K Karhunen Loeve Transform 83 Key Command 11 14 15 27 100 101 Shift 14 24 25 28 29 34 100 Keyboard Shortcuts 100 L Label Map 91 93 95 Levelslice 91 Linear Scale 69 Linear Stretc
8. Copy Paste Clear Select All lt ON LN a LN Y Y Y gt gt PLO lt OQxN Analysis Image Information Analysis Statistics and Histogram Analysis RMS Difference TH U Normalize Stretch Histogram Equalize Stretch Logarithmic Stretch Square Root Stretch Contrast Contrast Contrast Contrast Arms a A AN Q Filter Gradient Library Mask Windows Full Color Windows Session Log 9 Windows oldest image newest image Rom For most MacSADIE commands with or without keyboard shortcuts you can skip the dialog by holding down the Shift key when selecting the command via mouse or keyboard Skipping the dialog causes the command to be executed with its default parameters The exceptions to this rule are the _ About MacSADIE File Open File Import File SaveAs File Page Setup Edit Preferences and Analysis Image Information commands where this feature would defeat the purpose of the dialog as well as all commands from the Edit and Windows menu that do not have a dialog Holding down the Shift key when selecting the File Quit command adds statistical output to the session log and brings up the Print command s dialog for the session log 100 Dialogs Most buttons in MacSADIE s dialogs have Command key equivalents as shown in the following list lt enter gt EERE m C Cancel The File Open File Import and File Save
9. Directional Masks Optical Engineering Vol 16 No 6 November December 1977 pp 580 585 Note that the direction map for the Roberts filter is 7 4 radians out of phase with those for the other filters Gradient User Mask The Gradient User Mask command convolves an image with two spatial kernels a horizontal and a vertical mask It then combines the results in a vector calculation to produce two output images one representing the magnitude the other representing the direction of the gradient at each point of the input image The kernels gradient operators may be given either as images or they may be numerically specified as masks the default If the kernels are specified as masks matrices you need to provide the horizontal and vertical size of the matrices and the individual matrix values If the kernels are to be given as images you can choose from a pop up menu of all images currently on the desktop with all menu choices permanently enabled If there is only one image on the desktop both kernels defaults to that image otherwise they default to the image in the window behind the frontmost one The size of the kernel images must be odd in both the vertical and the horizontal direction and the kernel images must be single band 60 Mask Kernels eriga Kernel Horizontal ERRE Cancel Image Names GradDir The graylevel of pixels in the magnitude image M and the direction image D are computed from t
10. Hide Clipboard command from the Edit menu Note that hiding a window is different from closing it All information in the window is retained while the window is invisible The clipboard window is continually updated as the contents of the clipboard change independently of its visibility Hide Session Log Show Session Log The Hide Show Session Log command is a single toggled command If the session log window is visible the command reads Hide Session Log and executing it causes the window to be hidden If the window is hidden the command reads Show Session Log and executing it makes the window visible again Clicking on the close box of the session log window is equivalent to choosing the Hide Session Log command from the Edit menu Note that hiding a window is different from closing it All information in the window is retained while the window is invisible In the case of the session log new information is added independently of the window s visibility Preferences The Preferences command has not yet been implemented We welcome any and all suggestions from our users as to which features of MacSADIE you would like to be able to customize Please send your ideas to MacSADIE c o Digital Image Analysis Lab Dept of Electrical and Computer Engineering University of Arizona TUCSON AZ 85721 U S A macsadie O dialsun ece arizona edu 32 The Analysis Menu Analysis The Analysis menu provides you with a Image Information v
11. Save 27 Save As 27 Scattergram 38 Segment 93 Select All 13 32 Selection 13 31 32 Rectangle 13 31 32 Session Log 9 97 Hide 32 Show 32 Shift Key 14 24 25 28 29 34 100 Shortcuts 100 Show Clipboard 32 Session Log 32 Signature Map 95 Sinewave 21 Single Band Image 11 Software Requirements 8 Spatial Kernel Image 54 57 58 Square Root Stretch 46 Square Stretch 46 Startup 8 Statistics 34 Stretch Adaptive 50 Display 11 20 42 44 49 72 73 74 89 95 Histogram Equalize 42 Linear 43 Logarithmic 44 Normalize 41 Piecewise Linear 45 Reference 50 Square 46 Square Root 46 Table Lookup 47 Subsample Average 70 Import 26 Window 71 Supervised Classification 91 92 Synthetic Image 19 System Software 8 Menu 17 Table Lookup Stretch 47 Text Image 32 Threshold Graylevels 49 TIFF Image Open 8 24 Print 9 Transform Fourier 55 Hartley 56 Karhunen Loeve 83 Principal Components 83 U Undo 31 Unsupervised Classification 91 93 94 V Variance Map 61 Version Number 17 Vertical Mosaic 72 Ww Window 9 97 Window and Subsample 71 Window Entries 97 Window Subsample Button 26 Windows Menu 97 Wrap Around Convolution 54 55 Z Zoom In Button 34 Zoom Out Button 34 107
12. a Vertical O 45 Diagonal O 45 Diagonal Mirror Axis O Horizontal BERGE G 79 The graylevel of a pixel in the output image O is computed from an m by n by o input image Tas Lijn k 1 if Vertical is specified es Iikj if 45 Diagonal is specified IE ON Tyta n j 1 if 45 Diagonal is specified Iin j 1 k if Horizontal is specified where the output image is of size m by n by o if the input image is mirrored along the vertical or along the horizontal axis and of size m by o by n otherwise 80 The Miscellaneous Menu The Miscellaneous menu provides a Combine variety of useful commands for Compare composing images transforming images from one domain or format into another and for adding gridlines and hashmarks to an image The Combine and Compare commands compose two images into a single one and are enabled only when there are at least two images on the desktop The Principal Components Transform command operates on multi band images it is enabled only when the image in the frontmost window contains Complex gt Real a multi band image The RGB HSV E HSV RGB and BIL gt BSQ Been dd commands require three band color images they are enabled only when the image in the frontmost window is a three band image The BSQ gt BIL Complex Real Real gt Complex and Grid commands are enabled for all types of images Combine wt The Combine command computes a weighted li
13. assina e tea a aE aaa s TEE AEAT N eE EEE OE E TEA S ape ea 28 A O 28 en e oe es e 29 A Ree Ronee ey meen E MeN a Tote er a a nee Nanna een ene a eT 31 a E E E TE E oak wttecs NOS ats eo etan OSG uaa R oat ae aE 31 COPY e a mace lies o e dit e ia 31 Paste a eee tase Lie ia 31 Cleat Societe oh SE i NG ei eh Gea eae Be iON Sa des 32 A nite Gr Road ace eaea Oi e Poet Teh te ia et ade oa 32 Show Clipboard Hide Cbr AS 32 Hide Session Log Show Session Log A O oes 32 Preferentes ipcssiessnnseiii sisendirea bead ayes EA AEEA EE AEEA E I aera esia aa 32 TheAnalysis Me ca aa e 33 Image Mmformatiot A e a a a E a 33 Statistics and PASTOS di 34 Contour Map uni nna EA e E O RE EE EE EAE 35 Cova e innsin iii ita idad 36 a A yc EE E Sate vse als a cde Sc sce ale a Dee 37 RMS Difference andadas 38 A ET a ROEE AEE A Ri 38 The Contrast Men s endrei adas 41 Normalize O o O A 41 Histogram E alize Stretoh encens e a E E E ANA S 42 Linear Stretli n A O A hak a a a aa i aaa ec 43 LESA Stretch nanea a a a a a E e E EEE 44 Piecewise Lincar Sit 45 Square ROO eto albo e A 46 Square ota iaa 46 Table Lookup Setool 47 RE e e 47 Saturate Graylevels iii desa 48 di EVES scsi ton chee adel aide as os cose n beso rites aia dan otal RS 49 Adaptive SUBIC RR anata 50 Reterence e 50 FET Convolution issan i ie a T R i 53 IS A E E a a a daan 54 A E E D E E ET A E ET 55 FHT ocen nna aaa a ai eat e A a a A 56 Convolution Ten a A ere a A EE T E E 57 Gradient Li
14. commands have a number of additional keyboard shortcuts which are identical between applications The keyboard shortcuts for the Cancel button do not work with the Page Setup and Print commands 101 Appendix C MacSADIE Image File Format The following diagram shows the MacSADIE file format assuming an image size of m bands n lines and o pixels stored at p bits pixel Byte 0 yte gt 4 6 8 12 i Header 512 m l 0 p 512 8 512 m2 O Pp 8 ae OE oP 8 5124522 where EE is one line 0 pixels of image data from Band 1 SN is one line o pixels of image data from Band 2 and III is one line o pixels of image data from Band m 102 Appendix D MacSADIE Problem Report Hardware Configuration CPU Model Memory RAM Monitor Make and Model Color Board Make and Model Software Configuration System Software System Version from About the Finder Finder Version from About the Finder MultiFinder Version from About MultiFinder 32 Bit QuickDraw Version from Get Info MacSADIE Version from About MacSADIE INITs Problem Description Briefly describe the problem you are experiencing The description should include a specification of the data being used the exact sequence of commands issued together with their parameters and a description of the obtained versus the expected results Mail To MacSADIE c o Digital Image Analysis Lab Dept of Electrical and Computer Engin
15. difference between two images of the same size The dialog lets you choose the images to be compared via two pop up menus with all choices permanently enabled The first image defaults to the image in the frontmost window the second image to the one directly behind it The two images must have the same number of bands lines band and pixels line First Image Second Image BERGE Cancel The RMS difference between two m by n by o images J and J is defined as deus Y y y Lijk Sip Y i l j l k l The RMS difference represents an average difference between corresponding pixels in two images It is equal to zero for two identical images and increases as the two images become more and more dissimilar The RMS Difference command is useful for comparing the similarity of two images or the quality of a processed image relative to a reference image e g in a simulation of sensor degradation and image restoration It does not however correlate particularly well with visual image quality differences Scattergram The Scattergram command creates an output image representing a two dimensional histogram scattergram between two bands The bands may be from either the same or two different images but must have the same number of lines and pixels line They are chosen from two pop up menus which contain an entry for each band of every image on the desktop All choices on the pop up menus are always enabled The first ba
16. filter parameter as specified in the dialog The FFT Filter command uses cyclic wrap around convolution to determine the pixel values at the image borders The various filter functions F are defined as follows l r if r lt l Cone Fee da 0 otherwise Negative Exponential Fe e Gaussian Fee er 1 iffesre afes Box Fee aie O otherwise f1 ifrsi Cylinder Fee O otherwise where r N felre 4 fclr y 0 5 E N2 T and fg 0 5 c 2 T are normalized spatial frequencies rg Erp rg are the a ii POE the filter function as specified in the dialog and e is the base of the natural logarithm 1 e e In 1 2 718282 The FFT Filter command is faster than the FFT Convolution command because only two FFTs are required compared to three for the FFT Convolution command All filters available through the FFT Filter command are amplitude only and do not modify the phase term The parametric high boost filter is discussed in R A Schowengerdt Techniques for Image Processing and Classification in Remote Sensing Academic Press New York NY 1983 pp 75 79 Generally the larger the value of the filter parameter the less the degree of edge enhancement Note that FFT filtering an image is a memory intensive operation FFT The FFT fast Fourier transform command performs an image transformation The forward transform converts the image from the spatial to the frequency domain the inverse trans
17. gt o fAj gt 0 8fill otherwise where Aj is the vertical offset and ggu is the background fill graylevel as specified in the dialog The output image O is either of size m by max nr Aj nyj by or o if Aj lt 0 or of size m by maxin7 n HA by or o J Gf Aj gt 0 for a left image of size m by n by 0 and a right image of size m by n by 0 The Horizontal Mosaic command is useful for appending additional information such as grayscales or textual annotations to an image Another use of the Horizontal Mosaic command is for visually comparing the contrast in multiple images Due to MacSADIE s automatic display stretch mosaicing is one way of obtaining a relative comparison of the contrast in multiple images since the composite image will be displayed with the same graylevel minimum and maximum The background graylevel will only alter the contrast if it is outside the graylevel range of each one of the mosaiced images but even then the contrast is altered equally in all images Vertical Mosaic The Vertical Mosaic command concatenates two images vertically with the top image horizontally offset with respect to the bottom image Parameters are the top image which defaults to the image in the frontmost window the bottom image which defaults to the image in 12 the window behind the frontmost window a horizontal offset between the images which may be positive or negative and a graylevel value to be used for t
18. image as nni i y x if Nearest Neighbor Interpolation is specified Oik blif i y x if Bi Linear Interpolation is specified pei I i y x if Parametric Cubic Interpolation is specified where x a ay k a3 jtag k j as k a6 j y bi b2 k b3 b4 kk j b5 b b6 3 and nni bli and pci represent the different interpolation functions which for an input image J of size m by n by o are defined as follows Limay mato if 1 lt md y lt n 1 lt md x lt o nni i y x d 8111 otherwise where gau is the background fill graylevel as specified in the dialog and the function rnd rounds its real valued argument to the nearest integer Pa 01 18281 if I lt slylsnl a 1 lt lx lt 0 1 bli i y x iy del otherwise Tity jie bel iy Jj ily 113 where g and 82 Tityjy el Loy 42 ish ily i 10 ee pwpoly a y lyl 81 82 83 84 if 2 lt y lt n 2 A 2 lt x lt 02 ci i y x p 8fill otherwise where g pwpoly amp x lx 251 y 31 Leto di ly Ht lxb Lily et Lx ot Li Ly HI 11142 82 pwpoly amp x lx Ly 910 lily lx lily lie 2 83 pwpoly a x Lx 131 y jet ix ete lily 141 Lx lily Lx ed Zi Ly 41 10342 g4 pwpoly 0 x Lx L51 y j42 Lx et Lily 42 Lx Li Ly 42 Lx Jed Li Ly 42 Lx 42 and pwpolylo A e f 2 1 4 8 14A 5 14aP 144P 0 e 1 00 3 4 0 42 45 1 a 3 1 AF 042 1 4 g La 8 2 a 5 2 aP 2AP a h The di
19. into its real and imaginary or magnitude and phase parts with the Misc Complex gt Real command The FFT command is useful for analyzing the frequency characteristics of an image FHT The FHT fast Hartley transform command performs the same transformations between spatial and frequency domains as the FFT command but uses a different more efficient algorithm While MacSADIE s implementation of the FHT algorithm is approximately 30 faster than the FFT implementation it requires that the number of lines band equal the number of pixels line and that this number be a power of two The inverse FHT transform does not destroy its input image 56 a Forward Transform O Inverse Transform EMERGE Image Name Cancel The graylevel of a pixel in the output image O is computed from the input image as n Q Oz y y Iijk e E E if Forward Transform is specified j 1 k 1 T T On Y Y Tec ev i kC if Inverse Transform is specified En Go where and are frequency domain coordinates e is the base of the natural logarithm i e e 1n 1 2 718282 and 1 is the complex number V 1 The spatial domain image in the case of the forward transform O in the case of the inverse transform is assumed to be of size m by n by o For more information on the fast Hartley transform see R N Bracewell The Hartley Transform Oxford University Press New York NY 1986 The format of frequency domain complex images is describ
20. is used to scale image graylevels to some specific range without altering the relative relationship between pixels This is necessary for commands such as Misc RGB HSV which require image graylevels to be in a certain range You can also use the Linear Stretch command to create the negative of an image either by setting the new minimum graylevel to the old maximum and vice versa or by setting the bias to the old maximum and the gain to 1 Logarithmic Stretch The Logarithmic Stretch command logarithmically stretches the graylevels of the input image EERE Image Name ELELE Cancel The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as f logio ljk 1 if tix 2 0 Oik eee if Tix lt 0 where the function logio computes the base 10 logarithm of its argument 44 Since the logarithm of a negative number is undefined negative graylevels are not transformed but simply retained Note that one is added to the original graylevels to allow the transformation of images with graylevel values of zero The Logarithmic Stretch command is useful for transforming an image with a wide histogram a very large dynamic graylevel range skewed towards lower graylevels such as the images produced by the Analysis Power Spectrum or Filter Gradient commands Piecewise Linear Stretch The Piecewise Linear Stretch command stretches image graylevels via a three s
21. line co linearity condition It is therefore recommended that the number of control point pairs always be larger than the number of polynomial terms which also allows distribution of any errors in individual control point coordinates across the whole set of control points since the linear system is over determined as well as the computation of a meaningful transformation error Polynomial Warp The Polynomial Warp command performs a coordinate transformation on the input image Parameters are the size of the image to be created and a graylevel value to be used for the background The transformation is determined by the number of polynomial terms the values of the polynomial coefficients the interpolation method and in the case of parametric cubic interpolation an interpolation parameter o which defaults to a value of 0 5 The default size of the output image is taken as the size of the input image The number of polynomial terms and the polynomial coefficients default to the most recent values computed with the Control Points command Image Size Bm Line s 256 Pixel s Fill Graylevel Polynomial Terms w 3 O4 45 76 Polynomial Coefficients ASE H 0 000000 Y 0 000000 Cancel 1 000000 H 0 000000 H 0 000000 1 000000 Paget age Interpolation Nearest Neighbor O Bi Linear O Parametric Cubic figs T11 The graylevel of a pixel in the output image O is computed from the input
22. magnitude and the other representing the Prewitt direction of the gradient at each point of the input image The masks gradient operators are chosen from a pop up menu of common gradient operators with all menu choices permanently enabled Roberts2 Gradient Operator Image Names EE L aE EFESE The graylevel of pixels in the magnitude image M and the direction image D are computed from the input image 7 and two m by n kernels K and K as Mie V Vin tHix z Hijk where Vin hy ep neg Kio Hix E ep reg K o v and h p 1 q 1 p 1 q 1 denote vertical and horizontal components respectively and tan represents the trigonometric arc tangent function Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column Dix tan 59 The following choices are available for the horizontal and vertical kernels K h and K 1 01 121 Sobel K 202 K 000 101 1 2 1 1 01 111 Sobel2 K 101 K 000 1 0 1 1 1 1 0 1 1 111 Sobel3 K 011 K 1 1 1 0 1 1 000 000 000 Roberts K 001 K 010 0 1 0 0 0 1 000 010 Roberts2 K 011 K 010 000 000 1 1 1 1 11 Prewitt K 1 2 1 K 121 1 1 1 1 1 1 Gradient operators are useful for detecting edges i e sudden changes in graylevel in an image They are discussed in detail in G S Robinson Detection and Coding of Edges Using
23. maximum resulting in an identity transformation of the image Graylevel Minimum Maximum BERGE Image Name Satstr Cancel 48 The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Emin if Lijk lt 8min Oik Ij if 8min lt Tijk Emax Emax if Lijk gt Smax where 2min and max are the minimum and maximum graylevel values to be retained as specified in the dialog The Saturate Graylevels command is useful for discarding by saturation extreme graylevel values before further processing or in conjunction with MacSADIE s automatic display stretch for visually stretching the contrast in a displayed image Threshold Graylevels The Threshold Graylevels command converts the input image to a binary image by replacing all graylevel values below some threshold with the minimum graylevel of the input image Lmin and all other graylevel values with the maximum graylevel Zmax The default for the threshold parameter is computed from the minimum and maximum graylevel values as Imin Lnin Imax 2 Graylevel Threshold LETA BERG Image Name ThrStr Cancel The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Z Lis if Li lt t Oi ijk Imax otherwise where t is the threshold graylevel specified in the dialog The Threshold Graylevels command is
24. merged with either segment it is assigned the label of the closer segment again in the sense of the merge criterion Otherwise it begins a new region and is assigned a new label If the pixel is merged with one of the two neighboring segments a test is performed to see if those two segments can be merged This technique ensures that all created regions are four connected Two regions P and Q are merged if OPQ Vi 1 lt i lt m up Ho lt 1 20 where the input image is of size m by n by o t is the graylevel difference threshold and s is the graylevel variance threshold as specified in the dialog Up and Uy are the mean graylevel values for regions P and Q in band i respectively and Opg is the graylevel standard deviation for the resulting merged region in band 7 The details of the segmentation algorithm as well as the resampling and refining steps are described in G Mehldau An Image Segmentation Algorithm University of Arizona Digital Image Analysis Lab Technical Report No 90 3 November 1990 The segmentation procedure is a modification of the technique described in T Ryan Image Segmentation Algorithms SPIE Vol 534 1985 pp 172 178 The Segment command is useful for unsupervised image classification of spatially homogeneous regions Each such region has a unique label class assignment The label map may therefore be useful for counting objects on a uniform background When the label map is combine
25. of an image matching that of the display system but it also has a non obvious consequence different graylevel values in different images may be displayed on the screen with the same intensity value Consider for example an image with a graylevel range from 50 0 to 150 0 and a version of the same image that has been linearly stretched using Contrast Linear Stretch to have a graylevel range from 0 0 to 255 0 as shown below 50 150 As a result of the automatic display stretch these two images look identical on the screen It 1s important to keep this in mind when attempting to visually compare images on the screen We can achieve a correct relative comparison of the contrast in the two images above in two ways 11 One is to create a grayscale image with a graylevel range from 0 0 to 255 0 and append it to each image using Geometry Vertical Mosaic as shown below 50 150 Gray 0 255 Gray Now the minimum and maximum graylevels in each modified image are the same and equal to 0 0 and 255 0 respectively and they appear on the screen with the correct relative contrast Another way to compare the two original images is to mosaic them into one image using for example the Geometry Horizontal Mosaic command as shown below Again by virtue of combining the two images into one they are displayed using the same minimum and maximum graylevels 0 0 and 255 0 respectively derived from the composite image The d
26. on the current state of your desktop which desk accessories you have installed which application you are currently using and whether Alarm Clock you are running under Finder or MultiFinder Calculator The first i Chooser e first item on the menu always provides you with important information on the current application Control Panel MacSADIE in the example on the right Find File The second block of items on the menu lets you Key Caps choose from a list of installed desk accessories Scrapbook If you are running MacSADIE under MultiFinder the menu contains two additional blocks of choices a list of all open applications and an item on MultiFinder The currently active application MacSADIE in this 8 MacSADIE example is indicated by a check mark in front of its icon Switching between applications can be accomplished by About MultiFinder simply selecting another application it causes the application currently in front to be put in the background and the selected application is brought to the front Note that the contents and or the organization of the menu may change with future versions of Apple s system software About MacSADIE When you select this item MacSADIE displays a dialog similar to the one shown below It tells you which version of MacSADIE you are running and gives you other important information on MacSADIE as well To dismiss the dialog and continue simply click anywhere on the screen
27. order without speed penalty and the floating point representation avoids quantization errors that would be introduced by integer arithmetic with a limited number of bits The drawback however is the amount of memory required to store an image at four bytes pixel a 1 by 256 by 256 image requires 256 KBytes of memory In addition each image has associated with it a 512 Byte header some overhead for window management and an off screen pixel map to speed up display of the image Depending on the color mode the off screen pixel map requires either one or four bytes per pixel Color mode is described in detail in the section on Grayscale and Color Display The memory requirements in KBytes without image header and window overhead for some common image sizes are summarized in the table below Image Size Image Off screen pixel map Total Full color off on Full color off on 1 by 128 by 128 64 16 64 80 128 1 by 256 by 256 256 64 256 320 512 1 by 512 by 512 1024 256 1024 1280 2048 3 by 128 by 128 192 16 64 208 256 3 by 256 by 256 768 64 256 832 1024 3 by 512 by 512 3072 256 1024 3328 4096 10 Images are displayed on the desktop in standard Macintosh windows MacSADIE supports systems with multiple monitors with potentially different screen depths You can reposition a window by dragging its title bar across the screen change its size by dragging the size box in the lower right corner and re order it with respect to fore or b
28. range 0 0 1 0 of the spatial width of the adjacent classes Contour Lines Number Width EERE 35 The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as 0 ag y Tikin mali ae Z Oik max l min 255 otherwise l w 2 max min where n is the number of contour lines and w is their width as specified in the dialog and the function rnd rounds its real valued argument to the nearest integer The output image is created by dividing the graylevel range of the input image into n 1 subranges classes of equal width where n is the number of contour lines Each pixel from the input image is assigned to one of those classes The spatial boundaries between the classes form the contour lines Covariance The Covariance command computes the covariance and correlation matrices among the bands of a multi band image The subsample increment parameter lets you define the pixel and line increment for graylevel sampling Subsample Increment Pinel s and Line s BERGE Cancel The covariance and correlation matrices for an m by n by o image I are defined respectively as O11 Sim Mcov Om1 Om Pir Pim Mcor L Pmi Pmm 36 Ms n O O 5 L aw be k 1 l 1 1 l 1 Ik ln 0 1 pas k 1 l 1 n 0 where Oj n O n 10 n o n o Y y Iiki gt y y Tiki L La y de Lira L
29. rectangle you can either use the Edit Clear command or you can double click anywhere in the image Menus and Dialogs MacSADIE commands are normally selected by clicking on the menu bar pulling down a menu dragging the mouse to the desired command and releasing it there Some frequently used commands e g File Open File Save and File Quit can also be invoked directly from the keyboard by holding down the Command key and typing the single letter command shown on the menu O S and Q respectively for the commands in the example above All menu Command key shortcuts are summarized in Appendix B MacSADIE s image processing commands i e commands on menus other than the File Edit and Windows menus operate on the image in the frontmost window and create a new window containing the processed image Individual commands are enabled and disabled depending on this image and its characteristics If for example the frontmost image is a single band grayscale image all commands requiring a three band color image are disabled The exact conditions under which each command is enabled are described in the sections on the individual menus When you select a command from a menu MacSADIE prompts you for additional parameters to the command with a dialog Most MacSADIE dialogs have four buttons arranged as shown in the example at the right Clicking on the OK button initiates processing Pressing the Return or Enter key is equivalent
30. resulting lookup table is then applied to the transformation image The reference stretch is used mainly for visual comparison of images that are initially somewhat similar The Reference Stretch command can produce undesirable results if the two images are dissimilar or uncorrelated 51 52 The Filter Menu Filter The Filter menu provides commands for FFT Convolution filtering images in both the spatial and the FFT Filter frequency domain Like contrast stretching FFT filtering is a pixel by pixel transformation of Raz the image Unlike contrast stretching however the transformation depends not only on the graylevel of the pixel being processed Convolution but also on the graylevels of neighboring Gradient Library Mask pixels Consequently filtering is also termed a neighborhood or context dependent Gradient User Mask operation With the exception of the Convolution Variance Map command all items on the Filter menu are Diversity Map enabled for all types of images The Ma jority Filter Convolution command only operates on Median Filter single band images and is enabled only when the frontmost image contains such an image Minimum Filter Maximum Filter Conditional Average Filter FFT Convolution The FFT Convolution command convolves an image with either a spatial kernel or frequency domain filter This is done by computing the discrete Fourier transform of the image multiplyin
31. useful for simple segmentation and classification tasks 49 Adaptive Stretch The Adaptive Stretch command performs a spatially variable graylevel transformation where a different linear stretch function is computed for each pixel The input image which must be single band is partitioned into blocks and the transformation parameters are calculated for each pixel as a linear interpolation of the stretch parameters for adjoining blocks The default block size for an m by n by o image is computed as min n o 4 Block Size Pixel s and Line s EERE The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Ojk bjk 8jx Lik where both the bias b and the gain g depend on the input pixel For a detailed discussion including an exact description of the algorithm used for computing the stretch parameters see J D Fahnestock and R A Schowengerdt Spatially Variant Contrast Enhancement using Local Range Modification Optical Engineering Vol 22 No 3 May June 1983 pp 378 381 The Adaptive Stretch command is particularly well suited for enhancing the detail in local areas of a scene with widely different mean graylevels or contrasts Note however that the Adaptive Stretch command completely alters the radiometric relationship between pixels and that the transformation is therefore useful only for visual image enhancement Reference Stretch Th
32. window of size m by n as Oik max Lipg JS SP Sit A k 5 qs ken Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column The Maximum command is useful for dilating expanding light objects against a darker background or eroding thinning dark objects against a lighter background In general the results can not be exactly reversed by using the Minimum Filter command Conditional Average Filter The Conditional Average Filter command filters an input image by creating an output image where the graylevel of a pixel represents a conditional average of the graylevels within a window centered at the corresponding pixel of the input image Parameters are the vertical and horizontal window size which must both be odd a set size threshold and a graylevel difference threshold Window Size Line s EJ Pinel s Set Size Threshold o Graylevel Difference Threshold Image Name CAvgFltr 66 The graylevel of a pixel in the output image O is computed from the input image and a window of size m by n as ST de Me if S gt c Lipg S Oik 1_ 2L Lipg if S lt c A max ipg Lirs ling S A lirs S lt r K m n S Lipg E S Iijk otherwise where S Tog jy PSE A kSqSk 5 A Miglin lt t c is the set size cardinality threshold and is the graylevel difference threshold as specified in the dialog Rows an
33. 4 Progress Indicator and Background Processing Most MacSADIE functions display the wristwatch cursor while processing an image However when executing some particularly computation intensive functions e g the Filter FFT command MacSADIE displays a progress indicator as shown below The Cancel button lets you abort the computation in progress at any time Pressing Command or Command C is equivalent to clicking on the Cancel button Processing image brayscale Cancel Functions that display this progress indicator are capable of executing in the background If MacSADIE is running under MultiFinder you can switch to any other application including the Finder by either clicking on a window belonging to that application or by clicking on the small icon at the right end of the menu bar Be advised however that putting such a computation in the background will increase the amount of time required for the command to complete The exact amount of the increase depends on the particular foreground application and the type of activity you are performing with it Error Messages Occasionally MacSADIE may present you with an error message All error messages are intended to be self explanatory There are two types of errors reported input errors and memory related errors Input errors are usually caused by inconsistent parameters MacSADIE commands check all their parameters before processing an image and issue an error message
34. EMERGE Image Name Resamp Cancel The graylevel of a pixel in the output image O is computed from the input image as PpP q L L Lange k Ak y x y 1 Oik pq where p and q are the vertical and horizontal window sizes and Aj and Ak are the line and pixel increments as specified in the dialog An input image of size m by n by o results in an output image of size m by n p Ak by o q Ak The Average and Subsample command smooths and reduces the size of the input image simultaneously The amount of smoothing is dependent on the window size the larger the window the more the image is smoothed while the reduction is directly proportional to the step increment the larger the increment the larger the reduction 70 Window and Subsample The Window and Subsample command extracts a window of pixels from the input image and subsamples it to create the output image Parameters are the coordinates of the pixels in the window s upper left and lower right corner and the subsample increments for the band line and pixel dimensions Band Line Pixel To Band Line Pixel Increment Eandis Linelis Pinel s Rgs f The graylevel of a pixel in the output image O is computed from the input image as Oijk Li Atril j Ajtjpe 1 k Ak kpel where ipeg Jbeg and Kpeg are the coordinates of the first pixel to be subsampled and Ai Aj and Ak are the band line and pixel increments respectively as specified in the d
35. Image File Portuaria iia 102 Appendix D MacSADIE Problem Report cecccescsecssecesssececseccecssececsseceensecesssccecssceeenseeeenaes 103 Tjd a ie dt a 104 Introduction MacSADIE is a Macintosh application for processing grayscale or color images for scientific and engineering applications teaching and research It contains more than 50 commands for image analysis contrast enhancement spatial filtering geometric processing multispectral processing and classification MacSADIE was conceived at the University of Arizona by Dr Robert Schowengerdt of the Digital Image Analysis Lab and designed and written by Gerhard Mehldau of the Department of Computer Science with algorithm contributions from students in the Digital Image Analysis Lab This manual describes MacSADIE Version 1 2 which is based on SADIE Version 4 2 System at Arizona for Digital Image Experimentation a package of portable C functions in the public domain For more information on SADIE see the SADIE 4 2 User s Manual MacSADIE offers a wide variety of choices for analyzing and processing digital images According to function they are grouped into the Analysis Contrast Filter Geometry Miscellaneous and Classify menus In addition the File menu provides for the creation of synthetic images and the input and output of images in different formats the Edit menu allows for the transfer of data between applications and the Windows menu controls MacSADIE s color mode an
36. MacSADIE 1 2 User s Manual Digital Image Analysis Lab Department of Electrical and Computer Engineering University of Arizona Tucson Arizona 85721 Permission is hereby granted to reproduce this material for any non commercial purpose Apple the Apple logo LaserWriter Macintosh and MultiFinder are registered trademarks and Finder and QuickDraw are trademarks of Apple Computer Inc Other product names mentioned in this manual are the trademarks or registered trademarks of their manufacturers Contents A dd 7 Hard Ware Re Gigi MENS E a e a A a aaia 7 SOL Ware Requirements i enna e r e a a oa o ee aE aE iia 8 Instalan ia 8 A 8 SEO LO id tia 9 MA o he 9 Grayscale and Color DP a oi 11 Selection Rectangle mira daa 13 Menus A ii 14 Progress Indicator and Background Processing oococonoccconccononoccnoncnonnnnnonononcnnncnconnncnnncninns 15 A O 15 E ik decih ape et ec spnatisted nue eal ee heg stad dente EERE ia aasa 16 The Menuda 17 Abo t Macs aDIE O ts ede cg des ns Pose eee a oe 17 The Fle Mental anda 19 li fo Sear ARTE et CPPS CAD Se DUTE Onn er PATS SP MS ont POPC SER Oren tetany E 19 Checkerboard ieina erene e e eaa aae aa ora eA Ea e eaS TE ariant 19 Grayscaless arene e e le ca cer Gade henge age 20 O 21 A 21 NE 23 OP ii 24 Pl A a o oa Sat ai 24 A Gi tet aei tsaa tay gats e a aiaa Gest s tah esi eatae ae e nsii 26 SLAA EEEE EATE EEEE SEEE E ETR EEEE NE 27 A E E E E E OE Mee 27 Page SP
37. MultiFinder you can switch between applications while the dialog is displayed To dismiss the dialog click on the Done button or press the Return or Enter key Image Testimage n aft Ps Bands 1 Er t Lines 256 eO w Fy Pixels Line 256 A H 52 Bits Pinel 8 a a oe E Y 138 Graylevel So 2 2 0600e 02 Minimum 3 4000 e 01 y que Maximum 2 5500e 02 33 On the left side the dialog shows the name of the image its size and its graylevel minimum and maximum In the center the image itself is displayed in a 128 by 128 window You can scroll the image through the window by using the scroll bars to the right and underneath and zoom with the Zoom In and Zoom Out buttons to the right The minimum and default zoom is 1 1 G e one image pixel corresponds to one pixel in the window and the maximum zoom is 1 128 i e one image pixel fills the entire window with steps of 1 2 1 4 1 8 1 16 1 32 and 1 64 in between The Zoom In Zoom Out button is disabled once the maximum minimum zoom has been reached You can examine individual pixels by moving the cursor over the image When the cursor is on top of the image its shape changes to a crosshair and its location X and Y in image coordinates is displayed together with the graylevel value s at that location R G and B for three band color images and Z for single band and multi band images displayed in grayscale format To define a cross section move the cursor to one e
38. The format itself is chosen with the BIL and BSQ radio buttons respectively The size of the header which may be between O and 32K Bytes long the size of the image and the number of bits pixel between 1 and 31 for integral values or 32 for floating point values in Macintosh format must be specified explicitly The default header size is set for MacSADIE files see Appendix C for the MacSADIE file format Note that the main window not only lists sub folders and MacSADIE images but all types of files located in the current folder Needless to say the results may be unexpected if the imported file does not contain an image of the specified format In particular if the specified format does not exactly match the structure of the disk file a variety of I O related error messages may result As with the Open command the Shift key does not have any effect with the Import command 25 E MacsADIE AE Butes Header O Grayscale a MacSADIE fe lt 2 Bands Image O More Images O RGBColor 256 Lines Band O User s Manual 256 Pixels Line BitsPixel WHindow Ssubsample To read in only part of an image first specify the full image size as described above and then click on the Window Subsample button You will then find the secondary dialog shown below where you can specify the area to be windowed and or subsampled This area defaults to the entire image as specified in the primary dialog This option is useful if you want to vi
39. This feature is useful if you want to clean up your desktop before you switch to another application under MultiFinder but don t want to quit MacSADIE entirely Save The Save command lets you write an image to disk in MacSADIE s file format When the Save command is invoked for the first time on a particular image it prompts you with the Save As command s dialog see below to let you specify the file s name and location on disk as well as the number of bits to be used to store the graylevel of an individual pixel Since images on the desktop can not be modified in MacSADIE re saving an already saved image is redundant Therefore MacSADIE does nothing if the Save command is invoked more than once on the same image Use the Save As command if you want to create a copy of an already saved image Save As The Save As command lets you write an image to disk in MacSADIE s file format The dialog again is a Macintosh standard and is similar to the Open dialog you can navigate through the hierarchy of folders on all available disks in the same fashion The file name defaults to the name of the image to be saved If you try to save an image with the same name as an already existing file MacSADIE prompts you for confirmation of your choice before overwriting the old file To prevent any loss of accuracy graylevel values are written to disk as floating point quantities by default E MacsADIE fy PEPER GEGE Eject Drive Canc
40. ackground In addition you can scroll the image if the window is smaller than the image it contains Clicking on the close box of a window is equivalent to choosing the File Close command i e the window is removed from the desktop and all the memory associated with it is returned to the system You can close all of MacSADIE s windows with a single mouse click by holding down the Command key when clicking on the close box of the frontmost window Grayscale and Color Display MacSADIE is capable of simultaneously displaying grayscale and color images on the desktop One band images are displayed in grayscale format three band images are displayed in color RGB format and all other images have only their first band displayed in grayscale format This manual refers to those images as single band grayscale three band color and multi band respectively Most MacSADIE commands can process all three types of images in particular both the File Open and File Import commands can read and in the case of the File Import command simultaneously subsample images with any number of bands Commands which only process certain types of images are clearly noted in this manual When displaying images MacSADIE stretches the graylevel range of each image so as to utilize the full range of available grays or colors on the display This is a convenient feature for the user who doesn t have to be concerned about the graylevel range
41. age but this aspect of the filter can be suppressed by setting the set size threshold to zero 67 68 The Geometry Menu The Geometry menu provides a variety of commands for geometric manipulation such as scaling or resampling of images combining images via mosaicing or insertion computing and applying coordinate transformations and rotating or mirroring images These commands are useful for enlarging reducing images scaling simulating image acquisition systems resampling adding text or grayscales to existing images mosaicing or inserting and registering images to maps or to other images coordinate transforms The Horizontal Mosaic Vertical Mosaic General Mosaic and Insert commands combine two images into a single one and are therefore enabled only when there are two or more images on the desktop All other commands are enabled for all types of images Linear Scale Geometry Linear Scale Average and Subsample Window and Subsample Horizontal Mosaic Vertical Mosaic General Mosaic Insert Control Points Polynomial Warp Rotate Mirror The Linear Scale command lets you scale the input image independently in the horizontal and vertical direction Parameters are the vertical and horizontal scale factors the desired interpolation method and in the case of parametric cubic interpolation an interpolation parameter amp which defaults to a value of 0 5 cale Fa
42. all image windows on the desktop and hides the session log and clipboard windows if they are visible Holding down the Shift key when choosing the Quit command has an effect that is different from its effect on other commands First the session log window is made visible if it is not already and statistical data on the current session SADIE functions called number of calls absolute and relative time spent in each function is added After that MacSADIE brings up the dialog for the Print command see above to let you print the modified session log If you want to use a format other than the default for the printout you should specify that format using the Page Setup command before choosing the Quit command Also note that clicking on the Cancel button in the Print dialog only cancels printing it does not cancel the Quit command 29 30 The Edit Menu The Edit menu lets you exchange images and data Undo Selection between different applications via the clipboard and provides commands for changing the visibility of the clipboard and session log windows The Preferences command has not yet been implemented The Undo Redo command is enabled whenever the last edit command is undoable The Cut and Copy commands are enabled only when the frontmost window contains a regular image 1 e not for the clipboard or session log windows and when the selection rectangle of the image in the frontmost window is non empty The Paste command is ena
43. am command is useful for visualizing the correlation between graylevels in different bands of a multi band image prior to transforms such as the PCT see Misc Principal Components Transform that de correlate the different bands 39 40 The Contrast Menu The Contrast menu lets you choose from a large selection of commands for image contrast manipulation Contrast stretches are point operations 1 e the value of a pixel in the stretched image is a function only of the corresponding pixel in the original image designed to enhance the image for visual interpretation The image histogram often Contrast Normalize Stretch Histogram Equalize Stretch Linear Stretch Logarithmic Stretch Piecewise Linear Stretch Square Root Stretch Square Stretch Table Lookup Stretch is a good indicator for deciding which kind of contrast stretch to apply With the exception of the Adaptive Stretch and Reference Stretch commands all items on the Contrast menu are enabled for all types of images The Adaptive Stretch command only operates on single band images and is enabled only when the frontmost window contains such an image The Reference Stretch command modifies the graylevels of one image dependent on those of a second image and is therefore enabled only when there are at least two images available Requantize Graylevels Saturate Graylevels Threshold Graylevels Reference Stretch Normal
44. and see below the Majority Filter command is useful for smoothing an image The amount of smoothing can be controlled to some extent by the center pixel weight parameter A value of one results in unbiased smoothing a value less than one biases the smoothing in favor of neighboring pixels and a value greater than one biases the smoothing in favor of the center pixel The Majority Filter command is especially useful for classification map smoothing Median Filter The Median Filter command filters an input image by creating an output image where the graylevel of a pixel represents the median graylevel within a window centered at the corresponding pixel of the input image Parameters are the vertical and horizontal window size which must both be odd Window Size Line s 3 Pixel s EERE Image Name MedFltr Cancel The graylevel of a pixel in the output image O is computed from the input image and a window of size m by n as Om A where I 1 lt l lt m n is a list of the graylevel values of all pixels within the window in ascending order Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column The Median Filter command is useful for removing isolated pixel or line noise in an image For line or column noise removal the window should be rectangular and oriented perpendicular to the noise 64 Minimum Filte
45. ariety of commands for statistical and other Statistics and Histogram types of image analyses These commands are useful for deciding which type of image processing function to apply to a particular image or what parameters should be used with a given processing function Covariance The Image Information and Statistics and Power Spectrum Histogram commands are enabled for all types RMS Difference of images whereas the Contour Map and Power Spectrum commands are enabled only for single band images The Covariance command only operates on multi band images and is therefore enabled only when the frontmost window contains a multi band image The RMS Difference command compares two images and is enabled whenever there are two or more image windows on the desktop The Scattergram command operates on two bands from either the same or two different images and is therefore enabled only when at least two different bands are available Scattergram Image Information The Image Information command uses a type of dialog that is different from most MacSADIE commands This dialog does not prompt you for parameters nor does it initiate any processing but instead lets you interactively explore the image Besides listing general image attributes it lets you examine the graylevel values of individual pixels and arbitrary cross sections of the image You can move the dialog around the screen just like an ordinary window and under
46. bled whenever the clipboard is not empty The Clear and Select All commands are enabled when the frontmost window contains a regular image independently of the selection Preferences rectangle The Hide Show Clipboard Show Hide Session Log and Preferences commands are always enabled Show Clipboard Hide Session Log Undo Redo The Undo Redo command is a single toggled command which lets you undo the last edit operation The command normally reads Undo op where op is the last edit operation Cut Copy Paste Clear Selection you performed When you select Undo this operation is undone and the command changes to read Redo op Redo op re applies operation op i e it undoes the effects of the Undo command The window on which the Undo Redo command operates is brought to the front if it is not already there If the last edit operation cannot be undone for example if you make a selection within some window and then close that window or if you copy a selection to the clipboard and then replace the contents of the clipboard from within some other application the Undo command reads Can t Undo and is disabled Cut The Cut command copies the contents of the selection rectangle of the frontmost window to the clipboard and then sets that selection rectangle to the empty rectangle Invoking the Cut command is equivalent to choosing the Copy command followed by the Clear command Note that the Cut command performs a memory intensiv
47. brary Mask ias 59 Gradient User Mask ii a A a is 60 EN 61 Diversity Map sisi ian adeadase sync AE O en tpavaane apaa 62 Majority Pi tay ele a Me a adel ae eee 63 A A auratantaroasniduentgnaseobeacya euaatolueteg dereeeineda yun E E 64 Dlamini Filter li 65 Maximum Pitra dida 65 Conditional Average Biter vesical added edison tadas 66 Th Geometry Ment SNS A 69 Lita Scale calas adas 69 NETA AMC O a 70 Window and Subsamipleyiccis scccivsscvessssissacsacsscctassedeassadesoaceisecsateannevaaeasossneshanasecdesbesedsaavenaee 71 Hornz nt MS de doce 71 A O OE 12 General MOSES A a E a a a a o a 74 A E ai 75 Control Points umi adds 75 Polynomial A O E ER 77 Rot dada 79 A 79 TEMA A Aas 81 Combines inpe e Gea E ia 81 Compareren oars orc E 82 Principal Components Transit n 83 RGB gt HS Vrae ET E o 84 BIL BSQ OI E 86 BSO gt DIE A TA 86 A A coli en a a a N A a E N E aa 87 Real Complein ia a 88 A nte ete ad 88 The Clasif Mena din 91 E o oe 91 A A A DAR 92 A daresay lagvaianesuasisa ERa loeqae EE IE EEA E aa 93 Sina e a a 95 Th Windows Menta a a e dl sele rd e el e nets 97 A sath ates stones ceeds ue e as cb cuamciesianctaenez EE 97 Clipboard acid 97 SESSION LO ld ii 97 Window ENIES A A dE 97 Appendix A Mathematical Notation sis ccccsssectencessuycvsassatenacasavacnesayeansenasnensage seasaueoascedastanan delicada 99 Appendix B Keyboard ACES de 100 MCT eee EEE evade eet bi 100 WA res bes ar ON 101 Appendix Macs ADIB
48. ctor Lines Pixels Nearest Neighbor i Bi Linear Ci Parametric Cubic ipie Interpolation The graylevel of a pixel in the output image O is computed from the input image as nni i j s k s if Nearest Neighbor Interpolation is specified Oix dli l i j s k si if Bi Linear Interpolation is specified pei l i j sj k s if Parametric Cubic Interpolation is specified 69 where sj and sg are the vertical and horizontal scale factors respectively as specified in the dialog For a definition of the interpolation functions nni bli and pci together with a discussion of the advantages and disadvantages of the individual methods see the description of the Polynomial Warp command below The Linear Scale command is a special case of the more general Polynomial Warp command It simplifies the parameter input for the frequently occuring case of linear reductions and enlargements and is considerably faster than the Polynomial Warp command when both scale factors are integers and the nearest neighbor interpolation method is used Average and Subsample The Average and Subsample command resamples the input image by incrementally moving a window over the input image and averaging the graylevel values of all pixels within the window Parameters are the vertical and horizontal window size and the increments for vertical and horizontal movement Window Size Linel s Pinel s Increment Linel s Pinel s
49. d columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column This filter is a generalization of the conditional average filter described in T Ryan Image Segmentation Algorithms SPIE Vol 534 1985 pp 172 178 All pixels within the window whose graylevels differ from that of the center pixel by less than the graylevel threshold rf are collected into set S If the size of S is greater than the cardinality threshold c the average of the graylevel values in S is assigned as the new graylevel value of the center pixel If S has cardinality less than or equal to c and the maximum difference between any two pixels not in the set is less than f the center pixel is assigned the average graylevel of all pixels not in S If neither case is true the center pixel s graylevel value remains unchanged Like the Majority Filter command and the Median Filter command see above the Conditional Average Filter command is useful for smoothing an image The first case in the computation above represents the smoothing component of the filter where the amount of smoothing depends on both the set size threshold and the graylevel difference threshold The amount of smoothing decreases as the set size threshold increases from 0 to m n and it increases with an increasing graylevel difference threshold The second case is useful for eliminating isolated noise in the im
50. d gives easy access to any window on the desktop The first chapter of this manual describes the design and operating principles of MacSADIE It assumes that you are already familiar with the Macintosh environment in particular it assumes that you know about windows menus icons and dialogs and that you know how to point click select and drag If you do not recognize these terms you should refer to the Apple manual that accompanies your system software The remainder of this manual is organized into chapters by menus Each chapter contains a short introduction to the image processing functions provided by the current menu s commands Individual commands are then described in separate sections The first paragraph of each section gives a brief synopsis of the command its parameters and their default values The second paragraph provides more in depth coverage such as a mathematical formulation of the particular image processing function see Appendix A for a summary of the notation used reference publications expert advice on when and how to use a particular command useful tips and related commands To simplify references to MacSADIE commands from menus other than the current one those commands are referred to as Menu Command The manual assumes a knowledge of basic image processing concepts and terminology For an introductory text on image processing see for example R A Schowengerdt Techniques for Image Processing and Cla
51. d with the original image via the Signature Map command see below the result is as a non linearly smoothed version of the original image This smoothed image may then be submitted to the Levelslice or Cluster commands for feature space classification Note that resolution reduction is useful to avoid too small or too many segments however it does not necessarily result in a reduction in computation time Also note that segmenting an image is a memory intensive operation 94 Signature Map The Signature Map command creates a class signature map from a label map and the original image The two images which must have the same number of lines band and pixels line are chosen from pop up menus of all images currently on the desktop with all choices permanently enabled The label map defaults to the image in the frontmost window the original image to the one directly behind it Label Map Original Image EERE Image Name ETE ibis The graylevel of a pixel in the output image O is computed from the label of the corresponding pixel in the label map and from the original image J as Ok L y Jimn Isl JimES where S Jimn Llimn ijk i e each pixel in the class signature map is represented by the average graylevel of its class The Signature Map command is useful for visualizing the performance of a classifier in terms of its effect on the image signatures It is particularly useful for results produced by the Segment co
52. e s graylevel minimum and maximum Imin and Imax as max min If the number of bins is set to zero no histogram is computed 34 Histogram Resolution PEE Bins Subsample Increment i Pinel s and Line s BERGE Cancel The subsample increment parameter allows you a tradeoff between accuracy and speed A smaller value uses more pixels to compute the statistics and is therefore relatively slow a larger value uses fewer pixels and is faster Note however that the resulting values only approximate the correct statistics if the subsample increment is greater than one in particular the exact image minimum and maximum graylevels may be missed Also note that because of MacSADIBE s representation of graylevel values as floating point quantities the default value for the number of histogram bins may be a poor choice and may need to be overwritten The size and shape of an image s histogram s are important decision criteria for many image processing steps most notably the type and parameters of a contrast stretch For more details see the sections on individual contrast stretches in the next chapter Contour Map The Contour Map command creates from a single band input image a binary output image consisting of white contour lines lines of equal graylevel values on a black background Parameters are the number and width of the contour lines The width of a contour line is specified as a fraction a value in the
53. e Reference Stretch command transforms the graylevels of one image to match in a least squares sense those of another image This transformation is done via lookup table Parameters are the image to be transformed which defaults to the image in the frontmost window the reference image it defaults to the image in the window behind it and the number of entries in the lookup table this default is computed from the transformation image s minimum and maximum graylevels min and Imax as Tmax Imin 1 The two images which must have the same number of bands lines band and pixels line are chosen from pop up menus of all images currently on the desktop with all choices permanently enabled 50 Transformation Image Reference Image Lookup Table 2596 Entries EERE Image Name RefStr Cancel The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Lijk Lmin Orne LUT n 1 7A at max I min where LUTO is a lookup table and n is the number of lookup table entries specified in the dialog The exact algorithm for computating the lookup table is described in W J Dallas and W Mauser Preparing Pictures for Visual Comparison Applied Optics Vol 19 No 21 November 1980 pp 3586 3587 The Reference Stretch command computes for each graylevel in the transformation image the corresponding average graylevel in the reference image The
54. e operation Copy The Copy command copies the contents of the selection rectangle of the frontmost window to the clipboard Note that the Copy command performs a memory intensive operation Paste The Paste command creates a new untitled window and copies the contents of the clipboard into it Note that due to MacSADIE s display stretch a pasted image may look different from the original however graylevel values are preserved if the clipboard contents stem from a MacSADIE image 31 The Paste command may be used to create an image of text from the clipboard e g by copying from the Note Pad desk accessory or from a word processor document This text image can then be used to annotate a regular image by combing the two using one of several commands available from the Geometry and Misc menus Clear The Clear command sets the selection rectangle of the frontmost window to the empty rectangle Select All The Select All command sets the selection rectangle of the frontmost window to cover the entire image in that window Show Clipboard Hide Clipboard The Show Hide Clipboard command is a single toggled command If the clipboard window is visible the command reads Hide Clipboard and executing it causes the window to be hidden If the window is hidden the command reads Show Clipboard and executing 1t makes the window visible again Clicking on the close box of the clipboard window is equivalent to choosing the
55. e or of the session log As with the Page Setup command the Print command s dialog depends on your particular system configuration Shown below is the case of a LaserWriter Copies Pages All gt From i To Cancel LaserWriter Cover Page No O First Page gt Last Page Paper Source Paper Cassette O Manual Feed Print w Color Grayscale gt Black White 28 Images are printed centered and without header on a single page truncated 1f necessary You can use the Page Setup command to scale the image for printing or to change the orientation of the image with respect to the page The print quality color or grayscale dithered or halftoned depends on the capabilities of your printer and its software Note that printing a halftoned image may be a time consuming operation and the use of a print spooler such as Print Monitor from Apple which comes free of charge with the Macintosh system software or any of the commercially available spoolers for the Macintosh such as SuperSpool or SuperLaserSpool from SuperMac Technology TurboSpool from Peripheral Land Inc LaserServe from Infosphere or Grappler Spooler from Orange Micro is highly recommended The session log is printed on a single or on multiple pages dependent on its length You can obtain and print additional information if you use the Quit command see below to print out the session log Quit The Quit command terminates a MacSADIE session It closes
56. e the graylevel range of each one of the mosaiced images but even then the contrast is altered equally in all images 13 General Mosaic The General Mosaic command lets you compose two images in an arbitrary fashion The command creates an image of the specified size fills 1t with a background graylevel and places first one and then a second image Parameters are the size of the output image the images to be combined and the vertical and horizontal offsets for each image with respect to the origin of the output image The default values generate a sufficiently large output image with the first image in the upper left corner and the lower right corner of the first image touching the upper left corner of the second image The two images which must have the same number of bands are chosen from pop up menus of all images currently on the desktop with all menu choices permanently enabled The input images must be positioned so that they are located completely inside the output image If the two input images overlap the first input image is overwritten Image Size Lines 256 Pixel s First Image Offset o Line s o Pixel s Second Image una Offset Linelis Pixel s Cancel Fill Graylevel The graylevel of a pixel in the output image O is computed from the input images and J as if 1 lt j Aj7 lt ny A 1 lt k Ak lt 07 A Ti j Aj k Ak ae A 1 lt j Ajy lt ny a 1 lt k Aky lt 0 Oijk Tis Aj EAS 1f 1 lt j A
57. eckerboard pattern starting with a black rectangle a graylevel of 0 in the upper left corner and alternating between white and black graylevels of 255 and 0 respectively thereafter Parameters are the number of lines and the number of pixels per line of the output image and the vertical and horizontal extent of an individual rectangle Image Size Line s Pinel s Check Size Line s Pixel s 19 The graylevel value of a pixel in the output image O is computed as Ok 0 if mod 1 v k 1 h 2 0 255 otherwise where mod represents the modulo function and v and A are the vertical and horizontal extents respectively of an individual rectangle as specified in the dialog You can create a checkerboard pattern starting with a white rectangle in the upper left corner by doing a Contrast Linear Stretch with the appropriate parameters on the original checkerboard If you set the vertical check size equal to the number of lines in the image the Checkerboard command creates a vertical bar pattern Similarly setting the horizontal check size equal to the number of pixels per line results in a horizontal bar pattern A useful mask function may be created by doing a Contrast Linear Stretch to minimum and maximum graylevels of zero and one respectively Grayscale The Grayscale command creates a horizontal grayscale pattern Parameters are the size of the image to be generated the minimum and the maximum graylevel values
58. ed O otherwise 1 if Tye 0 A Jin 0 aria if and is specified O otherwise 1 if G 0 v Ji 0 jk ijk if or is specified O otherwise 1 if Ui ZOAT 4 0 v Win OA Ji 0 f el l ik jk jk ijk if xor is specified O otherwise 1 if Jijx 0 if not is specified O otherwise Note that the output image is a function of only the second input image in the case of the not combination function The Compare command is useful for creating and manipulating binary images and masks Principal Components Transform The Principal Components Transform PCT command performs a PCT also known as Karhunen Loeve KL transform on the input image The subsample increment parameter lets you define the pixel and line increment for graylevel subsampling 83 Subsample Increment Pinel s and Line s BERGE Image Name PCT Cancel The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as m Oi Y lye En l 1 where the input image is of size m by n by o and E 1 lt l lt m are the eigenvectors of the covariance matrix of the input image The covariance matrix see the description of the Analysis Covariance command for a definition is computed among the bands of the input image The subsample increment parameter allows you a tradeoff between accuracy and speed in the calculation of the covariance matrix A smaller value us
59. ed under the FFT command see above The FHT command is useful for analyzing the frequency characteristics of an image and for efficiently performing convolution and filtering operations on large images Convolution The Convolution command convolves an image with a kernel in the spatial domain The kernel may be given either as an image or it may be numerically specified as a mask the default up to a maximum size of 7 by 7 If the kernel is specified as a mask matrix you need to provide the horizontal and vertical size of the matrix and the individual matrix values Each matrix value is multiplied by a factor which for a mask of size m by n defaults to 1 m n The factor is adjusted automatically whenever you change the size of the mask If the spatial kernel is to be given as an image you can choose from a pop up menu of all images currently on the desktop with all menu choices permanently enabled If there is only one image on the desktop the spatial kernel defaults to that image otherwise it defaults to the image in the window behind the frontmost one The size of the spatial kernel image must be odd in both the vertical and the horizontal direction and the spatial kernel image must be single band If the spatial kernel is an image no normalization is performed 57 O Image Kernel Mask Kernel 10635 05 O7 Line s Factor 1 9 0 O1 as Os OF Pinel s Image Name M1 The graylevel of a pixel in the output image O i
60. eering University of Arizona TUCSON AZ 85721 U S A macsadie dialsun ece arizona edu 103 Index A About MacSADIE 17 Adaptive Stretch 50 Analysis Menu 33 Average and Subsample 70 B Background Processing 15 Band Interleaved Image 25 86 Band Sequential Image 25 86 Bi Linear Interpolation 69 78 BIL Image 25 86 gt BSQ 86 BSQ Image 25 86 gt BIL 86 Button Cancel 14 15 101 Done 33 101 Expert 14 101 Help 14 101 OK 14 101 Plot 34 Window Subsample 26 Zoom In 34 Zoom Out 34 Cc Cancel Button 14 15 101 Checkerboard 19 Classification Supervised 91 92 Unsupervised 91 93 94 Classify Menu 91 Clear 13 32 Clipboard 97 Hide 32 Show 32 Close 26 Cluster 92 Color 11 Display 11 Image 11 Mode 13 97 Combine 81 Command Disabled 14 19 31 33 41 53 69 81 91 97 104 Enabled 14 19 31 33 41 53 69 81 91 97 Key 11 14 15 27 100 101 Compare 82 Complex Image 56 57 87 88 gt Real 87 Conditional Average Filter 66 Contour Map 35 Contrast Menu 41 Control Panel 13 Control Points 75 Convolution 57 FFT 53 Wrap Around 54 55 Copy 13 31 Correlation Matrix 36 Covariance 36 Matrix 36 Covariance Matrix 84 Cut 13 31 D Dialog 14 101 Display Stretch 11 20 42 44 49 72 73 74 89 95 Diversity Map 62 Done Button 33 101 E Edit Menu 31 Error Code 15 Input Related 15 Memory Related 16 Message 15 Expert Button 14 101 F FFT 55 Convolution
61. egment piecewise linear transformation The default graylevel breakpoints in the input image Jj i 1 2 3 4 are computed from that image s graylevel minimum and maximum lin and Imax as I i 1 max Limin 3 Lin x Graylevel Breakpoints The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image J as max O a1 Ijk bi if lx lt h Oik a Tip bo if In lt Ijk lt B minbas Ijk b3 O4 if B lt Iik where a Oj41 Oj L 1 L and b O ai Ii The Piecewise Linear Stretch command is useful for images with asymmetric histograms because it makes it possible to control the amount of stretch applied to different portions of the histogram 45 Square Root Stretch The Square Root Stretch command performs a square root graylevel transformation BERGE Image Name Cancel The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Vix if in 20 Ok I ijk if Tijk lt 0 Since the square root of a negative number is undefined negative graylevels are not transformed but simply retained Like the Logarithmic Stretch command the Square Root Stretch command is useful for reducing the graylevel range of images with a large dynamic range and a histogram skewed towards lower graylevels Square Stretch The Square Stretch command performs a square graylevel
62. el Save image as Bits Pinel 27 With the number of bits pixel set to 32 graylevel values are written to disk in floating point format To reduce the disk space required to store an image you can set the number of bits pixel to any number n 1 lt n lt 31 if the image graylevel values are in the range 0 2 Each pixel is then converted to an integer in the range 0 2 1 by having its fractional part truncated and written to disk in n bit integer format Page Setup The Page Setup command lets you control the format of your printout The Page Setup command s dialog is not specific to MacSADIE rather the formatting options available depend on the particular type of printer you have chosen The dialog below shows the case of a LaserWriter Laserlriter Page Setup o Paper US Letter gt A4 Letter CUS Legal B5 Letter 21 Tabloid Cancel Reduce or Printer Effects Enlarge ool EJ Font Substitution Orientation EJ Text Smoothing i tE E Graphics Smoothing E E Faster Bitmap Printing All formatting parameters as specified with the Page Setup command are retained with the document image or session log during a single session it therefore suffices to specify the format of the printout once per document Holding down the Shift key when selecting the Page Setup command has no effect i e it does not cause the dialog to be skipped Print The Print command lets you create a hardcopy of an imag
63. es more pixels to compute the statistics and is therefore relatively slow a larger value uses fewer pixels and is faster The Principal Components Transform command decorrelates the different bands of an image and orders the transformed bands by decreasing graylevel variance RGB HSV The RGB HSV command transforms a color image from the RGB red green blue color space to the HSV hue saturation value or hue saturation brightness space The transformation requires that all graylevel values in the input image be equal to or greater than zero EMERGE 84 The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image J as Ok hsv 1 x where hsv is the color space transformation function This function is described in detail in A R Smith Color Gamut Transform Pairs Computer Graphics Vol 12 No 3 August 1978 pp 12 19 The RGB gt HSV command is the functional inverse of the HSV RGB command which 1s described below HSV gt RGB The HSV RGB command transforms a color image from the HSV hue saturation value or hue saturation brightness color space to the RGB red green blue space The transformation requires that all graylevel values in the input image be in the range 0 0 255 0 BERGE The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Oijk
64. ew or process only part of the image or if the entire image is too large to fit into available memory Bana i Line fi Pixel To ho Band Line Pixel Increment i Bandis fi Line s i Pinel s EHERGEG Cancel Close The Close command removes the frontmost image window from the desktop and returns all memory associated with it to the system MacSADIE does not ask whether you want to save a previously unsaved image before it closes that image This feature which runs counter to most Macintosh applications was implemented for two reasons Most images created with MacSADIE are of a temporary nature 1 e they represent intermediate results in a chain of processing steps and are normally discarded after some final image has been produced Since digital images take up large amounts of disk space MacSADIE actively discourages users from storing these intermediate images in this manner Furthermore since a particular image can not 26 be modified an image processed with some command always results in a new image it can easily be reproduced by re applying the processing sequence to the original image Clicking on the close box of a regular image window in the upper left corner is equivalent to choosing the Close command If you hold down the Command key when clicking on the close box all MacSADIE image windows on the desktop are closed and the session log and clipboard windows if visible are hidden
65. ference between a 7 bit and an 8 bit grayscale is virtually imperceptible e Monitors setting 256 colors color mode Full Color on This is the worst possible combination since it requires large amounts of memory while not improving the display quality e Monitors setting Millions of colors color mode Full Color on This setting results in the optimum display quality true color but requires large amounts of memory a 24 bit video card and causes a slight reduction in screen refresh speed Selection Rectangle Each MacSADIE image has associated with it a so called selection rectangle which determines the image section to be transferred to the clipboard with the Edit Cut and Edit Copy commands The selection rectangle is displayed and can be modified only for the image in the frontmost window however it persists when a window is put in the background Initially each selection rectangle is empty To define an arbitrary selection rectangle for the image in the frontmost window move the cursor to one corner of the rectangle push and hold down the mouse button drag the cursor to the opposite corner and release the mouse button The image scrolls automatically if you move the cursor outside the window You can extend an existing selection rectangle by holding down the Shift key when making the selection You can also use 13 the Edit Select All command to get a selection rectangle that covers the entire image To clear the selection
66. fferent interpolation methods offer a tradeoff between speed and accuracy The nearest neighbor interpolation is fastest whereas the parametric cubic interpolation is generally the most accurate bi linear interpolation is a compromise in speed and accuracy The common cubic interpolation method has amp 1 0 however 0 5 tends to give superior interpolation results For a detailed discussion see S K Park and R A Schowengerdt Image Reconstruction by Parametric Cubic Convolution Computer Vision Graphics and Image Processing Vol 23 No 3 September 1983 pp 258 272 78 The Polynomial Warp command is useful for registering an image to another reference image or map Note that the size of the output image should be equal to or greater than that of the reference image to ensure that all of the common area is included in the warped image Rotate The Rotate command rotates the frontmost image by multiples of 90 degrees Rotation Angle 90 O 90 180 BERGE Image Name Cancel The graylevel of a pixel in the output image O is computed from an m by n by o input image Tas Ti n k 1 j if 90 is specified Oik Liko j 1 if 90 is specified Tin j 1 o k 1 if 180 is specified where the output image is of size m by n by o if the input image is rotated by 180 and of size m by o by n otherwise Mirror The Mirror command mirrors the frontmost image along one of four axes
67. form converts the image from the frequency to the spatial domain For the FFT command both the number of lines band and the number of pixels line must be powers of two The inverse FFT transform destroys its input image 55 a Forward Transform O Inverse Transform EMERGE Image Name Cancel The graylevel of a pixel in the output image O is computed from the input image as n Q Oz y y Iijk e E E if Forward Transform is specified j 1 k 1 T T On Y Y Tec ev i kC if Inverse Transform is specified En Go where and are frequency domain coordinates e is the base of the natural logarithm i e e 1n 1 2 718282 and 1 is the complex number V 1 The spatial domain image in the case of the forward transform O in the case of the inverse transform is assumed to be of size m by n by o For more information on the fast Fourier transform see G D Bergland A guided tour of the fast Fourier transform IEEE Spectrum Vol 6 No 7 July 1969 pp 41 52 Pixel values in the frequency domain are complex numbers as opposed to graylevels in the spatial domain which are real numbers MacSADIE represents complex numbers with two graylevels one graylevel for the real part and one for the imaginary part Consequently a frequency domain image has twice as many pixels line as the corresponding spatial domain image with columns alternating between real and imaginary values You can separate a complex image
68. g it either by the Fourier transformed spatial kernel or by the frequency domain filter and computing the inverse Fourier transform of the result Both the number of lines band and the number of pixels line of the input image must be powers of two The filter image is chosen from a pop up menu of all images currently on the desktop with all menu choices permanently enabled If there is only one image on the desktop the filter image defaults to that image otherwise it defaults to the image in the window behind the frontmost one Filter Image Spatial Kernel O Frequency Transfer Function BERGE Image Name e Cancel 53 The graylevel of a pixel in the output image O is computed from the input image and the filter image F as l FFT FFT J FFT F ii if Spatial Kernel is specified Oik f FFT FFT I F ijk 1f Frequency Transfer Function is specified where FFT denotes the discrete Fourier transform and FFT the inverse Fourier transform see the description of the FFT command below for details The FFT Filter command uses cyclic wrap around convolution to determine the pixel values at the image borders You can easily create a spatial kernel image with the File New Function command Note that the spatial kernel image may be smaller than the input image the FFT Convolution command zero pads the spatial kernel image automatically as required While producing essentially the same output image as the Con
69. ggled command with the diamond symbol in front of the command indicating the current mode A hollow diamond indicates that Full Color mode is turned off a filled diamond indicates that Full Color mode is turned on The initial state of the Full Color command is dependent on the Monitors setting of the main screen at the time MacSADIE is started With a setting of 256 colors or less Full Color mode is initially turned off with a setting of more than 256 colors Full Color mode is initially turned on Note that the color mode of an image is determined solely by the color mode in effect at the time the image was created changing the color mode therefore does not affect existing images Clipboard Selecting the Clipboard entry from the Windows menu makes the clipboard window the frontmost window on the desktop Note that the Clipboard entry on the Windows menu is available enabled only when the clipboard window is visible You can change the visibility of the clipboard window with the Edit Show Clipboard Hide Clipboard command Session Log Selecting the Session Log entry from the Windows menu makes the session log window the frontmost window on the desktop Note that the Session Log entry on the Windows menu is available enabled only when the session log window is visible You can change the visibility of the session log window with the Edit Hide Session Log Show Session Log commands Window Entries The remaining entries on t
70. h gt Ah 2 A mod mod k 1 Ag Ah 0 v mod k 1 Ag An lt 2 A mod mod j 1 Ag An 0 v mod mod k 1 Ag Ah gt Ah 2 a mod mod j 1 Ag Ah 0 mod Oik Tix otherwise where Ag is the gridline spacing Ah is the hashmark spacing and g iq is the grid graylevel as specified in the dialog and mod represents the modulo function Note that due to MacSADIE s automatic display stretch the image contrast will be changed if the value of the grid graylevel is outside the graylevel range of the input image 89 90 The Classify Menu Classify The Classify menu provides commands for applying Levelslice supervised and unsupervised image classification labeling Cluster techniques to an image as well as a command for creating a class signature map from a label map and the original image The Levelslice command is enabled for all images with no more than three bands The Cluster and Segment commands are permanently enabled The Signature Map command operates on signature Map two input images and is therefore enabled only when there are at least two images on the desktop Levelslice The Levelslice command classifies pixels in the input image using a supervised level slice or box classifier The command allows the specification of up to six classes A class is defined by its graylevel minimum and maximum in each band of the image The input image must not have more than three bands Class boundaries are
71. h 43 Logarithmic Stretch 44 Low Pass Filter 54 M Macros 16 MacSADIE About 17 Image File Format 102 Open 8 24 Print 9 28 Save 27 Installation 8 Version Number 17 Majority Filter 63 Map Diversity 62 Label 91 93 95 Variance 61 Mathematical Notation 99 Matrix Correlation 36 Covariance 36 84 Maximum Filter 65 Median Filter 64 Memory Problems 16 Requirements 8 10 Menu 14 100 Analysis 33 Classify 91 Contrast 41 Edit 31 File 19 Filter 53 Geometry 69 Miscellaneous 81 Windows 97 17 Minimum Filter 65 Mirror 79 Miscellaneous Menu 81 Monitors Setting 13 Mosaic General 74 Horizontal 71 Vertical 72 Multi Band Image 11 N Nearest Neighbor Interpolation 69 78 New 19 Normalize Stretch 41 O OK Button 14 101 Open 24 MacSADIE Image 8 24 PICT Image 8 24 TIFF Image 8 24 P Page Setup 28 Parametric Cubic Interpolation 69 78 Parametric High Boost Filter 54 55 Paste 31 PICT Image Open 8 24 Print 9 Piecewise Linear Stretch 45 Plot Button 34 Polynomial Warp 77 Power Spectrum 37 106 Preferences 32 Principal Components Transform 83 Print 28 MacSADIE Image 9 28 PICT Image 9 TIFF Image 9 Problem Report 103 Progress Indicator 15 Q QuickDraw 8 Quit 29 R Random 23 Real Complex 88 Redo 31 Reference Stretch 50 Requantize Graylevels 47 Requirements Hardware 7 Memory 8 10 Software 8 RGB gt HSV 84 RMS Difference 38 Rotate 79 S Saturate Graylevels 48
72. he Windows menu show from top to bottom all image windows in the order of their creation Selecting one of those entries makes the corresponding image window the frontmost window on the desktop The diamond symbol in front of a window name indicates the color mode of the corresponding image as described under the Full Color command above 97 98 Appendix A Mathematical Notation X ijk X min gt X max f x1 x2 x y x y Graylevel value of image X at band i line j and pixel k The first index 1 is omitted if X is known to be a single band image Minimum and maximum graylevel values of image X Function f of arguments x1 x2 Examples trunc x the integer portion of a real number x mod x y the remainder of the integer division x y Interval from x to y including the boundary values Examples 0 255 all integers from 0 to 255 0 0 1 0 all non negative real numbers less than or equal to one Interval from x to y not including the boundary values Examples 0 255 all integers from 1 to 254 0 0 1 0 all positive real numbers less than one Note The interval notations above may be combined Example 0 0 256 0 all non negative real numbers less than 256 Ceiling of x X rounded up to the next integer Examples 1 2 2 3 8 4 1 2 1 Floor of x X rounded down to the next integer Examples 1 2 1 3 8 3 1 2 2 Size of x If x is a number
73. he background The two images which must have the same number of bands are chosen from pop up menus of all images currently on the desktop with all menu choices permanently enabled Top Image Bottom Image Horizontal Offset Pixels Fill Graylevel Expert The graylevel of a pixel in the output image O is computed from the top input image and the bottom input image J as Tijx lax If J Snr A 1 lt k Ak lt or Jijnk H1j gt nA1Sk lt o0j if Ak lt 0 8fill otherwise Oik Lij if j lt n A 1 lt k lt o Jij mk lakl iE j gt n a 1 lt k lAk lt oj if AK gt 0 gfu otherwise where Ak is the horizontal offset and gy is the background fill graylevel as specified in the dialog The output image O is either of size m by n n pFby maxloyH Ak oy f Ak lt 0 or of size m by nj n j by max o O yakl if Ak gt 0 for a top image of size m by n by 0 and a bottom image of size m by nj by o The Vertical Mosaic command is useful for appending additional information such as grayscales or textual annotations to an image Another use of the Vertical Mosaic command is for visually comparing the contrast in multiple images Due to MacSADIE s automatic display stretch mosaicing is one way of obtaining a relative comparison of the contrast in multiple images since the composite image will be displayed with the same graylevel minimum and maximum The background graylevel will only alter the contrast if it is outsid
74. he input image Z and two m by n kernels K and K as Mix V Ving Hix va Hix m n m n z PP o h where Vix Y Y Dj jep je Kio Hix yy Disp eg Kip V and h 1 g 1 7 2 1 g 1 2 2 p 1q p 1q denote vertical and horizontal components respectively and tan represents the trigonometric arc tangent function Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column Dijk tan Gradient operators are particularly useful for detecting edges 1 e sudden changes in graylevel in an image They are discussed in detail in G S Robinson Detection and Coding of Edges Using Directional Masks Optical Engineering Vol 16 No 6 November December 1977 pp 580 585 Note that you can use kernels of size 2 by 2 by simply padding a 3 by 3 kernel with zeros Variance Map The Variance Map command computes a map of the input image where the graylevel of a pixel in the map represents the graylevel variance within a window centered at the corresponding pixel of the input image Parameters are the vertical and horizontal window size which must both be odd 61 Window Size Line s EJ Pixel s The graylevel of a pixel in the output image O is computed from the input image and a window of size m by n as m n an Sy 2 a O 2 2 li a fia LL Lijml pr 2l a ik E m n m n Rows and columns within m
75. ialog The size of the output image is iena iveg Ai by jenioee 1 WAj by Kena Kbeg 1 Ak for an input image of size m by n by o The Window and Subsample command is useful for precisely extracting and possibly subsampling a subimage for further processing If the size and location of the window to be extracted is not critical and subsampling is not required you can use the Edit Cut and Edit Paste commands to quickly extract a subimage Horizontal Mosaic The Horizontal Mosaic command concatenates two images horizontally with the right image vertically offset with respect to the left image Parameters are the left image which defaults to the image in the frontmost window the right image which defaults to the image in the window behind the frontmost window a vertical offset between the images which may be positive or negative and a graylevel value to be used for the background The two images which must have the same number of bands are chosen from pop up menus of all images currently on the desktop with all menu choices permanently enabled 71 Left Image Right Image Vertical Offset Line s Fill Graylevel Enpari The graylevel of a pixel in the output image O is computed from the left input image and the right input image J as Lale if 1 lt j Ajl lt n A k lt or Jijk o H1SjEN a k gt or Gf Aj lt 0 Sill otherwise Oik Tix if l lt j lt snj A k lt o Jij lajlico if 1Sj Ajl lt n A k
76. if the parameters are not internally consistent Suppose you tried to use the File New Grayscale command to create a 1 by 1 by 128 grayscale with 256 different graylevels you would get the error message shown below To continue dismiss the message by clicking on the OK button or by pressing the Return or Enter key and re issue the command with the parameters modified appropriately equal to number of pixelsline Number of graylevels must be less than or Several 1 O related MacSADIE error messages contain a numeric Macintosh System error code in addition to the message itself For a listing of these error codes and their meanings refer to Apple Computer Inc Inside Macintosh Vols I VI Addison Wesley Reading MA 1985 1991 15 The most common memory related error message is shown below It is displayed whenever MacSADIE cannot allocate a sufficient amount of memory Keep in mind that memory is allocated not only for new images to be created some commands which are explicitly marked as memory intensive also need considerable amounts of memory temporarily in order to perform their function If you encounter this message you should first close any unneeded image windows and re issue the command you were trying to execute If that does not solve the problem you should save to disk and close all images but the one you are trying to process If there still is not enough space available it may be because of memory fragmentation I
77. ion log window entirely and also make it visible again If your Macintosh is connected to a printer you can at any time format and print out the contents of the session log with the File Page Setup and File Print commands Images and Windows Digital images in MacSADIE may be thought of as three dimensional arrays T as shown below Image coordinates for an m by n by o image range from one to m bands front to back one to n lines top to bottom and one to o pixels left to right respectively Each pixel has m graylevel values associated with it one for each band in the image The full precision of real numbers on the computer is used to represent graylevels during processing eliminating virtually any concern about unwanted numerical truncation or overflow Thus a disk file image with eight bits pixel will be converted upon opening to a memory resident image with possible graylevels 1 0 2 0 255 0 Subsequent image processing may introduce non integer pixel values which will be retained during processing Upon saving a processed image to disk the default storage format is 32 bits pixel i e the data is stored in floating point format but you have the option to pack the data to fewer bits pixel i Bands k Pixels j Lines MacSADIE stores all images in memory with each pixel value represented as a floating point quantity This approach has two advantages image data i e individual pixels can be accessed in random
78. ira KEINE KaL In 1 otherwise k 1 l 1 k 1 l 1 n 0 and pj w As with the Statistics and Histogram command the subsample increment allows you a tradeoff between accuracy and speed The diagonal terms of the covariance matrix represent the graylevel variances in the different bands whereas the off diagonal terms numerically quantify the amount of graylevel correlation between the bands Note that both the covariance and correlation matrices are symmetric with respect to the main diagonal Power Spectrum The Power Spectrum command computes the power spectrum the squared modulus of the Fourier transform of the input image which must be single band Image Name The graylevel value of a pixel in the output image O is computed as Ok re FFT x a im FFT Dix y where is the input image FFT is the discrete Fourier transform see the description of the Filter FFT command for details and functions re and im deliver the real and imaginary parts of a complex number respectively The typically large dynamic range in the image power spectrum usually benefits in visual display from contrast stretches such as Contrast Logarithmic Stretch or Contrast Square Root 37 Stretch The Power Spectrum command is useful for detecting periodic image or noise patterns Note that computing the Power Spectrum of an image is a memory intensive operation RMS Difference The RMS Difference command computes the root mean squared RMS
79. iscussion above applies equally well to display and comparison of color images in which case the three image bands are automatically and individually stretched to the full range of available colors on the display Note however that to append a grayscale image to a color image requires that the grayscale image also have three bands This can be done by combining three grayscale images with Misc BSQ gt BIL Two factors combine to control the appearance of grayscale and color images the Monitors setting of the screen and the color mode of an image 12 The Monitors setting determines the maximum number of colors that can be displayed simultaneously on the screen The Monitors setting can be changed with the Monitors control panel device cdev under the _ Control Panel command Possible settings range from two colors 1 e black and white to 256 colors to millions of colors depending on the video card and monitor used To achieve acceptable display quality a Monitors setting of at least 256 colors is required With a Monitors setting of 256 colors MacSADIE displays color and grayscale images by dividing the 8 bit color lookup table 256 entries into two halves of 7 bits 128 entries each One half holds a 7 bit grayscale the other half holds a 7 bit color spectrum MacSADIE creates and installs this custom lookup table at startup which explains the screen s color change you may notice at this point With a 24 bit video card a
80. ixel m 2 1 n 2 1 so that the image can be used as a kernel in a Filter Convolution or Filter FFT Convolution command 22 Distribution Random Uniform The Random command creates an image consisting Gaussian of a pseudo random pattern Parameters are the size of the image to be generated the probability distribution of the image s graylevel values and the graylevel deviation which corresponds to either the range in the case of a uniform distribution or the standard deviation in the case of a gaussian distribution The graylevel distribution is chosen from a pop up menu with all choices permanently enabled Image Size Line s Pinel s Distribution Deviation EERE Image Name Random Cancel The graylevel value of a pixel in the output image O is computed as d R__0 5 if Uniform Distribution is specified max 12 Ri d ___6 if Gaussian Distribution is specified Rmax where d is the deviation specified in the dialog and R and R 1 lt i lt 12 are uniformly distributed random variables in the range 0 R max The Random command is useful for simulating image noise You can use the Misc Combine command to add the generated noise to an existing image 23 Open The Open command reads an image from disk and displays it on the desktop MacSADIE can read images in its own format as well as PICT and TIFF images The dialog presented by the Open command is a standard
81. ize Stretch The Normalize Stretch command performs a linear graylevel transformation on the input image Parameters are the graylevel mean and variance in the output image and the pixel and line increment used for sampling when the histogram of the input image is computed eens Mean Standard Deviation Graylevel Subsample Increment i Pixel s and Line s Engari 41 The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as oO Oj 22 Li Ur ijk T Lijk uz Ho where the input image has graylevel mean uy and standard deviation 67 The mean value of the output image Uo and its standard deviation Og are the parameters specified in the dialog The subsample increment parameter allows you a tradeoff between accuracy and speed A smaller value uses more pixels to compute the histogram and is therefore relatively slow a larger value uses fewer pixels and is faster Note that due to the fact that MacSADIE stretches the graylevel range of each image individually before displaying it an image and its linearly stretched version look identical on the screen The Normalize Stretch command is useful for visually comparing images by adjusting them to have the same second order statistics Because of the automatic display stretch used by MacSADIE however the comparison can only be done if both images are then processed with the Contrast Saturate Graylevels command
82. ized dialog used by many applications On top of its main window it displays the name of the current folder The main window itself shows the contents of this folder that is all MacSADIE PICT and TIFF images as well as any sub folders located in the current folder You can traverse the hierarchy of folders on all available disks just as you would with any other Macintosh application To select and open an image either double click on the file name or select the file and click on the Open button O Grayscale O More Images O RGBColor Holding down the Shift key when selecting the Open command has no effect 1 e it does not cause the dialog to be bypassed Note that opening a PICT image is a memory intensive operation Import The Import command lets you read images created by applications other than MacSADIE or images transferred to the Macintosh from other computers generic images if they conform to one of the following two formats note that the formats are equivalent for a single band image 24 Band Interleaved BIL Band Sequential BSQ The diagram assumes an m by n by o image where AAA is one line o pixels of image data from Band 1 I is one line o pixels of image data from Band 2 and I is one line o pixels of image data from Band m In addition to the controls from the Open command s dialog the dialog for the Import command requires you to specify the parameters of the two formats above
83. j lt ny A 1 lt k Aky lt OJ Sfill otherwise where Aj and Ak are the vertical and horizontal offsets respectively of the first image Aj and Ak are the corresponding offsets for the second image and gay is the background fill graylevel as specified in the dialog The General Mosaic command is useful for appending additional information such as grayscales or textual annotations to an image Another use of the General Mosaic command is for visually comparing the contrast in multiple images Due to MacSADIE s automatic display 74 stretch mosaicing is one way of obtaining a relative comparison of the contrast in multiple images since the composite image will be displayed with the same graylevel minimum and maximum The background graylevel will only alter the contrast if it is outside the graylevel range of each one of the mosaiced images but even then the contrast is altered equally in all images Insert The Insert command lets you overlay one image within another one Parameters are the background image which defaults to the image in the frontmost window the foreground image which defaults to the image in the window behind the frontmost window and the offset of the foreground image with respect to the background image The two images which must have the same number of bands are chosen from pop up menus of all images currently on the desktop with all menu choices permanently enabled The foreground image must be posi
84. mmand because its label map typically has a very large dynamic range and the labels are not correlated to the graylevels of the original image The signature map may be subtracted from the original image using the Misc Combine command to visualize the classification reliability Generally the greater the deviation of a pixel from its classification signature class mean the lower the reliability Note that because of MacSADIE s automatic display stretch the displayed graylevels or colors of the signature map may not match those of the original image They can be made consistent with the techniques described in the section on Grayscale and Color Display in the Introduction chapter of this manual 95 96 The Windows Menu Windows The Windows menu provides a command for setting Full Color MacSADIE s color mode In addition it contains one entry for each MacSADIE window on the desktop Clipboard The Full Color command is permanently enabled The Session Log Clipboard and Session Log entries on the Windows menu are enabled only when the corresponding windows are visible The entries for all other windows are always enabled Grayscale RGEColor Full Color Testimage The Full Color command determines the color mode and thus the appearance of grayscale and color images on the desktop as described in the section on Grayscale and Color Display in the Introduction chapter of this manual The Full Color command is a to
85. n that case it is best to save the unprocessed image data to disk quit and re start MacSADIE If you are running MacSADIE under MultiFinder you can also increase MacSADIE s memory partition with the Get Info command from the Finder s File menu O Memory request failed If you encounter any other memory related problems it is probably best to save your image data to disk and then quit and re start MacSADIE If the problem persists and can be reliably reproduced you should file a report with the Digital Image Analysis Lab at the University of Arizona see Appendix D Macros MacSADIE is based on the toolbox concept which means that each command performs a basic image processing function However for many applications it is desirable to be able to combine multiple functions into more complex image processing sequences This can easily be done with so called macro utilities which let you define complex sequences of mouse movements mouse clicks and keyboard input and re play those sequences with a single keystroke MacSADIE itself does not provide a macro capability but is compatible with MacroMaker from Apple which comes free of charge with the Macintosh system software as well as with any of the commercially available macro packages for the Macintosh such as QuicKeys from CE Software or Tempo by Affinity Microsystems 16 The Menu The contents of the menu depend on the contents of your system file as well as
86. nd a Monitors setting of millions of colors MacSADIE is capable of displaying color and grayscale images in true color The color mode of an image determines the mapping between pixel values and colors There are two possible modes which can be set for each image individually with the Windows Full Color command In Full Color mode the red green and blue components of a pixel are combined to yield one of 274 colors Alternately the color components may be combined to yield either one of 2 shades of gray or one of 2 colors with 2 bits assigned to red 3 bits to green and 2 bits to blue The mapping from pixel values to colors is done with a so called off screen pixel map which is created together with each image With Full Color mode turned on at the time of image creation the pixel map requires four bytes of memory per pixel with Full Color mode turned off only one byte per pixel is allocated Taken together the Monitors setting and the color mode result in the following four combinations e Monitors setting 256 colors color mode Full Color off This is the recommended setting as 1t results in a good display of grayscale images and a reasonable display of color images while minimizing memory requirements and maximizing screen refresh speed e Monitors setting Millions of colors color mode Full Color off This combination is useful in tight memory situations or for displaying grayscale images as the dif
87. nd defaults to the first band of the image in the frontmost window If this is a multi band image the second band defaults to the image s second band otherwise it defaults to the first band of the image in the window behind the frontmost one Additional parameters are the number of bins to be used along both histogram axes and the pixel and line increment used for sampling in both images The output image is of size 1 by n by n where n is the number of histogram bins 38 First Band Testimage Band 1 second Band Testimage Band 2 Histogram Resolution Bins Subsample Increment i Pinel s and Line s EHRON The graylevel range of each input image is divided into n subranges of equal size where n is the number of histogram bins The graylevel value of a pixel in the output image O g is then computed as the number of pixel locations m n in the input images Z and J that have graylevel values in the jth and kth subrange R and Rx respectively Oj m n Im Rj A Jin Red As with the Statistics and Histogram command the subsample increment allows you a tradeoff between accuracy and speed Note that the coordinate origin 1 1 of the scattergram image is at the upper left corner consistent with all other MacSADIE images The typically large dynamic range of image scattergrams usually benefits in visual display from contrast stretches such as Contrast Logarithmic Stretch or Contrast Square Root Stretch The Scattergr
88. ndpoint of the line push and hold down the mouse button drag the cursor to the other endpoint and release the mouse button The image will scroll automatically if you move the cursor outside the window Once defined a cross section persists across scrolls and zooms until you either clear it by clicking on the window or until you define another cross section To get a profile of the graylevel values of the currently defined cross section click on the Plot button which is enabled only when a cross section is defined You can then chose the scale for the profile s graylevel axis from the secondary dialog shown below The Logarithmic option is enabled only if all pixels along the profile have non negative graylevel values You can skip over the secondary dialog by holding down the Shift key when clicking on the OK button Scale e Linear O Logarithmic C 10 1 BERGE G Cancel Statistics and Histogram The Statistics and Histogram command computes for each band of the image the mean graylevel and its standard deviation the minimum and maximum graylevels the graylevel range and the number of zero and non zero pixels in that band In addition the command optionally computes and draws in the sesson log the histogram of graylevels for each band Parameters are the number of bins to be used in the histogram and the pixel and line increment for sampling in each band The default number of histogram bins is computed from the input imag
89. near combination of two images Parameters are the two images their respective weights and the combination function The first image defaults to the image in the frontmost Fi window the second image to the one directly behind it The two images which must have the same number of bands lines band and pixels line are chosen from min pop up menus of all images currently on the desktop The combination function is mid chosen from a pop up menu with all menu choices permanently enabled Testimage Grayscale 81 The graylevel of a pixel in the output image O is computed from the graylevels of the corresponding pixels in the input images and J as mr Lie ws Jiu Gif is specified wr Lx wy Jije Gf is specified mw Tit wy Jr if is specified Oir o w J Six if 7 is specified w Lijk min w Ijk wy Jik Gf min is specified max w DL ik WJ Sin if max is specified where w and wy are the weights for the first and second image respectively as specified in the dialog Note that if you want to compute the quotient of images and J w z must not be equal to zero if Jijx equals zero then Oj is set to Oj z 1 or if Jijx equals zero and k equals one Ojjx is set to zero The Combine command is useful for example for detecting changes in images combination function or for overlaying binary text or graphics onto an image combination functi
90. o where p is the period and is the phase of the sinewave as specified in the dialog and sin is the trigonometric sine function The minimum graylevel in the generated image is 0 the maximum is 255 You can change the amplitude and bias level of the sinewave with the Contrast Linear Stretch command Function Function Type Cone The Function command lets you Negative Exponential generate a variety of two Gaussian dimensional test functions Parameters are the size of the generated image the function s radii and the function type selected from a pop up menu on the dialog All choices on the pop up menu are permanently enabled Bou Cylinder 21 Image Size Line s 128 Pinel s Function Radius Line s Pinel s Help Function Type The graylevel value of a pixel in the output image O is computed for the various types of test functions as 255 I if r lt l Cone Oik de 0 otherwise Negative Exponential Oj 255 e Gaussian Ox 255 e 5 A 255 if Gj lt r A K K S ra OX k 0 otherwise 255 if ri Cylinder Oik A on otherwise where r V GIA ME re je m 2 1 and ke n 2 1 are the coordinates of the center of the test function rj and rg are the radii of the test function as specified in the dialog and e is the base of the natural logarithm 1 e e In 1 2 718282 The center of the test function in an image of size 1 by m by n is located at p
91. og window at the bottom of the main screen It then waits for you to initiate actions via the mouse or the keyboard To print one or more MacSADIE PICT or TIFF images directly from the desktop you can select the image s as described above and then choose the Print command from the Finder s File menu In this case MacSADIE will prompt you with the Print command s dialog print the image s as specified and immediately return to the desktop Session Log MacSADIE maintains a record of the current session in a window at the bottom of the main screen This session log contains a list of the SADIE image processing functions in the order in which they were called from MacSADIE together with any textual or graphical output from these functions Examples of textual output are listings of the masks used in the Filter Convolution command or the coefficients computed by the Geometry Control Points command The graylevel profiles produced by the Analysis Image Information command or the histograms created by the Analysis Statistics and Histogram command are examples of graphical output that is kept in the session log Session Log MacSAQlE Version 1 2 2 1990 Digital Image Analysis Lab University of Arizona Code amp Design Gerhard Heh ldan Concept Or Robert Schowengerdt Horn Jan 01 00 00 00 1990 You can resize the session log window and move it around the screen as you like The Edit Hide Session Log command lets you hide the sess
92. ons min and max Compare The Combine command computes a binary output image representing a comparison between corresponding pixels in two input images Parameters are the two input images and the comparison function The first image defaults to the image in the frontmost window the second image to the one directly behind it The two images which must have the same number of bands lines band and pixels line are chosen from pop up menus of all images currently on the desktop The comparison function is chosen from a pop up menu with all menu choices permanently enabled The input images are treated as binary images in the case of the logical connectives and or xor and not with a graylevel value of zero being the equivalent of the boolean value false and all other graylevel values being equivalent to true Testimage Grayscale BERGE Image Name Cancel 82 The graylevel of a pixel in the output image O is computed from the graylevels of the corresponding pixels in the input images J and J as 1 Lx lt Six if lt is specified O otherwise 1 if Ig lt Ji a za ee if lt is specified O otherwise 1 if Lx gt Jijx if gt is specified O otherwise 1 if Ig gt Jy e ijk ijk if gt is specified O otherwise 1 if Tijk Jinn if is specified O otherwise Oik 1 if Ln Jj f ae JEE ik if is specifi
93. or press any key Foe MacSADIE Version 1 2 1990 DIAL Univ of Arizona Code Design Gerhard Mehldau Concept Or Robert Schowengerdt 17 18 The File Menu The File menu lets you create new images with the New command and read image data from disk in MacSADIE PICT or TIFF format with the Open command and in generic format with the Import command You can dispose of an image using the Close command and write image data to disk with the Save and Save As commands The Page Setup and Print commands let you format and print images or the contents of the session log window To terminate a session and to exit from MacSADIE select the Quit command The New Open Import and Quit commands are always available enabled whereas the Close Save and Save As commands are enabled only when the frontmost window contains a regular image as opposed to the session log or clipboard windows The Page Setup and Print commands are enabled only when either a window containing a regular image or the session log window is frontmost New The New command provides through a submenu commands for creating synthetic images Choose one of the five commands from the submenu according to the type of image you want to create All choices on the New submenu are permanently enabled Checkerboard New Open Close save Checkerboard Grayscale SiINeWwave Function Random The Checkerboard command generates a binary ch
94. pixels to determine the clusters and is therefore relatively slow a larger value uses fewer pixels and is faster When image subsampling is used an increase in the average mean vector migration value is common for the final classification This is usually a consequence of the change to full sampling and does not necessarily represent a true increase in average migration Note that if subsampling is used it may be advisable to increase the minimum class size Segment The Segment command classifies pixels in the input image based on graylevel homogeneity and region connectivity Parameters are two graylevel thresholds which together define the homogeneity of the resulting regions The spatial resolution of the input image may optionally be reduced by pixel averaging and subsampling before the image is subjected to the segmentation process In this case the resulting label map is refined back to the resolution of the original input image Resolution reduction is done in steps with one step the default when reduction is chosen being equal to a change in resolution by a factor of two 93 Graylevel Difference Threshold Graylevel Variance Threshold O Reduction Pure i EESE Pixels in the output image are processed from left to right and top to bottom If a pixel can be merged according to the criterion given below with either the region directly above or directly to the left of it it is assigned that region s label If it can be
95. put images which must have the same number of bands lines band and pixels line are chosen from pop up menus of all images currently on the desktop with all menu choices permanently enabled Real Imaginary O Magnitude Phase BERGE G Image Name The graylevel of a pixel in the output image O is computed from the input images and J as Oik iij ten 7 En if Real Imaginary is specified ijk 2 li j k 1 2 cos Jj k 1 2 if k is odd Oijk Lopera sin Fij472 Fee aun if Magnitude Phase is specified where cos and sin represent the trigonometric cosine and sine functions respectively The Real Complex command is useful for creating an image in complex format from two images in real format as required by the Filter FFT and Filter FHT commands Grid The Grid command overlays the input image with a grid of lines and hashmarks Parameters are the distances between the gridlines and the hashmarks respectively and the graylevel value to be used for pixels on the grid The grid graylevel defaults to the input image s maximum graylevel Imax 88 Gridline Spacing Pinel s and Line s Hashmark Spacing Pixel s and Line s Grid Graylevel 253 0 cepa The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as if mod j 1 Ag 0 v mod k 1 Ag 0 v mod mod j 1 Ag Ah lt 2 A mod mod k 1 Ag Ah 0 v ruse mod mod j 1 Ag A
96. r The Minimum Filter command filters an input image by creating an output image where the graylevel of a pixel represents the minimum graylevel within a window centered at the corresponding pixel of the input image Parameters are the vertical and horizontal window size which must both be odd Window Size Line s 3 Pixel s EERE Image Name MinFltr Cancel The graylevel of a pixel in the output image O is computed from the input image and a window of size m by n as minl m lt lt jy4M N lt g lt n Ok minyLipg J n PSDS Ak 7 2qSKk gt Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column The Minimum command is useful for dilating expanding dark objects against a lighter background or eroding thinning light objects against a darker background In general the results can not be exactly reversed by using the Maximum Filter command Maximum Filter The Maximum Filter command filters an input image by creating an output image where the graylevel of a pixel represents the maximum graylevel within a window centered at the corresponding pixel of the input image Parameters are the vertical and horizontal window size which must both be odd 65 Window Size Line s EJ Pixel s EERE Image Name MaxFltr Cancel The graylevel of a pixel in the output image O is computed from the input image and a
97. reshold are set to one and zero respectively the final number of classes is equal to the number of seed classes This type of clustering algorithm is described in more detail in R D Duda and P E Hart Pattern Classification and Scene Analysis J Wiley amp Sons New York NY 1973 In the final classification pass the label of a pixel in the output label map O is computed from the graylevel of the corresponding pixel in the input image as m m if Yd 1 lt d lt N Y lt Y lila i l reat Lijk Me VETS ame lt to Oc 0 otherwise where the input image is of size m by n by o N is the number of classes as determined by the iterative process uc and uq are the graylevel means for classes c and d in band i respectively Og is the graylevel standard deviation for class c in band i and fg is the outlier threshold as specified in the dialog The Cluster command is useful for non parametric unsupervised image classification The stability of the clusters is determined to a large extent by the number of iterations Using this algorithm image data generally converges to a stable result after three or four iterations however it is advisable to look at the average mean vector migration values to confirm stability The subsample increment parameter which is used only in the iterative determination of the clusters but not in the final classification allows a tradeoff between accuracy and speed A smaller value uses more
98. retained between invocations of the Levelslice command Band 1 Beng Y Classes Min Ma wiin minj G1 O 2 G3 G4 G5 6 Image Name Lulsii The label of a pixel in the output label map O is computed from the graylevel of the corresponding pixel in the input image as fe if Vi 1SiSm ga Siig Sho Ox O otherwise 91 where the input image is of size m by n by o and g and h are the graylevel minimum and maximum respectively for class c and band i as specified in the dialog Pixels falling within two or more class boundaries are assigned labels by the nearest mean algorithm The Levelslice command is useful for rapid non parametric supervised image classification Cluster The Cluster command classifies pixels in the input image based on their natural grouping in feature space The classes clusters are determined in an iterative process Parameters are the number of iterations the number of seed classes the minimum class size a distance threshold for merging adjacent classes the pixel and line increment for graylevel subsampling used only in the iterative determination of the clusters but not in the final classification and an outlier threshold which is used only in the final classification Number of Iterations Number of Seed Classes Minimum Class Size i Pixel s Class Merging Threshold cugat Subsample Increment i Line s and Pixel s Cancel Outlier Threshold Standard Deviation s
99. s command are automatically transferred as defaults to the Polynomial Warp command see below which performs the actual coordinate transformation Control Point Pairs 3 ei 4 O5 Transformation Image H E y Given the coordinates of m control point pairs in the image x y and in a reference coordinate system Ges ys 1 lt i lt m the Control Points command calculates a least squares fit polynomial to the set of control points by solving the following system of linear equations for the transformation coefficients a bj 1 Sj lt n 1 12 12 x Q 029 X 03 Y 04 X Y 05 X3 0d6 Y1 2 i i i 2 Xm A 02 Xm 03 Ym A4 Xm Ym t45 Xm 06 Ym ae 12 12 y by b2 x b3 y bax y b5 x1 be y Ym b bz xm b3 Ym b4 Xm Yin bs xm D6 Ym Coordinates x and y are in the coordinate system of the transformation image the image that will be warped by the transformation and coordinates x y are in the coordinate system of the reference image The number of control point pairs m and the number of polynomial terms n are as specified in the dialog Solving this system of linear equations requires that there be at least as many control point pairs as there are polynomial terms to be computed i e m 2 n To solve the linear system 76 MacSADIE uses a matrix inversion technique The matrix may become non invertible singular if there are more than two control points lying on a common
100. s computed from the input image and a spatial kernel K of size m by n as On jon ina Kr Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column You can easily create a spatial kernel image with the File New Function command You can save a mask kernel as an image for subsequent convolutions as follows First create a one pixel by one pixel wide box function image File New Function with radii of 0 5 at least twice as large as the desired kernel Then use the Convolution command to filter the box image with the desired kernel Include an extra factor of 1 255 to normalize the box image to a graylevel of one Finally use the Geometry Window and Subsample command to reduce the filtered image which is a replication of the mask kernel to the desired size While producing essentially the same output image as the FFT Convolution command the only difference is at the image borders due to the cyclic wrap around convolution used by the FFT Convolution command the Convolution command may be more efficient when the kernel is small 58 Gradient Library Mask Gradient Operator Sobel The Gradient Library Mask command Sobel convolves an image with two spatial kernels Sobel3 a horizontal and a vertical mask It then Roberts combines the results in a vector calculation to produce two output images one representing s the
101. sification map Majority Filter The Majority Filter command filters the input image by creating an output image in which the graylevel of a pixel represents the majority graylevel within a window centered at the corresponding pixel of the input image Parameters are the vertical and horizontal window size which must both be odd and a weight for the influence of the class of the pixel in the center of the window Window Size Line s E Pinel s Center Pixel Weight Class Count EERIE Image Name MajFltr Cancel The graylevel of a pixel in the output image O is computed from the input image and a window of size m by n as m n if dp q fp4 gt gt A fg W tik I pq 1 lt p sje tlen k 1 lt gs lt k 5 in Oik ijk otherwise 63 where fg 635 li eri Ls lipg A 1Er m an 1 s lt n and w is the center pixel weight specified in the dialog Rows and columns within m 2 lines or n 2 pixels of the borders of the convolved image are filled with graylevel values copied from the nearest valid row or column Pixels within the window are separated into classes according to graylevel values an input image with integer valued graylevels is therefore desirable but not required The majority filter is described in R A Schowengerdt Techniques for Image Processing and Classification in Remote Sensing Academic Press New York NY 1983 pp 188 190 Like the Median Filter command and the Conditional Average comm
102. ssification in Remote Sensing Academic Press New York NY 1983 or J A Richards Remote Sensing Digital Image Analysis An Introduction Springer Verlag Berlin Germany 1986 Hardware Requirements MacSADIE requires a Macintosh with at least an MC68020 processor and a floating point coprocessor FPU together with an RGB color monitor and a video card capable of displaying eight or more bits of color MacSADIE is set up to request 1024 KBytes 1 MByte of RAM but we strongly recommend that this number be increased with the Get Info command from the Finder s File menu especially if images are to be displayed in Full Color mode MacSADIE will run from a floppy disk however for performance reasons we recommend installing MacSADIE on a hard disk drive Software Requirements MacSADIE Version 1 2 requires System Software Version 6 0 5 or later together with 32 Bit QuickDraw Version 1 2 or later MacSADIE is compatible with Version 6 0 or later of MultiFinder Some computation intensive MacSADIE functions are capable of executing in the background under MultiFinder Installation On a Macintosh without a hard disk simply insert the MacSADIE disk into the floppy drive On a Macintosh equipped with a hard disk we recommend creating a separate folder for MacSADIE This folder can hold the application itself copied from the original MacSADIE disk as well as any image files created with MacSADIE If you purchased a single
103. tioned so that it 1s located completely inside the background image Background Image Foreground Image Offset Line s o Pixel s Engari The graylevel of a pixel in the output image O is computed from the background image and the foreground image J as Jivajiear if 1Sj AjSny A 1Sk AkS 0 Oik Li otherwise where Aj and Ak are the vertical and horizontal offsets respectively as specified in the dialog For a background image of size m by n by o and a foreground image of size m by n by o the output image is of size m by n by 0 The Insert command is useful for inserting additional information such as grayscales or textual annotations into an image It can also be used to create complex test targets convolution kernels or frequency filters by combining several simple images created with the File New commands Control Points The Control Points command computes the polynomial coefficients required to perform a coordinate transformation warp on an image The coefficients polynomial terms are 75 computed from the coordinates of a set of control points in both the image to be transformed and a reference image Parameters are the number of control point pairs the control point coordinates in both images and the number of polynomial terms to be computed The control point coordinates are retained between invocations of the Control Points command The polynomial coefficients computed by the Control Point
104. to clicking the OK button If you click on the Help button MacSADIE displays another small dialog containing a concise description of the command s function Instead of clicking on the Help button you can also press Command or Command H The Expert button iugari is currently disabled in all dialogs it will provide you with more detailed information on the chosen command in a future version of MacSADIE The Cancel button lets you change your mind and return to the desktop without any processing being done Pressing Command period or Command C is equivalent to clicking on the Cancel button All dialog Command key shortcuts are summarized in Appendix B Cancel All commands that lead to the creation of a new image have an Image Name parameter in their dialog to let you specify a name for the new window image The default name is an indication of the command used to create the image but it may be set to anything you desire MacSADIE provides reasonable default values for all parameters Most defaults are static 1 e as shown in the sample dialog for each command However some values are computed dynamically as a function of the characteristics of the frontmost image If that is the case the section on the particular command explains exactly how those defaults are computed If you know in advance that the defaults are acceptable you can skip over the dialog entirely by holding down the Shift key when selecting the command 1
105. transformation EERE Image Name Cancel 46 The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as 72 Oik Tik The Square Stretch command is useful for enlarging the graylevel range of images with a small dynamic range and with a histogram skewed to higher graylevels Table Lookup Stretch The Table Lookup Stretch command performs a graylevel mapping based on a lookup table The default lookup table for an image is the identity transformation for images with integer graylevel values To change a lookup table entry simply select the entry from the scrolling list and modify the value displayed in the edit field at the right Lookup Table Index Value Change Engari Cancel Image Name Els The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Oik LUT ix The Table Lookup Stretch command is particularly useful for making specific changes to just a few graylevels in an image or for relabeling the classes in a classification map Note that the graylevels are converted to integers before being used to index the lookup table the Table Lookup Stretch command is therefore not very well suited for images with non integer graylevel values Requantize Graylevels The Requantize Graylevels command requantizes the input image s graylevels Parameters are the gra
106. user license for MacSADIE you need to register the software to your Macintosh before it can be used Simply follow the instructions in the dialog If you obtained a temporary license for MacSADIE a dialog will remind you at startup of the expiration date of the license and provide information on how to receive a permanent license Startup Before starting MacSADIE you should verify that your monitor is set to at least 256 colors You can determine and if necessary change the setting with the Monitors cdev control panel device under the _ Control Panel command To invoke MacSADIE simply double click on the MacSADIE application icon This is equivalent to selecting the MacSADIE application icon and then choosing the Open command from the Finder s File Menu Alternately you can select and open or double click on one or more MacSADIE image icons on the Macintosh desktop To open PICT or TIFF images directly from the desktop you need to simultaneously select and open the MacSADIE application together with the image s this requires that the files reside in the same folder as the application Macs ADIE Grayscale RGBColar After startup MacSADIE installs its own color lookup table for more information see the section on Grayscale and Color Display below replaces the previous menu bar with its own and if you invoked MacSADIE by opening MacSADIE PICT or TIFF images displays those images on the desktop It also opens a session l
107. volution command the only difference is at the image borders due to the cyclic wrap around convolution the FFT Convolution command may be more efficient for large images and or large kernels Note that FFT convolving an image is a memory intensive operation FFT Filter Filter Function Cone The FFT Filter command Negative Exponential spatially convolves an image by Gaussian computing the discrete Fourier transform of the image multiplying it by a specified Cylinder frequency domain filter function and computing the inverse Fourier transform of the result Both the number of lines band and the number of pixels line of the input image must be powers of two The filter function is chosen from a pop up menu containing a variety of functions with all menu choices permanently enabled Other parameters are the radii of the filter function the filter type and in the case of a high pass filter a filter parameter A filter parameter value of one the default creates a high pass filter and values greater than one result in a parametric high boost filter Bou Filter Function Frequency Radius Cycles Line Cycles Pixel Filter Type e Low Pass gt High Boost E E 54 The graylevel of a pixel in the output image O is computed from the input image and the frequency domain filter F as FFT FFT J F jx if Low Pass is specified Oik j j FFT FET c F Gif High Boost is specified ij 8 p where c is the
108. with the same parameters for both images Histogram Equalize Stretch The Histogram Equalize Stretch command transforms the image histogram to one for which the histogram density number of pixels per graylevel is approximately uniform Parameters are the number of histogram bins and the pixel and line increment used for sampling when the input image histogram is computed Histogram Resolution Pe Bins Subsample Increment i Pinel s and Line s BERGE The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as I ijk Lmin Oijk CDF ke n n Imax Imin Iijk Tijk S where CDF g Lmax pal ijk tijk all m n O 42 CDE represents the normalized cumulative distribution function the normalized cumulative histogram of the m by n by o input image J and b is the number of histogram bins as specified in the dialog As with the Normalize Stretch command the subsample increment allows you a tradeoff between accuracy and speed For a typical image with a gaussian histogram the Histogram Equalize Stretch command tends to reduce image contrast in very light and very dark areas and to increase contrast in the middle graylevel range Linear Stretch The Linear Stretch command performs a linear graylevel transformation on the input image The parameters of the stretch may be specified either as the output image s minimum and maximum gra
109. ylevel values top dialog or as the two parameters of a linear coordinate transformation bias and gain bottom dialog You can use the radio buttons to switch between these two equivalent representations The default parameters are a minimum graylevel of 0 and a maximum graylevel of 255 resulting in a transformation which makes the image suitable to be stored on disk in 8 bits pixel format Min Man Minimum Graylevel 299 0 Maximum Graylevel O Bias Gain EERE Image Name LinStr Cancel O Min Man a Bias Gain ERERGIG Image Name LinStr Cancel 43 The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as Omax min Lijk Imin Omin if Min Max are specified Oijk max min b g Tijk if Bias Gain are specified where Imin and max are the minimum and maximum graylevels of the input image Omin and Omax are the minimum and maximum graylevels of the output image and b and g are the graylevel bias and gain respectively as specified in the dialog If you switch from Min Max representation to Bias Gain representation or vice versa the current parameter settings are transformed accordingly Note that due to the automatic display stretch MacSADIE stretches the graylevel range of each image individually before displaying it making an image and its linearly stretched version look identical on the screen The Linear Stretch command
110. ylevel values in the input image corresponding to the minimum and maximum graylevels in the output image and the number of quantization steps in the output image The minimum and maximum graylevel values default to the input image s graylevel minimum and maximum respectively Pixels in the input image with graylevel values outside that range are saturated at the range boundaries 47 Graylevel Minimum Maximum 56 Quantization Steps EERE Image Name OntStr Cancel The graylevel of a pixel in the output image O is computed from the graylevel of the corresponding pixel in the input image as I Ez ra ES h where the function trunc truncates the fractional part of a real number n is the number of quantization steps and 8min and Zmay are the minimum and maximum graylevel values as specified in the dialog Ong max 0 min tran amp max 8min Note that 8min and max need not necessarily be identical to the true image graylevel minimum and maximum The Requantize Graylevels command can be used for example for simulating an image acquisition system by setting the parameters to the values of the simulated system Saturate Graylevels The Saturate Graylevels command retains all pixels with graylevel values in a specified range and saturates all other graylevels at the appropriate range boundary Parameters are the minimum and maximum graylevel of the range to be retained They default to the image minimum and

MacSADIE 1.2 User`s Manual

Contents

Download Pdf Manuals

Related Search

Related Contents