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Renormalization Returns: Hyper-renormalization and Its Applications

  • Kenichi Kanatani
  • Ali Al-Sharadqah
  • Nikolai Chernov
  • Yasuyuki Sugaya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7574)

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.

Keywords

Minimization Principle Generalize Eigenvalue Problem Geometric Estimation True Shape Reprojection Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kenichi Kanatani
    • 1
  • Ali Al-Sharadqah
    • 2
  • Nikolai Chernov
    • 3
  • Yasuyuki Sugaya
    • 4
  1. 1.Department of Computer ScienceOkayama UniversityOkayamaJapan
  2. 2.Department of MathematicsUniversity of MississippiOxfordU.S.A.
  3. 3.Department of MathematicsUniversity of Alabama at BirminghamU.S.A.
  4. 4.Department of Information and Computer SciencesToyohashi University of TechnologyToyohashiJapan

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