Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion

Abstract:
A number of minimal problems of structure from motion for

cameras with radial distortion have recently been studied and solved

in some cases. These problems are known to be numerically very

challenging and in several cases there exist no known practical

algorithm yielding solutions in floating point arithmetic. We make

some crucial observations concerning the floating point implementation

of Gröbner basis computations and use these new insights to formulate fast and

stable algorithms for two minimal problems with radial distortion

previously solved in exact rational arithmetic only: (i) simultaneous

estimation of essential matrix and a common radial distortion

parameter for two partially calibrated views and six image point

correspondences and (ii) estimation of fundamental matrix and two

different radial distortion parameters for two uncalibrated views and

nine image point correspondences. We demonstrate on simulated and

real experiments that these two problems can be efficiently solved in

floating point arithmetic.