Renormalization Returns: Hyper-renormalization and Its Applications
Renormalization Returns: Hyper-renormalization and Its Applications
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DOI：
10.1007/978-3-642-33712-3_28
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
K. Kanatani;A. Al-Sharadqah;N. Chernov;Y. Sugaya
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文献类型：
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作者：
K. Kanatani;A. Al-Sharadqah;N. Chernov;Y. Sugaya
几何估计的“重整化”技术在20世纪90年代初被提出时，因其比当时已知的任何方法都具有更高的精度而受到广泛关注。后来，它被最小化重投影误差所取代。本文指出可以对重整化进行修改，使其优于重投影误差最小化。关键的事实是，重整化直接指定要解决的方程，就像统计学中的“估计方程”方法一样，而不是最小化一些成本。利用这一事实，我们修改了问题，使解决方案在高阶误差项下具有零偏差；我们称这种方案为超重整化。我们将其应用于椭圆拟合，以证明它确实超越了重投影误差最小化。我们认为这是目前最好的方法。
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 schemehyper-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.