- CiteSeer
Contents
1. Byla y e SECOND ORDER DISTORTIONS model 12 Lg 2 ax By Ya y yx by e SECOND ORDER RADIAL DISTORTIONS model 13 T 2 00 By er x y Ya y yu by eyl y INRIA CamCal v1 0 Manual 9 e DECENTERING THIN PRISM DISTORTIONS model 14 fq 2 ale y 2Bay 2 y Ya y Bla 3y 2axy y a y e DECENTERING RADIAL DISTORTIONS model 15 za 2 a 32 y 2Bxy yx z y Ya y Pla 3y 200 y yyla y e THIN PRISM RADIAL DISTORTIONS model 16 Ta 2 a x y Bula y Ya y ala y By x y The default camera model for accurate estimation is the radial distortion model but any of the previous models can be selected by using the following option m lt camera_model_id gt while running CamCal 3 Camera calibration Complete camera calibration consists in estimating both intrinsic and extrinsic pa rameters Knowing the camera position would be easy if one could register object positions accurately say with a laser based range finder Unfortunately this is not possible because we need to recover an imaginary position the optical center which cannot be observed directly somewhere inside the camera Moreover this point does not even have a fixed place in the camera It is known that the center of projection changes when a zoom lens is being used for example In other words one needs to recali2. ay Therefore the vertical and horizontal sample sizes are 1 a and 1 a respectively These ratios reflect the combined contribution of both the camera and the digitizer sampling processes The coordinates uo vo of the image center as well as the dimensions a a are the 4 intrinsic parameters of the pinhole camera model Thus the relationship between the 3D coordinates x y z of a 3D point in the camera reference frame and its image coordinate u v is x u Uo Qu 2 1 y U Vo Au z Remember it is assumed here that the final image has its origin 0 0 at the upper left corner 2 3 From 3D to 2D By combining the rigid displacement the conic projection and the image sampling we determine the relationship between the coordinates of a space point x y z INRIA CamCal v1 0 Manual 7 expressed in the absolute reference frame and its image u v This equation has a simple expression with homogeneous notations X x y z 1 for each point of the euclidian space LX GER LyX Fo or su Li su Lo X S La Thus the complete transformation is represented by a3 x 4 matrix often named Ly Qu O O M L gt 0 a v 0 de E Ls 0 0 1 0 2 4 Model with distortions The previous description is a very simple ideal model usually refined by taking into account the optical distortions of the camera lens for sake of realism Optical aberrations account for the discrepancy betwee
3. a Makefile is included This makefile should work fine on a Unix system To compile you can just send the command in the source directory to obtain the CamCal binary gt make 6 3 Running An example of data is given to check if your CamCal executable runs properly e araw image file named example e a 3d set up file named setup ex To run the calibration just run in the source directory gt CamCal You should obtain results identical to the references i e e exedg ref raw image of the extracted edges e expt ref 2d points extracted from original and edge files e excamtos ref perspective matrix obtained by Toscani s algorithm e excam ref final camera result RTn 0196 18 J Ph Tarel J M Vezien 7 Contact and copyright CamCal has been designed by Jean Philippe Tarel INRIA Domaine de Voluceau Rocquencourt BP 105 78153 LE CHESNAY Cedex France Tel 39 63 54 79 Fax 39 63 57 74 E mail Jean Philippe Tarel inria fr WWW http www syntim inria fr tarel The Inter deposit Digital Number of CamCal software version 1 0 is IDDN FR 001 290004 00 R P 1996 000 2 1000 so the CamCal software is under INRIA copyright 1996 Permission to use copy modify and distribute this software and its documenta tion for any purpose is hereby granted without fee provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentat
4. first axis circle 1 gt lt x second axis circle 1 gt lt y second axis circle 1 gt lt z second axis circle 1 gt lt circle n gt lt x center circle n gt lt y center circle n gt lt z center circle n gt lt x first axis circle n gt lt y first axis circle n gt lt z first axis circle n gt lt x second axis circle n gt lt y second axis circle n gt lt z second axis circle n gt When the calibration target is a set of ellipses the lt Type gt value is always 1 But CamCal can also be used to perform camera calibration based on simple point to point correspondences used point are then ellipse centers For this specify the lt type gt value to 0 In this case the calibration set up is described in the following manner lt type gt lt horizontal size of a grid gt lt vertical size of a grid gt lt number of grids gt lt point 1 gt lt x point 1 gt lt y point 1 gt lt z point 1 gt lt point n gt lt x point n gt lt y point n gt lt z point n gt RT n 0196 14 J Ph Tarel J M Vezien A default set up file is provided but you shall have to build your calibration target according to its specifications If you want to use your own 3D set up file use CamCal following option g lt 3d_setup_file gt by default lt 3d_setup_file gt setup ex 4 5 Control parameters Some parameters can be changed in case the program fails to produce a calibration with the default valu
5. three values for the three basic colors red green and blue also called an RBG image must be preprocessed and converted into a gray level image 4 2 Image After the acquisition all the pixels of an image frame are usually delivered in a file buffer This file is the raw image data used by CamCal CalCam only accept the specific raw image file format But an image has a format whose only role for us is to describe the size of the image frame by two values It just gives number of columns lt dimx gt and number of lines lt dimy gt In summary CamCal basically needs the following 2D informations e Image frame buffer the values of all the pixels saved as unsigned chars lt image_file gt This file is specified to CamCal by following option i lt image_file gt by default lt image_file gt example RTn 0196 12 J Ph Tarel J M Vezien e Format number of columns lt dimx gt and number of lines lt dimy gt These sizes are specified with following options x lt dimx gt and y lt dimy gt lt dimx gt 640 and lt dimy gt 512 by default The first step of the camera calibration is to obtain an edge image from the ori ginal image in lt image_file gt with Canny Deriche s algorithm The edge image is stored in a separate file lt image_file gt edg in the same directory If you want to change the edge image file name or use our own edge image use CamCal option e lt edge_image_file g
6. ISSN 0249 0803 VAINRIA INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE CamCal v1 0 Manual A complete software Solution for Camera Calibration Jean Philippe Tarel Jean Marc Vezien N 0196 September 1996 TH ME 3 apport technique VAINRIA ROCQUENCOURT CamCal v1 0 Manual A complete software Solution for Camera Calibration Jean Philippe Tarel Jean Marc Vezien Th me 3 Interaction homme machine images donn es connaissances Projet Syntim Rapport technique n 0196 September 1996 19 pages Abstract This technical report is the user manual of CamCal v1 0 CamCal is a software for geometric camera calibration from a 3D calibration set up image Key words Geometric camera calibration CamCal manual 3D calibration set up R sum tsvp CamCal software is distributed by INRIA For distribution contact Jean Philippe Tarel and or Jean Louis Bouchenez E mail Jean Louis Bouchenez inria fr Le programme CamCal est distribu par INRIA Pour obtenir le logiciel contacter Jean Philippe Tarel et ou Jean Louis Bouchenez E mail Jean Louis BouchenezOinria fr E mail Jean Philippe TarelO inria fr Unit de recherche INRIA Rocquencourt Domaine de Voluceau Rocquencourt BP 105 78153 LE CHESNAY Cedex France T l phone 33 1 39 63 55 11 T l copie 33 1 39 63 53 30 Manuel du programme Camcal v1 0 Une solution logicielle complete pour la calibration d
7. brate the camera everytime the focal length is changed As we have discussed an image of a certain calibration set up is needed for calibration see test image included in this distribution The 3D geometry of the template calibration object must be known accurately so that in the operation Image M 3D object RT n 0196 10 J Ph Tarel J M Vezien both image and object are known and the projection M can be estimated The steps of the whole calibration process are the following a Edge extraction from original image by Canny Deriche s edge detector For details see 1 b From edge image closed contour chains are linked using Giraudon s chain follower linker For details see 4 in french or 5 c Extract image features from calibration target These features are the center of gravity of image ellipses which are the images of planar ellipses drawn on two perpendicular grids which form the calibration target d Match 2D features with the set of known 3D patterns which are 3D ellipses on two perpendicular boards Matching is made easy by the grid like nature of the arrangement e Initial approximate pin hole camera calibration with Toscani s algorithm For details see 9 p33 34 35 and p21 22 2 in french and 3 f Accurate iterative camera calibration with distortions by minimizing of er ror function You can look in the paper 8 7 6 for more details in french or http www rocq inria fr s
8. distortion and image centers 9 ellipse to point correspondance mm error special radial distortion 10 ellipse to point correspondance mm error decentering distortion 11 ellipse to point correspondance mm error thin prism distortion 12 ellipse to point correspondance mm error second order distor tions 13 ellipse to point correspondance mm error second order and radial distortion 14 ellipse to point correspondance mm error thin prism and decen tering distortion 15 ellipse to point correspondance mm error radial and decentering distortion 16 ellipse to point correspondance mm error radial and thin prism distortion As a summary others options are e g lt 3d_setup file gt filename of the calibration setup by default we have lt 3d_setup file gt setup ex e i lt image_file gt filename of the original image by default we have lt image file gt example e x lt dimx gt and y lt dimy gt image size of the original image we have lt dimx gt 640 and lt dimy gt 512 by default e e lt edge_image_file gt filename of the edge raw format image extrac ted from the original image lt edge_image_file gt example edg by default RTn 0196 16 J Ph Tarel J M Vezien e p lt 2d_points_file gt name of the 2D points file extracted from the original image by default lt 2d_points_f
9. e cam ra R sum Ce rapport technique est le manuel d utilisation de CamCal v1 0 Cam Cal est un logiciel qui permet la calibration g om trique d une cam ra a partir de l image d une mire 3D Mots cle Calibration g om trique de cam ra Manuel de CamCal Mire 3D CamCal v1 0 Manual Contents 1 Introduction 2 Camera model 2 1 extrinsic parameters camera position 2 2 Imaging process the pin hole camera model and the intrinsic para MS a o io dr thins eh dh Ar 2 3 From 3DA02Dr is e a ar DS oe 2 4 Model with distortions 3 Camera calibration 4 Input data 4 1 Image acquisition zn er ira ar te ae SS 42 Amige lt a A ee NT ee a Eos AO ZIP DOES Te ha ae aes 44 3D calibration set up 4 5 Control parameters e Oke Mee AR Por Pee Oe ae ee Pe 5 Output data 6 Implementation aspects Gk Slee aa a ee Se A A A AA Se E N 6 2 Compiling ia desea hey Sew he Gia eke ee ee eS 62 RUNNING ne ee eee A e ee ei 7 Contact and copyright RT n 0196 10 11 11 12 12 14 16 16 16 17 17 18 J Ph Tarel J M Vezien INRIA CamCal v1 0 Manual 3 1 Introduction It is known for a long time that depth perception can be attained by merging the information captured from multiple images taken at different viewpoints a pro cess known as stereovision For this it is important to know among other things the relative positions of the sensors U
10. el Jean Philippe Calibration de cam ra fond e sur les el lipses Rapport de recherche n 2200 INRIA 1994 http www rocq inria fr syntim textes calib94 eng html Tarel Jean Philippe et Gagalowicz Andr Calibration de cam ra a base d ellipses In 9eme congr s AFCET Reconnaissance des Formes et Intelli gence Artificielle Paris France 1994 Tarel Jean Philippe et Gagalowicz Andr Calibration de cam ra base d ellipses Traitement du Signal vol 12 n 2 1995 pp 177 187 http www rocq inria fr syntim textes calib eng html Toscani G Syst mes de calibration et perception du mouvement en Vision Artificielle Th se de PhD Universit Paris Sud 1987 RT n 0196 As Unit de recherche INRIA Lorraine Technop le de Nancy Brabois Campus scientifique 615 rue du Jardin Botanique BP 101 54600 VILLERS LES NANCY Unit de recherche INRIA Rennes Irisa Campus universitaire de Beaulieu 35042 RENNES Cedex Unit de recherche INRIA Rh ne Alpes 655 avenue de l Europe 38330 MONTBONNOT ST MARTIN Unit de recherche INRIA Rocquencourt Domaine de Voluceau Rocquencourt BP 105 78153 LE CHESNAY Cedex Unit de recherche INRIA Sophia Antipolis 2004 route des Lucioles BP 93 06902 SOPHIA ANTIPOLIS Cedex Editeur INRIA Domaine de Voluceau Rocquencourt BP 105 78153 LE CHESNAY Cedex France ISSN 0249 6399
11. ence object is built with two orthogonal planes where elliptical shapes of an uniform color are painted on an uniform background e g white shape on INRIA CamCal v1 0 Manual 13 black background Moreover for accurate results the calibration set up must be illuminated by ambient light and the resulting image have good contrast The cali bration set up surface must be as diffuse as possible In our camera calibration experiments the calibration set up is placed at a dis tance of about 1 or 2 meters oriented in front of the camera What is important is the apparent ellipse radius in the image which should be more than 15 pixels the bigger the better with the obvious trade off that all the calibration target must be visible Avoid using lenses with large field of view which tend to distort images a lot The upper left corner of the object is chosen as the origin of the reference frame to describe positions and orientations of the circular features These circles are given from left to right and from top to bottom for each face from left to right You must provide CamCal with the 3D geometry of the calibration setup des cribed in a text file in the following maner lt type gt lt horizontal size of a grid gt lt vertical size of a grid gt lt number of grids gt lt circle 1 gt lt x center circle 1 gt lt y center circle 1 gt lt z center circle 1 gt lt x first axis circle 1 gt lt y first axis circle 1 gt lt z
12. es e L lt size in pixel of the blur gt size of the blurring zone around an edge 3 by default e lt distance in pixel between two ellipses gt shortest dis tance between two ellipse edges 7 by default e c lt distance close gt if the gap between one end and the other end of a chain is bigger than this threshold the chain is considered open 4 by default Calibration retains only closed chains according to this criterion e s lt down value gt down hysteresis threshold between 0 and 255 20 by default e S lt up value gt up hysteresis threshold between O and 255 40 by de fault e m lt camera model id gt between 0 and 16 7 by default 0 point to point correspondance without distortion and pixel error minimisation 1 point to point correspondance without distortion mm error 2 point to point correspondance with a fixed center mm error without distortion 3 point to point correspondance mm error radial distortion 4 ellipse to point correspondance pixel error without distortion 5 ellipse to point correspondance mm error without distortion INRIA CamCal v1 0 Manual 15 6 ellipse to point correspondance with fixed center mm error without distortion 7 ellipse to point correspondance mm error radial distortion 8 ellipse to point correspondance mm error radial distortion and gap between
13. eters We use the transformation from the camera frame to the world frame so that object coordinates are transformed the other way from the world to the camera with the same transform The origin of the right handed camera reference frame is positioned at the cen ter of projection of the lens So the camera looks from this point to the outside world The z axis of the camera frame corresponds to the optical axis This is an RT n 0196 6 J Ph Tarel J M Vezien imaginary axis passing through the middle of the lens the lens or system of lens is supposed perpendicular to it The x axis is parallel to the horizontal axis of the image from left to right and the y axis is parallel to the vertical axis in the down direction 2 2 Imaging process the pin hole camera model and the intrin sic parameters A camera transforms the real 3D space into a 2D image plane Usually the transfor mation is assumed to be a conic projection The center of the projection is defined as the camera center see above This camera model uses the pin hole assumption The center of the image wo vo expressed in pixels is defined as the intersec tion between the optical axis and the image on the CCD matrix the sensor plane is also assumed to be perpendicular to the optical axis This center is usually close to the ideal image center but can wander significantly from it Sampling is realized with a rectangular pattern whose dimensions are a
14. ile gt example pt e r lt camera_filename gt filename of the resulting camera by default lt image_filename gt cam All the filenames may be preceeded by a pathname 5 Output data Estimated parameters for the camera model and position are saved in the output file If you want to change the resulting camera filename use the following op tion r lt camera_filename gt with CamCal by default the camera name is lt image filename gt cam and lt image_filename gt cam tos contains the perspective matrix outputs Note that camera files are not recomputed if they are already present on the disk 6 Implementation aspects 6 1 Style All Programs are written in the C language Routines have been grouped according to their task type so that edge detection chain extraction image point extraction and camera calibration each have their own set of files Task Files edge detection Deriche c Deriche h chain extraction Chain c ChainIma c ChainExam c Chain h chain approximation AppChain c AppChain h image point extraction ExtPoint c ExtPoint h ExtBary c ExtBary h camera calibration Toscani c Toscani h Callter c Callter h main I O CamCal c CamCal h linear algebra Matrix c Matrix h memory management Mem c Mem h INRIA CamCal v1 0 Manual 17 Besides for each task type there is a special header file with all the information required to make use of the functions 6 2 Compiling In order to compile the programs
15. ion and that the names of authors and the Institut National de Recherches en Informatique et Automatique INRIA not be used in advertising or publicity pertaining to distribution of the software without specific written prior permission CamCal software is distributed by INRIA For distribution contact Jean Philippe Tarel and or Jean Louis Bouchenez Jean Louis Bouchenez inria fr INRIA CamCal v1 0 Manual 19 References 1 2 3 4 5 6 7 8 9 Deriche R Using canny s criteria to derive an optimal edge detector re cursively implemented International Journal of Computer Vision vol 1 n 2 1987 Faugeras O Lustman F et Toscani G Calcul du mouvement et de la structure partir de points et de droites In 6 me congr s AFCET Reconnais sance des Formes et Intelligence Artificielle pp 75 89 Antibes November 1987 Faugeras O D et Toscani G The calibration problem for stereo In Pro ceedings CVPR 86 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Miami Beach FL June 22 26 1986 pp 15 20 IEEE Giraudon G Chainage efficace de contours Rapport de recherche 605 INRIA 1987 Giraudon G A real time parallel edge following in single pass In Work shop on Computer Vision Proceedings published by IEEE Computer Society Press Washington DC pp 228 230 Miami Beach FL 1987 Tar
16. n the real and the ideal image of a light ray on the camera sensor As we deal here with geometric calibration only geometric distortions are considered Distortions are a special type of aberrations independent of the orientation of the incoming light ray The modeling of distor tion effects adds nonlinear terms to the projective relationship between a 3D space point and an image point To get the complete 3D to 2D correspondence relations it is therefore necessary to combine the rigid displacement the conic projection the distortions and the sampling in this order Usually the three more important distortions are e The RADIAL DISTORTION produces generally the most important effect model 7 a ax x y RT n 0196 8 J Ph Tarel J M Vezien Ya y ay x y e The DECENTERING of a lens on the axe of view is described by the follo wing equation model 10 za 0 32 y 26xy Ya y B x 34 2axy e The effect of an error in lens parallelism is the THIN PRISM distortion mo del 11 Ta 3 alx y Ya y a x y The last two distortion types can be made very low in good quality camera lenses More exotic distortion types are added in CamCal for instance e RADIAL DISTORTION effect with a gap between image and distortion cen ters model 8 za 2 ar x y Br Ya y ay a y yy e SPECIAL RADIAL DISTORTION effect model 9 Ta 1 ar x y Ya y
17. nfortunately the precise camera locations are usually unknown at the time of acquisition To solve this problem a range of methods exist called CAMERA CALIBRATION This manual briefly presents a specific implementation of such methods the CamCal software The resulting ca libration can be applied to stereovision but also to a wide range of other machine vision algorithms Briefly put our algorithm estimates for a given set up the position of the ca mera extrinsic parameters and its internal viewing characteristics intrinsic para meters by using both 2D points and 3D ellipses drawn on a calibration device whose geometry is known with great accuracy Let us now first briefly explain whose parameters we plan on actually recovering and how the calibration proce dure computes them Then we will see how the program named CamCal actually works 2 Camera model 2 1 extrinsic parameters camera position Although self calibration methods have recently arisen it is still customary to use the image of a special calibration pattern to recover the imaging process parameters The first and most natural information one needs is the camera location with respect to a fixed coordinate frame To describe the position of the camera we will use the translation 7 and the rotation R of an absolute coordinate system fixed on the calibration target expressed in the camera coordinate sytem This set of 6 numbers unambiguously defines the extrinsic param
18. t by default lt edge_image_file gt example edg Note that the edge image buffer is not recomputed if a file of the same name is present on the disk 4 3 2D points Correct 2D measurements are required to perform an accurate estimation of the camera model A feature detection accuracy of 1 10 pixel is typically necessary in real situations for a5 mm positionning of the calibration set up After steps a though d of the camera calibration 2D positions of the centers of gravity of the ellipses present in the image are obtained from the original image with high accuracy Result is stored in a text file lt image file gt pt inthe same directory If you want to change the 2D points filename or use your own 2D points file use CamCal option p lt 2d points_file gt by default lt 2d_points_file gt example pt Note that the 2D points file is not recomputed if it is already present on the disk 4 4 3D calibration set up The intrinsic and extrinsic parameters are computed by estimating the orientation of all the circles of the calibration set up on the image To make the overall estimation as significant as possible many circles are drawn on the object Usually our cali bration set up is composed of two orthogonal planes where a regular grid of 7 x 6 disks are affixed at known locations The accuracy of the calibration set up should be high in our case the target was machined with a 1 30 mm precision The refer
19. yntim textes calib eng html Tsai s algorithm is not implemented in this version of CamCal To download the Tsai s software SEE http www cs cmu edu afs cs cmu edu user rgw www TsaiCode html or the following adresse ftp ftp teleosresearch com VISION LIST ARCHIVE SHAREWARE CODE CALIBRATION 4 Input data Basically camera calibration algorithm inputs are e a gray level 2D image of the calibration setup e the 3D geometric model of the calibration setup INRIA CamCal v1 0 Manual 11 e some control parameters Optionally other data inputs can be used e the edge image of the original image if you want to use another edge detector than the one provided e the 2D points of center of gravity of the ellipses from the original image if you want to provide pre processed data In this case no image is needed 4 1 Image acquisition Digital 2D image frames are usually obtained via a CCD camera connected to a di gitizer An image frame is a name for all the pixels PICture ELement of an image whereas an image contains more than only an image frame buffer In particular it also contains the image size The pixels are all delivered consecutively from left to right and from top to bottom The coding of image frame buffers depends a lot on your digitizing equipment In our case 1t is supposed to be a monochrome image frame buffer Thus each pixel is represented by an 8 bit value Color images where each pixel is coded as
Download Pdf Manuals
Related Search