Camera Calibration Camera Calibration Steve Steve Seitz Seitz - - PDF document

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Steve Steve Seitz Seitz Carnegie Mellon Carnegie Mellon University University

http http:// ://www www. .cs cs. .cmu cmu. .edu edu/~ /~seitz seitz

Camera Calibration Camera Calibration

SIGGRAPH 99 Course on SIGGRAPH 99 Course on 3D Photography 3D Photography

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” . . .

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Geometric Camera Calibration Geometric Camera Calibration

2D 2D ⇔ ⇔ 2D 2D

correspondence correspondence SFM, SFM, “ “Self-calibration Self-calibration” ”

2D 2D ⇔ ⇔ 3D 3D

correspondence correspondence “ “Classical Classical” ” calibration 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

Linear Geometric Calibration Linear Geometric Calibration

Know 3D Know 3D coords coords, 2D , 2D coords coords

• Find projection matrix

Find projection matrix Π

Π

                      =           1 1

34 33 32 31 24 23 22 21 14 13 12 11

Z Y X p p p p p p p p p p p p v u d

u = u = Π Π X X

11 unknowns (up to scale) 11 unknowns (up to scale) 2 equations per point 2 equations per point (eliminate d) (eliminate d) 6 points is sufficient 6 points is sufficient

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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]

• Parameterize

Parameterize Π

Π in terms of

in terms of > > rotation: rotation: θ θ, ,φ φ, ,ψ ψ > > 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: k1

1,

,

k

k2

2

Code Available Via Course Web Page Code Available Via Course Web Page

Calibration Patterns Calibration Patterns

Chromaglyphs Chromaglyphs Bruce Bruce Culbertson Culbertson, HP-labs , HP-labs Calibration grid Calibration grid Z.

• Z. Zhang

Zhang, Microsoft Research , Microsoft Research

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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.

http://www.cs cs. .cmu cmu. .edu edu/ /afs afs/ /cs cs/project/ /project/cil cil/ftp/html/vision. /ftp/html/vision.html html

Matlab Matlab and C Implementations and C Implementations

• 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

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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, Robotics and Automation, Vol

• Vol. 3, No. 4, 1987,

. 3, No. 4, 1987, pp

• pp. 323-344.

. 323-344.

Radiometric Calibration Radiometric Calibration

• Paul E.

Paul E. Debevec 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

• pp. 137-154.

. 137-154.

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.

Bibliography Bibliography