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

Sun, Ju; Zhang, Yuqian; Wright, John N.

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 ℓ1 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 (ℓ1 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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Also Published In

Title
Computer Vision -- ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012: Proceedings, Part IV
DOI
https://doi.org/10.1007/978-3-642-33765-9_30

More About This Work

Academic Units
Electrical Engineering
Publisher
Springer
Series
Lecture Notes in Computer Science, 7575
Published Here
October 16, 2012
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