Thesis (Ph. D.)--Drexel University, 2007. / Includes abstract and vita. Includes bibliographical references (leaves 96-103).

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 47-51). Also available in electronic version.

This thesis is in two parts. Part I concerns simulation of random fields using the circulant embedding method, and Part II studies the numerical solution of stochastic differential equations (SDEs).

Markov Random Fields (MRFs) are used in computer vision as an effective method for reconstructing a function starting from a set of noisy, or sparse data, or in the integration of early vision processes to label physical discontinuities. The MRF formalism is attractive because it enables the assumptions used to be explicitly stated in the energy function. The drawbacks of such models have been the computational complexity of the implementation, and the difficulty in estimating the parameters of the model. In this thesis, the deterministic approximation to the MRF models derived by Girosi and Geiger[10] is investigated, and following that approach, a MIMD based algorithm is developed and implemented on a network of T800 transputers under the Trollius operating system. A serial version of the algorithm has also been implemented on a SUN 4 under Unix. The network of transputers is configured as a 2-dimensional mesh of processors (currently 16 configured as a 4 x 4 mesh), and the input partitioning method is used to distribute the original image across the network. The implementation of the algorithm is described, and the suitability of the transputer for image processing tasks is discussed. The algorithm was applied to a number of images for edge detection, and produced good results in a small number of iterations. / Science, Faculty of / Computer Science, Department of / Graduate

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No description available.

This dissertation examines properties and representations of several isotropic Gaussian random fields in the unit ball in d-dimensional Euclidean space. First we consider Lévy's Brownian motion. We use an integral representation for the covariance function to find a new expansion for Lévy's Brownian motion as an infinite linear combination of independent standard Gaussian random variables and orthogonal polynomials. Next we introduce a new family of isotropic Gaussian random fields, called the p-processes, of which Lévy's Brownian motion is a special case. Except for Lévy's Brownian motion the p-processes are not locally stationary. All p-processes also have a representation as an infinite linear combination of independent standard Gaussian random variables. We use these expansions of the random fields to simulate Lévy's Brownian motion and the p-processes along a ray from the origin using the Cholesky factorization of the covariance matrix. / Graduation date: 2013

The extension of Conditional Random Fields (CRF) from discrete states to continuous states will help remove the limitation of the number of states and allow new applications for CRF. In this work, our attempts to obtain a correct procedure to train continuous state conditional random fields through maximum likelihood are presented. By deducing the equations governing the extension of the CRF to continuous states it was possible to merge with the Particle Filter (PF) concept to obtain a formulation governing the training of continuous states CRFs by using particle filters. The results obtained indicated that this process is unsuitable because of the low convergence of the PF integration rate in the needed integrations replacing the summation in CRFs. So a change in concept to an adaptive integration scheme was made. Based on an extension of the Binary Space Partition (BSP) algorithm an adaptive integration process was devised with the aim of producing a more precise integration while retaining a less costly function evaluation than PF. This allowed us to train continuous states conditional random fields with some success. To verify the possibility of increasing the dimension of the states as a vector of continuous states a scalable version was also used to briefly assess its fitness in two-dimensions with quadtrees. This is an asymmetric two-dimensional space partition scheme. In order to increase the knowledge of the problem it would be interesting to have further information of the relevant features. A feature selection embedded method was used based on the lasso regulariser with the intention of pinpointing the most relevant feature functions indicating the relevant features.

published_or_final_version / Computer Science / Master / Master of Philosophy

This thesis is devoted to dense deformable image registration/fusion using discrete methods. The main contribution of the thesis is a principled registration framework coupling iconic/geometric information through graph-based techniques. Such a formulation is derived from a pair-wise MRF view-point and solves both problems simultaneously while imposing consistency on their respective solutions. The proposed framework was used to cope with pair-wise image fusion (symmetric and asymmetric variants are proposed) as well as group-wise registration for population modeling. The main qualities of our framework lie in its computational efficiency and versatility. The discrete nature of the formulation renders the framework modular in terms of iconic similarity measures as well as landmark extraction and association techniques. Promising results using a standard benchmark database in optical flow estimation and 3D medical data demonstrate the potentials of our methods.