# Flexible Camera Calibration by Viewing a Plane from Unknown Orientations - PowerPoint PPT Presentation

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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

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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

• 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)

• Use precisely known 3D points

Known displacement

• Shortcomings:Not flexible

• very expensive to make such a calibration apparatus.

### 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)

• 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

• Flexible!

• Robust?

Yes. See RESULTS

m

C

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:

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

Absolute conic

### Geometric interpretation

Plane at infinity

C

### Linear Equations

• Let

• Define

up to a scale factor

• Rewrite

as linear equations:

symmetric

### 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.

Better! More constraints than unknowns.

### 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

Original image

Corrected image

### 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!

• 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.