Affine Subspace Representation for Feature Description

This paper proposes a novel Affine Subspace Representation (ASR) descriptor to deal with affine distortions induced by viewpoint changes. Unlike the traditional local descriptors such as SIFT, ASR inherently encodes local information of multi-view patches, making it robust to affine distortions while maintaining a high discriminative ability. To this end, PCA is used to represent affine-warped patches as PCA-patch vectors for its compactness and efficiency. Then according to the subspace assumption, which implies that the PCA-patch vectors of various affine-warped patches of the same keypoint can be represented by a low-dimensional linear subspace, the ASR descriptor is obtained by using a simple subspace-to-point mapping. Such a linear subspace representation could accurately capture the underlying information of a keypoint (local structure) under multiple views without sacrificing its distinctiveness. To accelerate the computation of ASR descriptor, a fast approximate algorithm is proposed by moving the most computational part (ie, warp patch under various affine transformations) to an offline training stage. Experimental results show that ASR is not only better than the state-of-the-art descriptors under various image transformations, but also performs well without a dedicated affine invariant detector when dealing with viewpoint changes.Comment: To Appear in the 2014 European Conference on Computer Visio

Subspace procrustes analysis

Postprint (author's final draft

Rank-based optimal tests of the adequacy of an elliptic VARMA model

We are deriving optimal rank-based tests for the adequacy of a vector autoregressive-moving average (VARMA) model with elliptically contoured innovation density. These tests are based on the ranks of pseudo-Mahalanobis distances and on normed residuals computed from Tyler's [Ann. Statist. 15 (1987) 234-251] scatter matrix; they generalize the univariate signed rank procedures proposed by Hallin and Puri [J. Multivariate Anal. 39 (1991) 1-29]. Two types of optimality properties are considered, both in the local and asymptotic sense, a la Le Cam: (a) (fixed-score procedures) local asymptotic minimaxity at selected radial densities, and (b) (estimated-score procedures) local asymptotic minimaxity uniform over a class F of radial densities. Contrary to their classical counterparts, based on cross-covariance matrices, these tests remain valid under arbitrary elliptically symmetric innovation densities, including those with infinite variance and heavy-tails. We show that the AREs of our fixed-score procedures, with respect to traditional (Gaussian) methods, are the same as for the tests of randomness proposed in Hallin and Paindaveine [Bernoulli 8 (2002b) 787-815]. The multivariate serial extensions of the classical Chernoff-Savage and Hodges-Lehmann results obtained there thus also hold here; in particular, the van der Waerden versions of our tests are uniformly more powerful than those based on cross-covariances. As for our estimated-score procedures, they are fully adaptive, hence, uniformly optimal over the class of innovation densities satisfying the required technical assumptions.Comment: Published at http://dx.doi.org/10.1214/009053604000000724 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org