SIGGRAPH 99 Course on SIGGRAPH 99 Course on 3D Photography 3D Photography Camera Calibration Camera Calibration Steve Steve Seitz Seitz Carnegie Mellon University University Carnegie Mellon http http:// ://www www. .cs cs. .cmu cmu. .edu edu/~ /~seitz seitz Camera Calibration Camera Calibration Geometry Geometry • Where is the camera? Where is the camera? • • Where is it pointing? Where is it pointing? • • What are the internal parameters? What are the internal parameters? • • What’s the point spread function? What’s the point spread function? • Radiometry Radiometry • What is the mapping from light to pixel values? What is the mapping from light to pixel values? • • [ [Debevec Debevec 97] 97] • If Only Cameras Were “Smart” . . . If Only Cameras Were “Smart” . . . 1
Geometric Camera Calibration Geometric Camera Calibration Augmented pin-hole camera model Augmented pin-hole camera model • Focal point, orientation Focal point, orientation • • Focal length, aspect ratio, center, lens distortion Focal length, aspect ratio, center, lens distortion • 2D ⇔ 3D 2D ⇔ 2D 2D ⇔ 3D 2D ⇔ 2D correspondence correspondence correspondence correspondence “Classical “ Classical” ” calibration calibration SFM, “ SFM, “Self-calibration Self-calibration” ” Linear Geometric Calibration Linear Geometric Calibration Know 3D Know 3D coords coords, 2D , 2D coords coords Find projection matrix Π Π • Find projection matrix • X 11 unknowns (up to scale) 11 unknowns (up to scale) u p p p p 11 12 13 14 Y 2 equations per point 2 equations per point = d v p p p p 21 22 23 24 Z (eliminate d) (eliminate d) 1 p p p p 31 32 33 34 1 6 points is sufficient 6 points is sufficient u = u = Π Π X X 2
Nonlinear Methods Nonlinear Methods Problems with Linear Method Problems with Linear Method • Too many free parameters Too many free parameters • • Doesn’t model lens distortion Doesn’t model lens distortion • Nonlinear Methods [ Nonlinear Methods [Tsai Tsai, 1985] , 1985] Π in terms of Parameterize Π • Parameterize in terms of • rotation: θ θ , , φ φ , , ψ ψ > rotation: > > translation: X, Y, Z > translation: X, Y, Z > intrinsics intrinsics: f, aspect ratio, image center : f, aspect ratio, image center > > radial lens distortion: k radial lens distortion: k 1 , k 2 > 1 , k 2 Code Available Via Course Web Page Code Available Via Course Web Page Calibration Patterns Calibration Patterns Calibration grid Calibration grid Chromaglyphs Chromaglyphs Z. Zhang Zhang, Microsoft Research , Microsoft Research Bruce Culbertson Culbertson, HP-labs , HP-labs Z. Bruce 3
Calibration From 2D Motion Calibration From 2D Motion Structure From Motion (SFM) Structure From Motion (SFM) • Track points over a sequence of images Track points over a sequence of images • • Solve for 3D positions and camera positions Solve for 3D positions and camera positions • • Calibrate internal parameters beforehand Calibrate internal parameters beforehand • Self-Calibration Self-Calibration • Solve for internal Solve for internal and and external parameters external parameters • • E.g., [ E.g., [Polleyfeys Polleyfeys, 98] , 98] • Resources Resources Computer Vision Home Page Computer Vision Home Page http://www.cs http://www. cs. .cmu cmu. .edu edu/ /afs afs/ /cs cs/project/ /project/cil cil/ftp/html/vision. /ftp/html/vision.html html • • Matlab and C Implementations and C Implementations Matlab • Via course web page Via course web page • http http:// ://www www. .cs cs. .cmu cmu. .edu edu/~ /~seitz seitz/course/3DPhoto. /course/3DPhoto.html html • • 4
Bibliography Bibliography Geometric Calibration Geometric Calibration • • R. J. R. J. Tsai Tsai, A Versatile Camera Calibration Technique for High Accuracy 3D Machine , A Versatile Camera Calibration Technique for High Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses, IEEE Journal of Vision Metrology Using Off-the-Shelf TV Cameras and Lenses, IEEE Journal of Robotics and Automation, Vol Robotics and Automation, Vol. 3, No. 4, 1987, . 3, No. 4, 1987, pp pp. 323-344. . 323-344. Radiometric Calibration Radiometric Calibration • • Paul E. Debevec Paul E. Debevec and and Jitendra Malik Jitendra Malik, “Recovering High Dynamic Range Radiance , “Recovering High Dynamic Range Radiance Maps from Photographs”, Maps from Photographs”, Proc Proc. SIGGRAPH 97, . SIGGRAPH 97, pp pp. 369-378. . 369-378. Structure-from-Motion Structure-from-Motion • • Carlo Tomasi & Carlo Tomasi & Takeo Kanade Takeo Kanade, ”Shape and Motion from Image Streams Under , ”Shape and Motion from Image Streams Under Orthography: A Factorization Method", Orthography: A Factorization Method", Int Int. Journal of Computer Vision, 9(2), 1992, . Journal of Computer Vision, 9(2), 1992, pp. 137-154. . 137-154. pp Self-Calibration Self-Calibration • • Marc Pollefeys Marc Pollefeys, , Reinhard Koch Reinhard Koch, and , and Luc Luc Van Van Gool Gool, "Self-Calibration and Metric Reconstruction , "Self-Calibration and Metric Reconstruction in spite of Varying Unknown Internal Camera Parameters", in spite of Varying Unknown Internal Camera Parameters", Proc Proc. Sixth . Sixth Int Int. . Conf Conf. on Computer . on Computer Vision,1998, Vision,1998, pp pp. 90-91. . 90-91. 5
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