Renormalization Returns: Hyper-renormalization and Its Applications
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.
KeywordsMinimization Principle Generalize Eigenvalue Problem Geometric Estimation True Shape Reprojection Error
- 7.Kanatani, K.: Renormalization for unbiased estimation. In: Proc. 4th Int. Conf. Comput. Vis., Berlin, Germany, pp. 599–606 (May 1993)Google Scholar
- 16.Okatani, T., Deguchi, K.: On bias correction for geometric parameter estimation in computer vision. In: Proc. IEEE Conf. Computer Vision Pattern Recognition, Miami Beach, FL, U.S.A., pp. 959–966 (June 2009)Google Scholar
- 17.Okatani, T., Deguchi, K.: Improving accuracy of geometric parameter estimation using projected score method. In: Proc. 12th Int. Conf. Computer Vision, Kyoto, Japan, pp. 1733–1740 (September/October 2009)Google Scholar