Nearness to Local Subspace Algorithm for Subspace and Motion Segmentation

There is a growing interest in computer science, engineering, and mathematics for modeling signals in terms of union of subspaces and manifolds. Subspace segmentation and clustering of high dimensional data drawn from a union of subspaces are especially important with many practical applications in computer vision, image and signal processing, communications, and information theory. This paper presents a clustering algorithm for high dimensional data that comes from a union of lower dimensional subspaces of equal and known dimensions. Such cases occur in many data clustering problems, such as motion segmentation and face recognition. The algorithm is reliable in the presence of noise, and applied to the Hopkins 155 Dataset, it generates the best results to date for motion segmentation. The two motion, three motion, and overall segmentation rates for the video sequences are 99.43%, 98.69%, and 99.24%, respectively

A Fusion Framework for Camouflaged Moving Foreground Detection in the Wavelet Domain

Detecting camouflaged moving foreground objects has been known to be difficult due to the similarity between the foreground objects and the background. Conventional methods cannot distinguish the foreground from background due to the small differences between them and thus suffer from under-detection of the camouflaged foreground objects. In this paper, we present a fusion framework to address this problem in the wavelet domain. We first show that the small differences in the image domain can be highlighted in certain wavelet bands. Then the likelihood of each wavelet coefficient being foreground is estimated by formulating foreground and background models for each wavelet band. The proposed framework effectively aggregates the likelihoods from different wavelet bands based on the characteristics of the wavelet transform. Experimental results demonstrated that the proposed method significantly outperformed existing methods in detecting camouflaged foreground objects. Specifically, the average F-measure for the proposed algorithm was 0.87, compared to 0.71 to 0.8 for the other state-of-the-art methods.Comment: 13 pages, accepted by IEEE TI

Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.Comment: 17 pages, 7 figures, submitted to IEEE Transactions on Signal Processin