Particle filtering on large dimensional state spaces and applications in computer vision

Tracking of spatio-temporal events is a fundamental problem in computer vision and signal processing in general. For example, keeping track of motion activities from video sequences for abnormality detection or spotting neuronal activity patterns inside the brain from fMRI data. To that end, our research has two main aspects with equal emphasis - first, development of efficient Bayesian filtering frameworks for solving real-world tracking problems and second, understanding the temporal evolution dynamics of physical systems/phenomenon and build statistical models for them. These models facilitate prior information to the trackers as well as lead to intelligent signal processing for computer vision and image understanding.;The first part of the dissertation deals with the key signal processing aspects of tracking and the challenges involved. In simple terms, tracking basically is the problem of estimating the hidden state of a system from noisy observed data(from sensors). As frequently encountered in real-life, due to the non-linear and non-Gaussian nature of the state spaces involved, Particle Filters (PF) give an approximate Bayesian inference under such problem setup. However, quite often we are faced with large dimensional state spaces together with multimodal observation likelihood due to occlusion and clutter. This makes the existing particle filters very inefficient for practical purposes. In order to tackle these issues, we have developed and implemented efficient particle filters on large dimensional state spaces with applications to various visual tracking problems in computer vision.;In the second part of the dissertation, we develop dynamical models for motion activities inspired by human visual cognitive ability of characterizing temporal evolution pattern of shapes. We take a landmark shape based approach for the representation and tracking of motion activities. Basically, we have developed statistical models for the shape change of a configuration of "landmark" points (key points of interest) over time and to use these models for automatic landmark extraction and tracking, filtering and change detection from video sequences. In this regard, we demonstrate superior performance of our Non-Stationary Shape Activity(NSSA) model in comparison to other existing works. Also, owing to the large dimensional state space of this problem, we have utilized efficient particle filters(PF) for motion activity tracking. In the third part of the dissertation, we develop a visual tracking algorithm that is able to track in presence of illumination variations in the scene. In order to do that we build and learn a dynamical model for 2D illumination patterns based on Legendre basis functions. Under our problem formulation, we pose the visual tracking task as a large dimensional tracking problem in a joint motion-illumination space and thus use an efficient PF algorithm called PF-MT(PF with Mode Tracker) for tracking. In addition, we also demonstrate the use of change/abnormality detection framework for tracking across drastic illumination changes. Experiments with real-life video sequences demonstrate the usefulness of the algorithm while many other existing approaches fail. The last part of the dissertation explores the upcoming field of compressive sensing and looks into the possibilities of leveraging from particle filtering ideas to do better sequential reconstruction (i.e. tracking) of sparse signals from a small number of random linear measurements. Our preliminary results show several promising aspects to such an approach and it is an interesting direction of future research with many potential computer vision applications.