arXiv subjects

Rene Vidal

Publications and source records attributed to Rene Vidal.

57 records · Page 4Linked to original sources

arXiv2012

Dynamic Template Tracking and Recognition

In this paper we address the problem of tracking non-rigid objects whose local appearance and motion changes as a function of time. This class of objects includes dynamic textures such as steam, fire, smoke, water, etc., as well as articulated objects such as humans performing various actions. We model the temporal evolution of the object's appearance/motion using a Linear Dynamical System (LDS). We learn such models from sample videos and use them as dynamic templates for tracking objects in novel videos. We pose the problem of tracking a dynamic non-rigid object in the current frame as a maximum a-posteriori estimate of the location of the object and the latent state of the dynamical system, given the current image features and the best estimate of the state in the previous frame. The advantage of our approach is that we can specify a-priori the type of texture to be tracked in the scene by using previously trained models for the dynamics of these textures. Our framework naturally generalizes common tracking methods such as SSD and kernel-based tracking from static templates to dynamic templates. We test our algorithm on synthetic as well as real examples of dynamic textures and show that our simple dynamics-based trackers perform at par if not better than the state-of-the-art. Since our approach is general and applicable to any image feature, we also apply it to the problem of human action tracking and build action-specific optical flow trackers that perform better than the state-of-the-art when tracking a human performing a particular action. Finally, since our approach is generative, we can use a-priori trained trackers for different texture or action classes to simultaneously track and recognize the texture or action in the video.

cs.CV↗

arXiv2012

Block-Sparse Recovery via Convex Optimization

Given a dictionary that consists of multiple blocks and a signal that lives in the range space of only a few blocks, we study the problem of finding a block-sparse representation of the signal, i.e., a representation that uses the minimum number of blocks. Motivated by signal/image processing and computer vision applications, such as face recognition, we consider the block-sparse recovery problem in the case where the number of atoms in each block is arbitrary, possibly much larger than the dimension of the underlying subspace. To find a block-sparse representation of a signal, we propose two classes of non-convex optimization programs, which aim to minimize the number of nonzero coefficient blocks and the number of nonzero reconstructed vectors from the blocks, respectively. Since both classes of problems are NP-hard, we propose convex relaxations and derive conditions under which each class of the convex programs is equivalent to the original non-convex formulation. Our conditions depend on the notions of mutual and cumulative subspace coherence of a dictionary, which are natural generalizations of existing notions of mutual and cumulative coherence. We evaluate the performance of the proposed convex programs through simulations as well as real experiments on face recognition. We show that treating the face recognition problem as a block-sparse recovery problem improves the state-of-the-art results by 10% with only 25% of the training data.

math.OC↗

arXiv2012

Generalized Principal Component Analysis (GPCA)

This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high- dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as K-subspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.

cs.CV↗