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Flexible Camera Calibration by Viewing a Plane from Unknown Orientations. Zhengyou Zhang Vision Technology Group Microsoft Research. Problem Statement. Determine the characteristics of a camera (focal length, aspect ratio, principal point) from visual information (images). Motivations.

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Flexible camera calibration by viewing a plane from unknown orientations l.jpg

Flexible Camera Calibration by Viewing a Plane from Unknown Orientations

Zhengyou Zhang

Vision Technology Group

Microsoft Research


Problem statement l.jpg
Problem Statement Orientations

  • Determine the characteristics of a camera (focal length, aspect ratio, principal point) from visual information (images)


Motivations l.jpg
Motivations Orientations

  • Recovery of 3D Euclidean structure from images is essential for many applications.

  • This requires camera calibration.

  • Look for a flexible and robust technique, suitable for desktop vision systems.

    (such that it can be used by the general public)


Classical approach photogrammetry l.jpg
Classical Approach Orientations(Photogrammetry)

  • Use precisely known 3D points

Known displacement

  • Shortcomings:Not flexible

    • very expensive to make such a calibration apparatus.


Futuristic approach self calibration l.jpg
Futuristic Approach Orientations(Self-calibration)

  • Move the camera in a static environment

    • match feature points across images

    • make use of rigidity constraint

  • Shortcoming:Not always reliable

    • too many parameters to estimate


Realistic approach my new method l.jpg
Realistic Approach Orientations(my new method)

  • Use only one plane

    • Print a pattern on a paper

    • Attach the paper on a planar surface

    • Show the plane freely a few times to the camera

  • Advantages:

    • Flexible!

    • Robust?

Yes. See RESULTS


Camera model l.jpg

Orientations

m

C

Camera Model


Plane projection l.jpg

Orientations

C

m

with

Plane projection

  • For convenience, assume the plane at z = 0.

  • The relation between image points and model points is then given by:


What do we get from one image l.jpg

Given OrientationsH, which is defined up to a scale factor,

And let

, we have

What do we get from one image?

  • We can obtain two equations in 6 intermediate homogeneous parameters.

This yields


Geometric interpretation l.jpg

Absolute conic Orientations

Geometric interpretation

Plane at infinity

C


Linear equations l.jpg
Linear Equations Orientations

  • Let

  • Define

    up to a scale factor

  • Rewrite

    as linear equations:

symmetric


What do we get from 2 images l.jpg
What do we get from 2 images? Orientations

  • If we impose  = 0, which is usually the case with modern cameras, we can solve all the other camera intrinsic parameters.

How about more images?

Better! More constraints than unknowns.


Solution l.jpg
Solution Orientations

  • Show the plane under n different orientations (n > 1)

  • Estimate the n homography matrices

    (analytic solution followed by MLE)

  • Solve analytically the 6 intermediate parameters (defined up to a scale factor)

  • Extract the five intrinsic parameters

  • Compute the extrinsic parameters

  • Refine all parameters with MLE


Experimental results l.jpg
Experimental results Orientations



Result 1 l.jpg
Result (1) Orientations


Result 2 l.jpg
Result (2) Orientations


Correction of radial distortion l.jpg

Original image Orientations

Correction of Radial Distortion

Corrected image









Reconstructed vrml model l.jpg
Reconstructed Orientations VRML Model


Conclusion l.jpg
Conclusion Orientations

  • We have developed a flexible and robust technique for camera calibration.

  • Analytical solution exists.

  • MLE improves the analytical solution.

  • We need at least two images if c = 0.

  • We can use as many images of the plane as possible to improve the accuracy.


It really works l.jpg
It really works! Orientations

  • Currently used routinely in both Vision and Graphics Groups.

  • Binary executable will be distributed on the Web to the public soon.

  • Source code will also be made available.