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. © 2012 Springer-Verlag.
CITATION STYLE
Sun, J., Zhang, Y., & Wright, J. (2012). Efficient point-to-subspace query in ℓ 1 with application to robust face recognition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7575 LNCS, pp. 416–429). https://doi.org/10.1007/978-3-642-33765-9_30
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