Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Anuj Srivastava, Florida State University, College of Arts and Sciences, Dept. of Statistics. Title and description from dissertation home page (viewed Jan. 12, 2005). Includes bibliographical references.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Computer Science." Includes bibliographical references (p. 96-101).

Thesis (Ph.D.)--University of Melbourne, Dept. of Computer Science and Software Engineering, 2009. / Typescript. Includes bibliographical references (p. 131-146)

Thesis (M. Sc.)--Carleton University, 2001. / Includes bibliographical references (p. 106-108). Also available in electronic format on the Internet.

Thesis (Ph.D.)--Ohio University, August, 2004. / Title from PDF t.p. Includes bibliographical references (p. 100-105)

This thesis mainly addresses two issues: 1) to investigate how to perform the lip segmentation without knowing the true number of segments in advance, and 2) to investigate how to select the local optimal observation scale for each structure from the viewpoint of lip segmentation e.ectively. Regarding the .rst issue, two number of prede.ned segments independent lip segmentation methods are proposed. In the .rst one, a multi-layer model is built up, in which each layer corresponds to one segment cluster. Subsequently, a Markov random .eld (MRF) derived from this model is obtained such that the segmenta­tion problem is formulated as a labeling optimization problem under the maximum a posteriori-Markov random .eld (MAP-MRF) framework. Suppose the pre-assigned number of segments may over-estimate the ground truth, whereby leading to the over-segmentation. An iterative algorithm capable of performing segment clusters and over-segmentation elimination simultaneously is presented. Based upon this algorithm, a lip segmentation scheme is proposed, featuring the robust performance to the estimate of the number of segment clusters. In the second method, a fuzzy clustering objective function which is a variant of the partition entropy (PE) and implemented using Havrda-Charvat’s structural a-entropy is presented. This objec­tive function features that the coincident cluster centroids in pattern space can be equivalently substituted by one centroid with the function value unchanged. The minimum of the proposed objective function can be reached provided that: (1) the number of positions occupied by cluster centroids in pattern space is equal to the truth cluster number, and (2) these positions are coincident with the optimal cluster centroids obtained under PE criterion. In the implementation, the clusters provided that the number of clusters is greater than or equal to the ground truth are ran­domly initialized. Then, an iterative algorithm is utilized to minimize the proposed objective function. The initial over-partition will be gradually faded out with the redundant centroids superposed over the convergence of the algorithm. For the second issue, an MRF based method with taking local scale variation into account to deal with the lip segmentation problem is proposed. Supposing each pixel of the target image has an optimal local scale from the segmentation viewpoint, the lip segmentation problem can be treated as a combination of observation scale selection and observed data classi.cation. Accordingly, a multi-scale MRF model is proposed to represent the membership map of each input pixel to a speci.c segment and local-scale map simultaneously. The optimal scale map and the correspond­ing segmentation result are obtained by minimizing the objective function via an iterative algorithm. Finally, based upon the three proposed methods, some lip segmentation exper­iments are conducted, respectively. The results show the e.cacy of the proposed methods in comparison with the existing counterparts.

This thesis explores metric properties of Liouville quantum gravity (LQG), a random geometry with conformal symmetries introduced in the context of string theory by Polyakov in the 80’s. Formally, it corresponds to the Riemannian metric tensor “e^{γh}(dx² + dy²)” where h is a planar Gaussian free field and γ is a parameter in (0, 2). Since h is a random Schwartz distribution with negative regularity, the exponential e^{γh} only makes sense formally and the associated volume form and distance functions are not well-defined. The mathematical language to define the volume form was introduced by Kahane, also in the 80’s. In this thesis, we explore a renormalization approach to make sense of the distance function and we study its basic properties.

Thermal cameras are used in numerous computer vision applications, such as human detection and scene understanding. However, the cost of high quality and high resolution thermal sensors is often a limiting factor. Conversely, high resolution visual spectrum cameras are readily available and generally inexpensive. Herein, we explore the creation of higher quality upsampled thermal imagery using a high resolution visual spectrum camera and Markov random fields theory. This paper also presents a discussion of the tradeoffs from this approach and the effects of upsampling, both from quantitative and qualitative perspectives. Our results demonstrate the successful application of this approach for human detection and the accurate propagation of thermal measurements within images for more general tasks like scene understanding. A tradeoff analysis of the costs related to performance as the resolution of the thermal camera decreases are also provided.

Recently, Bayesian methods have become the essence of modern statistics, specifically, the ability to incorporate hierarchical models. In particular, correlated data, such as the data found in spatial and temporal applications, have benefited greatly from the development and application of Bayesian statistics. One particular application of Bayesian modeling is Gaussian Markov Random Fields. These methods have proven to be very useful in providing a framework for correlated data. I will demonstrate the power of GMRFs by applying this method to two sets of data; a set of temporal data involving car accidents in the UK and a set of spatial data involving Provo area apartment complexes. For the first set of data, I will examine how including a seatbelt covariate effects our estimates for the number of car accidents. In the second set of data, we will scrutinize the effect of BYU approval on apartment complexes. In both applications we will investigate Laplacian approximations when normal distribution assumptions do not hold.

The undirected graphical model or Markov Random Field (MRF) is one of the more popular models used in computer vision and is the type of model with which this work is concerned. Models based on these methods have proven to be particularly useful in low-level vision systems and have led to state-of-the-art results for MRF-based systems. The research presented will describe a new discriminative training algorithm and its implementation. The MRF model will be trained by optimizing its parameters so that the minimum energy solution of the model is as similar as possible to the ground-truth. While previous work has relied on time-consuming iterative approximations or stochastic approximations, this work will demonstrate how implicit differentiation can be used to analytically differentiate the overall training loss with respect to the MRF parameters. This framework leads to an efficient, flexible learning algorithm that can be applied to a number of different models. The effectiveness of the proposed learning method will then be demonstrated by learning the parameters of two related models applied to the task of denoising images. The experimental results will demonstrate that the proposed learning algorithm is comparable and, at times, better than previous training methods applied to the same tasks. A new segmentation model will also be introduced and trained using the proposed learning method. The proposed segmentation model is based on an energy minimization framework that is iii novel in how it incorporates priors on the size of the segments in a way that is straightforward to implement. While other methods, such as normalized cuts, tend to produce segmentations of similar sizes, this method is able to overcome that problem and produce more realistic segmentations.