Curve evolution and estimation-theoretic techniques for image processing

Thesis (Ph.D.)--Harvard--Massachusetts Institute of Technology Division of Health Sciences and Technology, 2001.Includes bibliographical references (p. 205-216) and index.The broad objective of this thesis is the development of statistically robust, computationally efficient, and global image processing algorithms. Such image processing algorithms are not only useful, but in high demand within the image processing arena. Recently, curve evolution and estimation-theoretic approaches to image processing have received considerable attention. Their role in the development of novel image processing algorithms is the focus of this thesis. The main contributions of this thesis lie in the development of three different, but interrelated, image processing algorithms with strong connections to curve evolution and estimation theory. One contribution of this thesis is the development of a new class of computationally-efficient algorithms designed to solve incomplete data problems in which part of the data is not observed, or hidden. These incomplete data problems are frequently encountered in image processing and computer vision. The basis of this framework is the marriage of the expectation-maximization procedure with two powerful methodologies-optimal multiscale estimators and mean field theory. Another contribution of this thesis is the development of a new class of deformable contour models for the segmentation of images which exhibit a known number of features. The key behind this approach is the use of geometric curve evolutions which maximally separate a predetermined set of statistics within the image. In addition, by introducing a geometric constraint on the segmenting curve, we modify this segmentation algorithm to produce a geometric clustering algorithm as well.(cont.) The final contribution of this thesis is the development of an active contour model that offers a tractable implementation of the original Mumford-Shah model to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner. By generalizing the Mumford-Shah model, we are able to apply this active contour model to problems in which data quality varies between different locations in the image and, in the limiting case, to images in which pixel measurements are missing. We then modify this active contour model to obtain a novel PDE-based approach to image magnification, yielding a new application of the Mumford-Shah paradigm. Finally, we demonstrate the utility of this thesis by applying one of the image processing methodologies that we developed to a medical application, specifically, MR guided prostate brachytherapy.by Andy Tsai.Ph.D