Sparse Methods in Image Understanding and Computer Vision

Image understanding has been playing an increasingly crucial role in vision applications. Sparse models form an important component in image understanding, since the statistics of natural images reveal the presence of sparse structure. By representing data as a sparse linear combination of atoms from a “dictionary” matrix, these methods lead to parsimonious models, in addition to being efficient for large scale learning. This dissertation focuses on understanding different aspects of sparse learning, and enhancing sparse methods by incorporating tools from machine learning. With the growing need to adapt models for large scale data, it is important to design dictionaries that can generalize to the entire probability space of data using a finite training set. By exploring the relation between dictionary learning and one-dimensional subspace clustering, a multilevel dictionary learning algorithm is developed, and it is shown to outperform conventional sparse models in compressed recovery, and image denoising. Theoretical aspects of learning such as algorithmic stability and generalization are considered, and ensemble methods are incorporated for effective large scale learning. In addition to building strategies for efficiently implementing onedimensional subspace clustering, a discriminative clustering approach is designed to estimate the unknown mixing process in blind source separation. By exploiting the non-linear relation between the image descriptors, and allowing the use of multiple features, sparse methods can be made more effective in recognition problems. The idea of multiple kernel sparse representations is developed, and algorithms for learning dictionaries in the feature space are presented. Using object recognition experiments on standard datasets it is shown that the proposed approaches outperform other sparse coding-based recognition frameworks. Furthermore, a segmentation technique based on multiple kernel sparse representations is developed, and successfully applied for automated brain tumor identification. Using i sparse codes to define the relation between data samples can lead to a more robust graph embedding for unsupervised clustering. By performing discriminative embedding using sparse coding-based graphs, an algorithm for measuring the glomerular number in kidney MRI images is developed. Finally, approaches to build dictionaries for local sparse coding of image descriptors are presented, and applied to object recognition and image retrieval.