Издательство Springer, 2015, -108 pp.With the evolution of modern cameras, it is possible to acquire images with extremely high resolutions from diverse perspectives. However, due to some physical constraints in the practical world, the quality of high-dimensional visual information is relatively low in some cases. Such low-quality properties include redundancy, incompleteness, and noise in both data and labels. To better process and understand the high-dimensional and low-quality data, in this thesis, we propose a computational framework by exploiting the inherent structures among visual data. The contributions of this thesis are four-fold: This dissertation revisits the typical compressive sensing framework by introducing the log-sum function as the basic term for sparse computation. We have unified the tasks of low rank matrix recovery and sparse signal optimization into a general framework of low rank structure learning (LRSL). In the LRSL problem, we have revealed that log-sum term is the limitation of general nonconvex p norm when p approximates to 0+ and then proposed the log-sum heuristic recovery (LHR) model. Theoretically, we have proven that LHR could converge to a stationary point after successive iterations. Practical applications on image processing, data analysis, and 3D reconstruction prove that the proposed method could exactly recover the intrinsic structure of signal from redundant and noisy observations. Two computational models are proposed on a graph structure for visual information reduction and completion. Inspired by the fundamental observation in field theory that information uniformly propagates on a graph, we respectively propose a random walk-based method for feature extraction and a Graph Laplace method for damaged image completion. These two models are applied to biometric recognition. A discriminative parsing algorithm is proposed by utilizing the discriminative structure of visual information and their labels. In the work, a psychology inspired Bayesian model is introduced to automatically identify the common characters and the differences among different images from multiple classes. Moreover, an image encoding algorithm is proposed in the framework which is more suitable for practical applications on image understanding. Thanks to the proposed discriminative method, the classification accuracy could be greatly improved on SAR images. To handle the uncertainty in visual information understanding, this work proposes a robust information theoretic embedding method in the framework of information theory. By maximizing the mutual information of labels and features in the latent space, we propose a manifold learning to encourage data discrimination understanding. In the bag-of-feature framework, the proposed information theoretic model improves the quality of the generated codewords and outperforms other image coding methods on the benchmark computer vision dataset as well as our own airborne images.Introduction Sparse Structure for Visual Information Sensing: Theory and Algorithms Sparse Structure for Visual Signal Sensing: Application in 3D Reconstruction Graph Structure for Visual Signal Sensing Discriminative Structure for Visual Signal Understanding Information-Theoretic Structure for Visual Signal Understanding Conclusion
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