Image segmentation is one of the most important components of many image analysis systems. It deals with the estimation of pixel values of a discrete-valued image, often based on noisy observations. A succesful segmentation scheme has to take advantage of prior knowledge about the images to be estimated. This knowledge could be represented by a statistical model, such as a Markov random field (MRF), or by deterministic descriptions of the shapes and sizes of features in the images. Statistical models almost always involve approximations, and estimator performance can be severely degraded by deviation of the true image from the model. On the other hand, purely deterministic models usually fail to incorporate all of our prior knowledge. In this dissertation, we develop methods for reducing the sensitivity of segmentation algorithms to inaccuracy in the models, and methods for combining MRF models with morphological constraints on region shapes.
We first consider some robust methods for image segmentation. Robust segmentation algorithms are derived for the case of observation distribution uncertainty for both binary and multi-level images. These algorithms are simple modifications of some nominal segmentation algorithms such as those based on simulated annealing or iterated conditional modes. They perform nearly as well as the nominal algorithms under model conditions, and much better than the nominal algorithms when the noise is heavier-tailed than the nominal model. We then show the existence of minimax-robust MAP estimators under very general conditions, and consider some applications to robust segmentation given knowledge of local distributions. We next consider iterative segmentation algorithms that use MRF models for prior probabilities, and use morphological operations in update steps. These algorithms generate segmented images that have high posterior probabilities according to the MRF models and meet specified morphological shape and size constraints, and they perform well even with very noisy observations. The robust and iterative morphological segmentation methods are then applied to the specific problem of small object detection. An algorithm using both robust and morphological processing is developed to recover both large regions and small features in images. Test results for both real and simulated images show that the segmentation and small object detection algorithms are very effective.
