Renormalization returns: hyper-renormalization and its applications

Authors:
Kenichi Kanatani;Ali Al-Sharadqah;Nikolai Chernov;Yasuyuki Sugaya
Affiliations:
Department of Computer Science, Okayama University, Okayama, Japan;Department of Mathematics, University of Mississippi, Oxford, MS;Department of Mathematics, University of Alabama at Birmingham, AL;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi, Japan
Venue:
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Year:
2012

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Abstract

The technique of "renormalization" for geometric estimation attracted much attention when it was proposed in early 1990s for having higher accuracy than any other then known methods. Later, it was replaced by minimization of the reprojection error. This paper points out that renormalization can be modified so that it outperforms reprojection 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 error terms; we call the resulting scheme hyper-renormalization. We apply it to ellipse fitting to demonstrate that it indeed surpasses reprojection error minimization. We conclude that it is the best method available today.