Bayesian Methods for Segmentation of Objects from Multimodal and

Complex Shape Densities using Statistical Shape Priors

Ertunç Erdil

Computer Science, PhD Dissertation, 2017

Thesis Jury

Assoc. Prof. Dr. Müjdat Çetin (Thesis Advisor),

Assoc. Prof. Dr. Devrim Ünay (Thesis Co-advisor),

Assoc. Prof. Dr. Selim Balcısoy

Assist. Prof. Dr. Sinan Yıldırım

Assoc. Prof. Dr. Tolga Taşdizen

Assist. Prof. Dr. Ender Konukoğlu

Date &Time: 13th December 2017 –  08:00 AM

Place: FENS L047

Keywords : shape prior, kernel density estimation, level set, Markov chain Monte

Carlo, image segmentation, multimodal shape density.

Abstract

In many image segmentation problems involving limited and low-quality data, employing

statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result. However, defining probability densities in the space of shapes is an open and challenging problem, especially if the object to be segmented comes from a shape density involving multiple modes (classes).

In the literature, there are some techniques that exploit nonparametric shape priors to learn multimodal prior densities from a training set. These methods solve the problem of segmenting objects of limited and low-quality to some extent by performing maximum a posteriori (MAP) estimation. However, these methods assume that the boundaries found by using the observed data can provide at least a good initialization for MAP estimation so that convergence to a desired mode of the posterior density is achieved. There are two major problems with this assumption that we focus in this thesis. First, as the data provide less information, these approaches can get stuck at a local optimum which may not be the desired solution. Second, even though a good initialization directs the segmenting curve to a local optimum solution that looks like the desired segmentation, it does not provide a picture of other probable solutions, potentially from different modes of the posterior density, based on the data and the priors.

In this thesis, we propose methods for segmentation of objects that come from multimodal posterior densities and suffer from severe noise, occlusion and missing data. The first framework that we propose represents the segmentation problem in terms of the joint posterior density of shapes and features. We incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation. In our second proposed framework, we approach the segmentation problem from the approximate Bayesian inference perspective. We propose two different Markov chain Monte Carlo (MCMC) sampling based image segmentation approaches that generates samples from the posterior density. As a final contribution of this thesis, we propose a new shape model that learns binary shape distributions by exploiting local shape priors and the Boltzmann machine. Although the proposed generative shape model has not been used in the context of object segmentation in this thesis, it has great potential to be used for this purpose.