Why are there 3 conflicting OpenCV camera calibration formulas?

There is no one and only formula for camera calibration, they are all valid. Notice the first one contains constants K1, K2 & K3 for r^2, r^4 & r^6, and the other two only have constants for r^2 and r^4? That is because they are all approximate models.

The first one is likely to be more accurate since it has more parameters.

There is no one and only formula for camera calibration, they are all valid. Notice the first one contains constants K1, K2 & K3 for r^2, r^4 & r^6, and the other two only have constants for r^2 and r^4? That is because they are all approximate models.

The first one is likely to be more accurate since it has more parameters. Anytime you see: r = sqrt( x^2 + y^2 ) it is probably safe to assume x = (the x coordinate pixel) - (the camera center in pixels) since r usually means radius from the center. What are you trying to do by the way?

Estimate the camera parameters, correct for lens distortion, or both?

Thanks Doug for your input. Unfortunately I might not have posed the question clearly enough for it seems you miss the point of contention among the three formulations. It is not the difference in the number of terms used in the various approximations that is of concern here, but rather, the fact---at least as I figure it---that the three different formulations are not mathematically equivalent (even assuming they all have the same number of terms in their approximation.) I am trying to write a program that corrects for camera distortions given fx, fy, cx, and cy.

John – John Jul 29 '10 at 14:08.

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