Abstract

The technique of “renormalization” for geometric estimation attracted much attention when it was proposed in early 1990s for hav- ing higher accuracy than any other then known methods. Later, it was replaced by minimization of the repro jection error. This paper points out that renormalization can be modified so that it outperforms repro- jection error minimization. The key fact is that renormalization directly specifies equations to solve, just as the “estimation equation” approach in statistics, rather than minimizing some cost. Exploiting this fact, we modify the problem so that the solution has zero bias up to high order er- ror terms; we call the resulting scheme hyper-renormalization . We apply it to ellipse fitting to demonstrate that it indeed surpasses repro jection error minimization. We conclude that it is the best method available today.