Dimensionality Reduction and Sparse Representations in Computer Vision

The proliferation of camera equipped devices, such as netbooks, smartphones and game stations, has led to a significant increase in the production of visu al content. This visual information could be used f or understanding the environment and offering a natura l interface between the users and their surrounding s. However, the massive amounts of data and the high c omputational cost associated with them, encumbers the transfer of sophisticated vision algorithms to real life systems, especially ones that exhibit res ource limitations such as restrictions in available memor y, processing power and bandwidth. One approach for tackling these issues is to generate compact and de scriptive representations of image data by exploiti ng inherent redundancies. We propose the investigation of dimensionality reduction and sparse representations in order to accomplish this task. In dimensionality reduction, the aim is to reduce t h dimensions of the space where image data reside in order to allow resource constrained systems to hand le them and, ideally, provide a more insightful description. This goal is achieved by exploiting th e inherent redundancies that many classes of images , such as faces under different illumination conditio ns and objects from different viewpoints, exhibit. We explore the description of natural images by low di mensional non-linear models called image manifolds and investigate the performance of computer vision tasks such as recognition and classification using these low dimensional models. In addition to dimens io ality reduction, we study a novel approach in representing images as a sparse linear combination of dictionary examples. We investigate how sparse image representations can be used for a variety of asks including low level image modeling and higher level semantic information extraction. Using tools from dimensionality reduction and spars e representation, we propose the application of the se methods in three hierarchical image layers, namely low-level features, mid-level structures and high-l evel attributes. Low level features are image descriptor s hat can be extracted directly from the raw image pixels and include pixel intensities, histograms, a nd gradients. In the first part of this work, we ex plore how various techniques in dimensionality reduction, ranging from traditional image compression to the recently proposed Random Projections method, affect the performance of computer vision algorithms such as face detection and face recognition. In add ition, we discuss a method that is able to increase the spatial resolution of a single image, without using any training examples, according to the sparse representations framework. In the second part, we e xplore mid-level structures, including image manifolds and sparse models, produced by abstractin g information from low-level features and offer compact modeling of high dimensional data. We propo se novel techniques for generating more descriptive image representations and investigate t heir application in face recognition and object tra cking. In the third part of this work, we propose the inve stigation of a novel framework for representing the semantic contents of images. This framework employs high level semantic attributes that aim to bridge the gap between the visual information of an image nd its textual description by utilizing low level features and mid level structures. This innovative paradigm offers revolutionary possibilities includi ng recognizing the category of an object from purely t extual information without providing any explicit visual example.