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Renormalization Returns: Hyper-renormalization and Its Applications
Kenichi Kanatani1, Ali Al-Sharadqah2, Nikolai Chernov3, and Yasuyuki Sugaya4
1Department of Computer Science, Okayama University, Okayama 700-8530, Japan
kanatani@suri.cs.okayama-u.ac.jp
2Department of Mathematics, University of Mississippi, Oxford, MS 38677, U.S.A.
aalshara@olemiss.edu
3Department of Mathematics, University of Alabama at Birmingham, AL 35294, U.S.A.
chernov@math.uab.edu
4Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441-8580, Japan
sugaya@iim.ics.tut.ac.jp
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.
LNCS 7574, p. 384 ff.
lncs@springer.com
© Springer-Verlag Berlin Heidelberg 2012