Over the last few years, commodity Graphics Processing Units (GPUs) have evolved from fixed graphics pipeline processors into more flexible and powerful data-parallel processors. These stream processors are capable of sustaining computation rates of greater than ten times that of a single-core CPU. GPUs are inexpensive and are becoming ubiquitous in a wide variety of computer architectures including desktop and laptop computers, PDAs and cell phones. This research works investigates possible ways to use modern GPUs for real-time computer vision and pattern classification tasks. Special attention is paid to algorithms, where the power of the CPU is a limiting factor. This is in particular the case for real-time tracking algorithms on video streams, where many candidate regions must be evaluated at once to allow stable tracking of features. They impose a high computational burdon on sequential processing units such as the CPU. The proposed implementation presented in this thesis is considering standard PC platforms rather than expensive special dedicated hardware to allow a broad variety of users to benefit from powerful computer vision applications. In particular, this thesis includes following topics: 1. First, we present a framework for computer vision on the GPU, which is used as a foundation for the implementation of computer vision methods. 2. We continue with the discussion of GPU-based implementation of Kernel Methods, including Support Vector Machines and Kernel PCA. 3. Finally, we propose GPU-accelerated implementations of two tracking algorithms. The first algorithm uses geometric templates in a gradient vector field. The second algorithm is a color-based approach in a particle filter framework. Both are able to track objects in a video stream. This thesis concludes with a final discussion of the presented methods and will propose directions for further research work. It will also briefly present the features of the next generation of GPUs.

Recent advances in robust subspace estimation have made dimensionality reduction and noise and outlier suppression an area of interest for research, along with continuous improvements in computer vision applications. Due to the nature of image and video signals that need a high dimensional representation, often storage, processing, transmission, and analysis of such signals is a difficult task. It is therefore desirable to obtain a low-dimensional representation for such signals, and at the same time correct for corruptions, errors, and outliers, so that the signals could be readily used for later processing. Major recent advances in low-rank modelling in this context were initiated by the work of Cand`es et al. [17] where the authors provided a solution for the long-standing problem of decomposing a matrix into low-rank and sparse components in a Robust Principal Component Analysis (RPCA) framework. However, for computer vision applications RPCA is often too complex, and/or may not yield desirable results. The low-rank component obtained by the RPCA has usually an unnecessarily high rank, while in certain tasks lower dimensional representations are required. The RPCA has the ability to robustly estimate noise and outliers and separate them from the low-rank component, by a sparse part. But, it has no mechanism of providing an insight into the structure of the sparse solution, nor a way to further decompose the sparse part into a random noise and a structured sparse component that would be advantageous in many computer vision tasks. As videos signals are usually captured by a camera that is moving, obtaining a low-rank component by RPCA becomes impossible. In this thesis, novel Approximated RPCA algorithms are presented, targeting different shortcomings of the RPCA. The Approximated RPCA was analysed to identify the most time consuming RPCA solutions, and replace them with simpler yet tractable alternative solutions. The proposed method is able to obtain the exact desired rank for the low-rank component while estimating a global transformation to describe camera-induced motion. Furthermore, it is able to decompose the sparse part into a foreground sparse component, and a random noise part that contains no useful information for computer vision processing. The foreground sparse component is obtained by several novel structured sparsity-inducing norms, that better encapsulate the needed pixel structure in visual signals. Moreover, algorithms for reducing complexity of low-rank estimation have been proposed that achieve significant complexity reduction without sacrificing the visual representation of video and image information. The proposed algorithms are applied to several fundamental computer vision tasks, namely, high efficiency video coding, batch image alignment, inpainting, and recovery, video stabilisation, background modelling and foreground segmentation, robust subspace clustering and motion estimation, face recognition, and ultra high definition image and video super-resolution. The algorithms proposed in this thesis including batch image alignment and recovery, background modelling and foreground segmentation, robust subspace clustering and motion segmentation, and ultra high definition image and video super-resolution achieve either state-of-the-art or comparable results to existing methods.