Sparse representation based classification (SRC) has gained great success in image recognition. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which may help improve the separability and margin between nearby data points, we propose Euler SRC for image classification, which is essentially the SRC with Euler sparse representation. To be specific, it first maps the images into the complex space by Euler representation, which has a negligible effect for outliers and illumination, and then performs complex SRC with Euler representation. The major advantage of our method is that Euler representation is explicit with no increase of the image space dimensionality, thereby enabling this technique to be easily deployed in real applications. To solve Euler SRC, we present an efficient algorithm, which is fast and has good convergence. Extensive experimental results illustrate that Euler SRC outperforms traditional SRC and achieves better performance for image classification.
A variety of real-world tasks involve the classification of images into pre-determined categories. Designing image classification algorithms that exhibit robustness to acquisition noise and image distortions, particularly when the available training data are insufficient to learn accurate models, is a significant challenge. This dissertation explores the development of discriminative models for robust image classification that exploit underlying signal structure, via probabilistic graphical models and sparse signal representations. Probabilistic graphical models are widely used in many applications to approximate high-dimensional data in a reduced complexity set-up. Learning graphical structures to approximate probability distributions is an area of active research. Recent work has focused on learning graphs in a discriminative manner with the goal of minimizing classification error. In the first part of the dissertation, we develop a discriminative learning framework that exploits the complementary yet correlated information offered by multiple representations (or projections) of a given signal/image. Specifically, we propose a discriminative tree-based scheme for feature fusion by explicitly learning the conditional correlations among such multiple projections in an iterative manner. Experiments reveal the robustness of the resulting graphical model classifier to training insufficiency.