Randomized Hybrid Linear Modeling by Local Best-Fit Flats
Abstract
The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in RD. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global ℓ1 error measure. The size of the local neighborhoods is determined automatically by the Jones' β2 numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.
Cite
Text
Zhang et al. "Randomized Hybrid Linear Modeling by Local Best-Fit Flats." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2010. doi:10.1109/CVPR.2010.5539866Markdown
[Zhang et al. "Randomized Hybrid Linear Modeling by Local Best-Fit Flats." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2010.](https://mlanthology.org/cvpr/2010/zhang2010cvpr-randomized/) doi:10.1109/CVPR.2010.5539866BibTeX
@inproceedings{zhang2010cvpr-randomized,
title = {{Randomized Hybrid Linear Modeling by Local Best-Fit Flats}},
author = {Zhang, Teng and Szlam, Arthur and Wang, Yi and Lerman, Gilad},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2010},
pages = {1927-1934},
doi = {10.1109/CVPR.2010.5539866},
url = {https://mlanthology.org/cvpr/2010/zhang2010cvpr-randomized/}
}