ML Anthology

Efficient Point-to-Subspace Query in ℓ1 with Application to Robust Face Recognition

Ju Sun, Yuqian Zhang, John Wright
ECCV 2012 pp. 416-429
doi:10.1007/978-3-642-33765-9_30 /eccv/2012/sun2012eccv-efficient/

Abstract

Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in ℓ^1 distance. We show in theory this problem can be solved with a simple two-stage algorithm: (1) random Cauchy projection of query and subspaces into low-dimensional spaces followed by efficient distance evaluation (ℓ^1 regression); (2) getting back to the high-dimensional space with very few candidates and performing exhaustive search. We present preliminary experiments on robust face recognition to corroborate our theory.

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Cite

Text

Sun et al. "Efficient Point-to-Subspace Query in ℓ1 with Application to Robust Face Recognition." European Conference on Computer Vision, 2012. doi:10.1007/978-3-642-33765-9_30

Markdown

[Sun et al. "Efficient Point-to-Subspace Query in ℓ1 with Application to Robust Face Recognition." European Conference on Computer Vision, 2012.](https://mlanthology.org/eccv/2012/sun2012eccv-efficient/) doi:10.1007/978-3-642-33765-9_30

BibTeX

@inproceedings{sun2012eccv-efficient,
  title     = {{Efficient Point-to-Subspace Query in ℓ1 with Application to Robust Face Recognition}},
  author    = {Sun, Ju and Zhang, Yuqian and Wright, John},
  booktitle = {European Conference on Computer Vision},
  year      = {2012},
  pages     = {416-429},
  doi       = {10.1007/978-3-642-33765-9_30},
  url       = {https://mlanthology.org/eccv/2012/sun2012eccv-efficient/}
}