There is significant interest in the synthesis of discrete-state random fields, particularly those possessing structure over a wide range of scales. However, given a model on some finest, pixellated scale, it is computationally very difficult to synthesize both large and small-scale structures, motivating research into hierarchical methods. This thesis proposes a frozen-state approach to hierarchical modelling, in which simulated annealing is performed on each scale, constrained by the state estimates at the parent scale. The approach leads significant advantages in both modelling flexibility and computational complexity. In particular, a complex structure can be realized with very simple, local, scale-dependent models, and by constraining the domain to be annealed at finer scales to only the uncertain portions of coarser scales, the approach leads to huge improvements in computational complexity. Results are shown for synthesis problems in porous media.

This thesis deals with the use of Conditional Random Fields (CRFs; Lafferty et al. (2001)) for Natural Language Processing (NLP). CRFs are probabilistic models for sequence labelling which are particularly well suited to NLP. They have many compelling advantages over other popular models such as Hidden Markov Models and Maximum Entropy Markov Models (Rabiner, 1990; McCallum et al., 2001), and have been applied to a number of NLP tasks with considerable success (e.g., Sha and Pereira (2003) and Smith et al. (2005)). Despite their apparent success, CRFs suffer from two main failings. Firstly, they often over-fit the training sample. This is a consequence of their considerable expressive power, and can be limited by a prior over the model parameters (Sha and Pereira, 2003; Peng and McCallum, 2004). Their second failing is that the standard methods for CRF training are often very slow, sometimes requiring weeks of processing time. This efficiency problem is largely ignored in current literature, although in practise the cost of training prevents the application of CRFs to many new more complex tasks, and also prevents the use of densely connected graphs, which would allow for much richer feature sets. (For complete abstract open document)

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 4, 2009) Vita. Includes bibliographical references.

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

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 (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)

We seek to both detect and segment objects in images. To exploit both local image data as well as contextual information, we introduce Boosted Random Fields (BRFs), which uses Boosting to learn the graph structure and local evidence of a conditional random field (CRF). The graph structure is learned by assembling graph fragments in an additive model. The connections between individual pixels are not very informative, but by using dense graphs, we can pool information from large regions of the image; dense models also support efficient inference. We show how contextual information from other objects can improve detection performance, both in terms of accuracy and speed, by using a computational cascade. We apply our system to detect stuff and things in office and street scenes.

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.