Continuous Ratio Optimization via Convex Relaxation with Applications to Multiview 3D Reconstruction
Abstract
We introduce a convex relaxation framework to optimally minimize continuous surface ratios. The key idea is to minimize the continuous surface ratio by solving a sequence of convex optimization problems. We show that such minimal ratios are superior to traditionally used minimal surface formulations in that they do not suffer from a shrinking bias and no longer require the choice of a regularity parameter. The absence of a shrinking bias in the minimal ratio model is proven analytically. Furthermore we demonstrate that continuous ratio optimization can be applied to derive a new algorithm for reconstructing three-dimensional silhouette-consistent objects from multiple views. Experimental results confirm that our approach allows to accurately reconstruct deep concavities even without the specification of tuning parameters.
Cite
Text
Kolev and Cremers. "Continuous Ratio Optimization via Convex Relaxation with Applications to Multiview 3D Reconstruction." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2009. doi:10.1109/CVPR.2009.5206608Markdown
[Kolev and Cremers. "Continuous Ratio Optimization via Convex Relaxation with Applications to Multiview 3D Reconstruction." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2009.](https://mlanthology.org/cvpr/2009/kolev2009cvpr-continuous/) doi:10.1109/CVPR.2009.5206608BibTeX
@inproceedings{kolev2009cvpr-continuous,
title = {{Continuous Ratio Optimization via Convex Relaxation with Applications to Multiview 3D Reconstruction}},
author = {Kolev, Kalin and Cremers, Daniel},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2009},
pages = {1858-1864},
doi = {10.1109/CVPR.2009.5206608},
url = {https://mlanthology.org/cvpr/2009/kolev2009cvpr-continuous/}
}