Subspace Matching: Unique Solution to Point Matching with Geometric Constraints
Abstract
Finding correspondences between feature points is one of the most relevant problems in the whole set of visual tasks. In this paper we address the problem of matching a feature vector (or a matrix) to a given subspace. Given any vector base of such a subspace, we observe a linear combination of its elements with all entries swapped by an unknown permutation. We prove that such a computationally hard integer problem is uniquely solved in a convex set resulting from relaxing the original problem. Also, if noise is present, based on this result, we provide a robust estimate recurring to a linear programming-based algorithm. We use structure-from-motion and object recognition as motivating examples.
Cite
Text
Marques et al. "Subspace Matching: Unique Solution to Point Matching with Geometric Constraints." IEEE/CVF International Conference on Computer Vision, 2009. doi:10.1109/ICCV.2009.5459318Markdown
[Marques et al. "Subspace Matching: Unique Solution to Point Matching with Geometric Constraints." IEEE/CVF International Conference on Computer Vision, 2009.](https://mlanthology.org/iccv/2009/marques2009iccv-subspace/) doi:10.1109/ICCV.2009.5459318BibTeX
@inproceedings{marques2009iccv-subspace,
title = {{Subspace Matching: Unique Solution to Point Matching with Geometric Constraints}},
author = {Marques, Manuel and Stosic, Marko and Costeira, João Paulo},
booktitle = {IEEE/CVF International Conference on Computer Vision},
year = {2009},
pages = {1288-1294},
doi = {10.1109/ICCV.2009.5459318},
url = {https://mlanthology.org/iccv/2009/marques2009iccv-subspace/}
}