Multiphase image segmentation based on intensity statistics: Modeling and applications

In this research, after reviewing existing image segmentation methods in Chapter 1, we developed three models based mainly on stochastic theory. In all these models, we assume that the intensity of the image at each pixel is a random variable with Gaussian distribution (or mixed Gaussian distribution). Chapter 2 - 5 describe these models. In Chapter 2, we extend the Sine-Sinc model to Gaussian-distribution-like image. Moreover, we choose a normalization of the original image as an initialization of the iterations so that it helps converge to the "true segmentation". Furthermore, we replaced the sinc function by the exponential function. With this change, the new model is more adaptable, and can still be implemented using convex-concave procedure (CCCP) which is guaranteed to converge to a local minimum or saddle point. In Chapter 3, we define a piecewise function h(x ) ∈ C1 to replace the exponential function in the first model and the Sinc function in Sine-Sinc model (discussed in Chapter 2). The advantage of this change lies in the fact that the constructed function has a sum of 1 at each point over all phases. This makes the set of composition functions { hk(x) = h(z (x) -- k) &cubr0;k=1K be essentially a set of membership functions. Another advantage of this function is that only the nearest neighbor branches can have an overlap of their supports. This property is similar to the partial volume effect in MRI partial volume segmentation where, approximately, different types of matter, called white matter, gray matter and CSF overlap only at their border. This similarity motivated us to apply our model to partial volume segmentation for MRI brain images. In Chapter 4, we start from considering the piecewise constant Mumford-Shah model for images with intensity-inhomogeneity and develop a stochastic variational soft-segmentation model with mixed Gaussian distribution. The model is more robust to noise and robust to intensity-inhomogeneity too. The problem is formulated as a minimization problem to estimate the mixture coefficients, spatially varying means and variances in the Gaussian mixture. The optimized mixture coefficients lead to a desirable soft segmentation, as well as a hard segmentation. We apply the primal-dual-hybrid-gradient (PDHG) algorithm to our model for iterations of membership functions and use a novel algorithm for explicitly computing the projection from RK to simplex DeltaK--1 for any dimension K using dual theory. Our algorithm is more efficient in both coding and implementation than existing projection methods.;Unsupervised image segmentation models are usually efficient only for a specific kind of image. For example, intensity-based unsupervised models usually assumes images to be smooth. It usually fails to work on textured images. Another example is in medical images. When the interested part of some tissue in the image has the same or similar intensity as other tissues, the segmentation will lead to an incorrect result. On the other hand, supervised image-segmentation methods take a learning procedure with a labeled training set to form a classifier. Although supervised methods are likely to give a better result than unsupervised methods, marking the training set is very time-consuming. Semi-supervised segmentation can save the time of machine learning while still utilizing the advantage of unsupervised methods. So far, most of the semi-supervised segmentation methods are developed for two-phase case. Only a few papers have dressed this topic for multiphase segmentation. In Chapter 5, we develop a framework for semi-supervised image segmentations based on the model in Chapter 4. The frame work can be implemented interactively, and can actually be applied to many static image-segmentation models. By using semi-supervised and interactive image segmentation framework developed in this chapter, people can expected more meaningful segmentation results. (Abstract shortened by UMI.).