image - Accurate Approximations of Fisheye lense distortion via non polynomial FET method? -


i'm trying approximate fisheye lense distortion. used polynomial method described in this paper, , worked fine forward transform, forgot need sort of interpolation backward transform needed, , need inverse function transformation, proved problematic (i used non alternating power sign version ie sum( polynomial_coefficients[i] * radius^i)) division model didn't appear appropriate (and spit out bad results if tried use non alternating power version because dividing radius). switched appears more accurate method (correct me if i'm wrong , provide more accurate method) via 

r_distorted = scalar * ln(1 + lambda * r_undistorted)

and

r_undistorted = (e^(r_distorted/scalar) - 1)/lambda

which featured in same paper. i in source paper didn't understand how ever end no distortion lower values of lambda, or heck supposed scalar value. wanted test code in situatiations lense distortion zero, formula not seem provide way me set parameters value forward transform of (r_undistorted) = r_distorted or inverse transform (r_distorted) = r_undistorted r_undistorted , r_distorted. trivial in polynomial example.

currently have algorithm implemented, values of 0 lambda , 1 scale not result in no distortion (indeed obvious see why) since 1*ln(1 - 0 *x) = 0. this source alters equation instead of terms of distance image plane (f in images) , tan(theta), , leaves me more confused. seem there must variable implicitly involved equation allow such transformation (no transform) happen. appears un-intuitive how control distortion using these 2 equations.

in short, how use equation apply no distortion, , both lambda , scalar mean physically, , do? there better methods accuracy in approximating fisheye transform inverse?


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