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In recent years, the theory of sparse representation has emerged as a powerful tool for efficient processing of data in non-traditional ways. This is mainly due to the fact that most signals and images of interest tend to be sparse or compressible in some dictionary. In other words, they can be well approximated by a linear combination of a few elements (also known as atoms) of a dictionary. This dictionary can either be an analytic dictionary composed of wavelets or Fourier basis or it can be directly trained from data. It has been observed that dictionaries learned directly from data provide better representation and hence can improve the performance of many practical applications such as restoration and classification.

In this dissertation, we study dictionary learning and recognition under supervised, unsupervised, and semi-supervised settings. In the supervised case, we propose an approach to recognize humans in unconstrained videos, where the main challenge is exploiting the identity information in multiple frames and the accompanying dynamic signature. These identity cues include face, body, and motion. Our approach is based on video-dictionaries for face and body. We design video-dictionaries to implicitly encode temporal, pose, and illumination information. Next, we propose a novel multivariate sparse representation method that jointly represents all the video data by a sparse linear combination of training data. To increase the ability of our algorithm to learn nonlinearities, we apply kernel methods to learn the dictionaries. Next, we address the problem of matching faces across changes in pose in unconstrained videos. Our approach consists of two methods based on 3D rotation and sparse representation that compensate for changes in pose. We demonstrate the superior performance of our approach over several state-of-the-art algorithms through extensive experiments on unconstrained video datasets.

In the unsupervised case, we present an approach that simultaneously clusters images and learns dictionaries from the clusters. The method learns dictionaries in the Radon transform domain. The main feature of the proposed approach is that it provides in-plane rotation and scale invariant clustering, which is useful in many applications such as Content Based Image Retrieval (CBIR). We demonstrate through experiments that the proposed rotation and scale invariant clustering provides not only good retrieval performances but also substantial improvements and robustness compared to traditional Gabor-based and several state-of-the-art shape-based methods.

We then extend the dictionary learning problem to a generalized semi-supervised formulation, where each training sample is provided with a set of possible labels and only one label among them is the true one. Such applications can be found in image and video collections where one often has only partially labeled data. For instance, given an image with multiple faces and a caption specifying the names, we can be sure that each of the faces belong to one of the names specified, while the exact identity of each face is not known. Labeling involves significant amount of human effort and is expensive. This has motivated researchers to develop learning algorithms from partially labeled training data. In this work, we develop dictionary learning algorithms that utilize such partially labeled data. The proposed method aims to solve the problem of ambiguously labeled multiclass-classification using an iterative algorithm. The dictionaries are updated using either soft (EM-based) or hard decision rules. Extensive evaluations on existing datasets demonstrate that the proposed method performs significantly better than state-of-the-art approaches for learning from ambiguously labeled data.

As sparsity plays a major role in our research, we further present a sparse representation-based approach to find the salient views of 3D objects. The salient views are categorized into two groups. The first are boundary representative views that have several visible sides and object surfaces that may be attractive to humans. The second are side representative views that best represent side views of the approximating convex shape. The side representative views are class-specific views and possess the most representative power compared to other within-class views. Using the concept of characteristic view class, we first present a sparse representation-based approach for estimating the boundary representative views. With the estimated boundaries, we determine the side representative views based on a minimum reconstruction error criterion. Furthermore, to evaluate our method, we introduce the notion of geometric dictionaries built from salient views for applications in 3D object recognition, retrieval and sparse-to-full reconstruction. By a series of experiments on four publicly available 3D object datasets, we demonstrate the effectiveness of our approach over state-of-the-art algorithms and baseline methods.