Camera calibration add radial distortion

Hi

[Stephen23]

Original question by NASIR FARMANI on 20th December 2020 and many of their (since deleted) comments (not shown here) retrieved from Google Cache:

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Camera calibration add radial distortion.

Hi, i have 20 checkerboard images, and i have to add radial distortion without using MATLAB camera calibration libraries.

I have already estimated the projection matrix P for all images, and i have add radial distortion.

I understood i have first estimated P, after i have to estimate k1,k2 from this equations:

where u,v are the idea projections, uhat, vhat are the actual projection and rd.^2 is:

i actual find k1,k2 from this equation = inv(A' * A)* A' * b

after i have to iterate the all process with the new u,v using newton method for find the new u,v.

someone can help me to write this iterative process for find the ideal undistorted image?

Answer 1

[Image Analyst]

Do you have the Computer Vision Toolbox? There is an undistortImage() function and undistortpoints() function in it.

[Image Analyst]

Can you turn in my code for your assignment?

[Image Analyst]

What are the alphas? Angles? And the K's?

Actually I don't think that is distortion. Distortion is where the distance the point moved from the ideal location is a function of radius (distance from optical axis) cubed. So

Rdistorted = Rideal + (someFactor * RIdeal ^3)

Which is essentially what your equations show. Actually they're adding in the higher order term - the 5th order polynomial. There are several optical aberrations that have explicit formulas that can be found in the links below:

The most common monochromatic aberrations are:

• Defocus
• Spherical aberration
• Coma
• Astigmatism
• Field curvature
• Image distortion

There is also longitudinal chromatic aberration, lateral chromatic aberration, etc.

[Stephen23]