ML Anthology

Discrete Minimum Ratio Curves and Surfaces

Fred Nicolls, Philip H. S. Torr
CVPR 2010 pp. 2133-2140
doi:10.1109/CVPR.2010.5539892 /cvpr/2010/nicolls2010cvpr-discrete/

Abstract

Graph cuts have proven useful for image segmentation and for volumetric reconstruction in multiple view stereo. However, solutions are biased: the cost function tends to favour either a short boundary (in 2D) or a boundary with a small area (in 3D). This bias can be avoided by instead minimising the cut ratio, which normalises the cost by a measure of the boundary size. This paper uses ideas from discrete differential geometry to develop a linear programming formulation for finding a minimum ratio cut in arbitrary dimension, which allows constraints on the solution to be specified in a natural manner, and which admits an efficient and globally optimal solution. Results are shown for 2D segmentation and for 3D volumetric reconstruction.

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Cite

Text

Nicolls and Torr. "Discrete Minimum Ratio Curves and Surfaces." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2010. doi:10.1109/CVPR.2010.5539892

Markdown

[Nicolls and Torr. "Discrete Minimum Ratio Curves and Surfaces." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2010.](https://mlanthology.org/cvpr/2010/nicolls2010cvpr-discrete/) doi:10.1109/CVPR.2010.5539892

BibTeX

@inproceedings{nicolls2010cvpr-discrete,
  title     = {{Discrete Minimum Ratio Curves and Surfaces}},
  author    = {Nicolls, Fred and Torr, Philip H. S.},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2010},
  pages     = {2133-2140},
  doi       = {10.1109/CVPR.2010.5539892},
  url       = {https://mlanthology.org/cvpr/2010/nicolls2010cvpr-discrete/}
}