Hyper-renormalization: Non-minimization approach for geometric estimation

Abstract

The technique of "renormalization" for geometric estimation attracted much attention when it appeared in early 1990s for having higher accuracy than any other then known methods. The key fact is that it directly specifies equations to solve, rather than minimizing some cost function. This paper expounds this "non-minimization approach" in detail and exploits this principle to modify renormalization so that it outperforms the standard reprojection error minimization. Doing a precise error analysis in the most general situation, we derive a formula that maximizes the accuracy of the solution; we call it hyper-renormalization. Applying it to ellipse fitting, fundamental matrix computation, and homography computation, we confirm its accuracy and efficiency for sufficiently small noise. Our emphasis is on the general principle, rather than on individual methods for particular problems.