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In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices. [ABSTRACT FROM AUTHOR]

Object recognition algorithms often focus on determining the class of a detected object in a scene. Two significant phases are usually involved in object recognition. The first phase is the object representation phase, in which the most suitable features that provide the best discriminative power under constraints such as lighting, resolution, scale, and view variations are chosen to describe the objects. The second phase is to use this representation space to develop models for each object class using discriminative classifiers. In this paper, we focus on composite objects, i.e., objects with two or more simpler classes that are interconnected in a complicated manner. One classic example of such a scenario is a bicyclist. A bicyclist consists of a bicycle and a human who rides the bicycle. When we are faced with the task of classifying bicyclists and pedestrians, it is counterintuitive and often hard to come up with a discriminative classifier to distinguish the two classes. We explore global image analysis based on bag of visual words to compare the results with local image analysis, in which we attempt to distinguish the individual parts of the composite object. We also propose a unified naive Bayes framework and a combined histogram feature method for combining the individual classifiers for enhanced performance. [ABSTRACT FROM PUBLISHER]