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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

Flexible Camera Calibration by Viewing a Plane from Unknown Orientations

Zhengyou Zhang

Vision Technology Group

Microsoft Research

problem statement
Problem Statement
  • Determine the characteristics of a camera (focal length, aspect ratio, principal point) from visual information (images)
motivations
Motivations
  • 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
Classical Approach(Photogrammetry)
  • Use precisely known 3D points

Known displacement

  • Shortcomings:Not flexible
    • very expensive to make such a calibration apparatus.
futuristic approach self calibration
Futuristic Approach(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
Realistic Approach(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

plane projection

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

Given H, 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

linear equations
Linear Equations
  • Let
  • Define

up to a scale factor

  • Rewrite

as linear equations:

symmetric

what do we get from 2 images
What do we get from 2 images?
  • 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
Solution
  • 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
conclusion
Conclusion
  • 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
It really works!
  • 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.
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