Reconstructive and Discriminative Sparse Representation for Visual Object Categorization

Generic Visual Object Categorization (VOC) aims at predicting whether at least one or several objects of some given categories are present in an image. In fact, VOC is a fundamental problem in computer vision and pattern recognition, and has become an important research topic due to the wide range of possible applications such as video monitoring, video coding systems, security access control, automobile driving support as well as automatic image and video indexation and retrieval [4]. Until now, many VOC methods have been proposed and applied to the classification of numerous objects categories like, for example, cars, motorbikes, animals, people, furniture etc. Despite many efforts and much progress that have been made during the past years, it remains an open problem and is still considered as one of the most challenging topics in computer vision [2]. In particular, the image representation is a key problem since, from the image visual content presented in the form of image features, it has to be able to model effectively this content in a discriminative way to allow an efficient classification of the image. In this paper, we propose to adapt the principles of sparse representation theory to the problem of VOC. Thus, we have elaborated a reconstructive and discriminative sparse representation of images, which incorporates a discriminative term, such as Fisher discriminative measure or the output of a SVM classifier, into the standard sparse representation objective function in order to learn a reconstructive and discriminative dictionary. Let consider a set of N training signals {yi}i=1 belonging to M categories. Y = [y1,y2, ...,yN ] is a signal matrix with the corresponding sparse coefficients based on the dictionary D as X = [x1,x2, ...,xN ]. Moreover, we suppose that Ni signals are in the category Mi, for 1≤ i≤M. The objective function of the standard reconstructive sparse representation can be expressed as: