A Deep-structured Conditional Random Field Model for Object Silhouette Tracking

In this work, we introduce a deep-structured conditional random field (DS-CRF) model for the purpose of state-based object silhouette tracking. The proposed DS-CRF model consists of a series of state layers, where each state layer spatially characterizes the object silhouette at a particular point in time. The interactions between adjacent state layers are established by inter-layer connectivity dynamically determined based on inter-frame optical flow. By incorporate both spatial and temporal context in a dynamic fashion within such a deep-structured probabilistic graphical model, the proposed DS-CRF model allows us to develop a framework that can accurately and efficiently track object silhouettes that can change greatly over time, as well as under different situations such as occlusion and multiple targets within the scene. Experiment results using video surveillance datasets containing different scenarios such as occlusion and multiple targets showed that the proposed DS-CRF approach provides strong object silhouette tracking performance when compared to baseline methods such as mean-shift tracking, as well as state-of-the-art methods such as context tracking and boosted particle filtering.Comment: 17 page

Inference via low-dimensional couplings

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map---e.g., representing and evaluating it---grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization---to the non-Gaussian case---of the square-root Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure

A probabilistic reasoning and learning system based on Bayesian belief networks

SIGLEAvailable from British Library Document Supply Centre- DSC:DX173015 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Randomly-connected Non-Local Conditional Random Fields

Structural data modeling is an important field of research. Structural data are the combination of latent variables being related to each other. The incorporation of these relations in modeling and taking advantage of those to have a robust estimation is an open field of research. There are several approaches that involve these relations such as Markov chain models or random field frameworks. Random fields specify the relations among random variables in the context of probability distributions. Markov random fields are generative models used to represent the prior distribution among random variables. On the other hand, conditional random fields (CRFs) are known as discriminative models computing the posterior probability of random variables given observations directly. CRFs are one of the most powerful frameworks in image modeling. However practical CRFs typically have edges only between nearby nodes. Utilizing more interactions and expressive relations among nodes make these methods impractical for large-scale applications, due to the high computational complexity. Nevertheless, studies have demonstrated that obtaining long-range interactions in the modeling improves the modeling accuracy and addresses the short-boundary bias problem to some extent. Recent work has shown that fully connected CRFs can be tractable by defining specific potential functions. Although the proposed frameworks present algorithms to efficiently manage the fully connected interactions/relatively dense random fields, there exists the unanswered question that fully connected interactions are usually useful in modeling. To the best of our knowledge, no research has been conducted to answer this question and the focus of research was to introduce a tractable approach to utilize all connectivity interactions. This research aims to analyze this question and attempts to provide an answer. It demonstrates that how long-range of connections might be useful. Motivated by the answer of this question, a novel framework to tackle the computational complexity of a fully connected random fields without requiring specific potential functions is proposed. Inspired by random graph theory and sampling methods, this thesis introduces a new clique structure called stochastic cliques. The stochastic cliques specify the range of effective connections dynamically which converts a conditional random field (CRF) to a randomly-connected CRF. The randomly-connected CRF (RCRF) is a marriage between random graphs and random fields, benefiting from the advantages of fully connected graphs while maintaining computational tractability. To address the limitations of RCRF, the proposed stochastic clique structure is utilized in a deep structural approach (deep structure randomly-connected conditional random field (DRCRF)) where various range of connectivities are obtained in a hierarchical framework to maintain the computational complexity while utilizing long-range interactions. In this thesis the concept of randomly-connected non-local conditional random fields is explored to address the smoothness issues of local random fields. To demonstrate the effectiveness of the proposed approaches, they are compared with state-of-the-art methods on interactive image segmentation problem. A comprehensive analysis is done via different datasets with noiseless and noisy situations. The results shows that the proposed method can compete with state-of-the-art algorithms on the interactive image segmentation problem

Bayesian clustering in decomposable graphs

In this paper we propose a class of prior distributions on decomposable graphs, allowing for improved modeling flexibility. While existing methods solely penalize the number of edges, the proposed work empowers practitioners to control clustering, level of separation, and other features of the graph. Emphasis is placed on a particular prior distribution which derives its motivation from the class of product partition models; the properties of this prior relative to existing priors is examined through theory and simulation. We then demonstrate the use of graphical models in the field of agriculture, showing how the proposed prior distribution alleviates the inflexibility of previous approaches in properly modeling the interactions between the yield of different crop varieties.Comment: 3 figures, 1 tabl