MULTIPHASE IMAGE SEGMENTATION BASED ON INTENSITY STATISTICS: MODELING AND APPLICATIONS By FUHUA CHEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MULTIPHASE IMAGE SEGMENTATION BASED ON INTENSITY STATISTICS: MODELING AND APPLICATIONS By Fuhua Chen August 2012 Chair: Yunmei Chen Major: Mathematics Image segmentation is the first stage of image processing and analysis. The result of image segmentation is used for image post-processing. In computer vision, segmentation refers to the process of partitioning a digital image into multiple segments, called phases (or classes). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. An important task of image segmentation is to distinguish objects from background without (or least) affected by noise, intensity-inhomogeneity and artifacts. Based on the classification policy that each pixel is classified to only one phase exclusively, or each pixel can partly belong to more than one phase, image segmentation methods are divided into two categories: hard segmentations and soft segmentations. Variational methods are powerful in hard segmentation. Roughly speaking, variational models for hard segmentations contain region-based methods and edge-based methods. The level-set technique is extensively used in the implementation of these models. However, the non-convexity of the energy functional in the level-set formulation is an inherent drawback of the level-set method. As a result, many level-set-based variational segmentation models are sensitive to initial values. This problem is more difficult to deal with for multiphase image segmentation. Another problem of hard segmentation is its applications to some real world problems. For example, in MRI brain image