ML Anthology

Efficient Reduction of L-Infinity Geometry Problems

Hongdong Li
CVPR 2009 pp. 2695-2702
doi:10.1109/CVPR.2009.5206653 /cvpr/2009/li2009cvpr-efficient/

Abstract

This paper presents a new method for computing optimal L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> solutions for vision geometry problems, particularly for those problems of fixed-dimension and of large-scale. Our strategy for solving a large L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> problem is to reduce it to a finite set of smallest possible subproblems. By using the fact that many of the problems in question are pseudoconvex, we prove that such a reduction is possible. To actually solve these small subproblems efficiently, we propose a direct approach which makes no use of any convex optimizer (e.g. SOCP or LP), but is based on a simple local Newton method. We give both theoretic justification and experimental validation to the new method. Potentially, our new method can be made extremely fast.

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Cite

Text

Li. "Efficient Reduction of L-Infinity Geometry Problems." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2009. doi:10.1109/CVPR.2009.5206653

Markdown

[Li. "Efficient Reduction of L-Infinity Geometry Problems." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2009.](https://mlanthology.org/cvpr/2009/li2009cvpr-efficient/) doi:10.1109/CVPR.2009.5206653

BibTeX

@inproceedings{li2009cvpr-efficient,
  title     = {{Efficient Reduction of L-Infinity Geometry Problems}},
  author    = {Li, Hongdong},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2009},
  pages     = {2695-2702},
  doi       = {10.1109/CVPR.2009.5206653},
  url       = {https://mlanthology.org/cvpr/2009/li2009cvpr-efficient/}
}