Level Set Segmentation Using Statistical Shape Priors

A novel and robust 3-D segmentation approach is proposed using level sets based on shape constraints. The approach depends on both the gray level and shape information. A partial differential equation (PDE) is developed to control the evolution of the level sets. The PDE does not include weighting coefficients to be tuned, overcoming the disadvantages of other PDE approaches. The shape information is gathered from a set of the signed distance maps representing the training data as a histogram of the occurrences of the points inside and outside the object. We use a novel statistical approach to get a probability density function (pdf) for the signed distance map of the points inside and outside and also the distribution of gray level inside and outside the object. The proposed statistical approach is based on modelling the empirical density function (normalized histogram of occurrence) for either the gray level distribution or signed distance map with a linear combination of Gaussians (LCG) with positive and negative components. We modify an Expectation-Maximization (EM) algorithm to deal with the LCGs and also propose a novel EM-based sequential technique to get a close initial LCG approximation for the modified EM algorithm to start with. The pdf’s of the signed distance and intensity gray level are embedded in the speed function of the level set specifying the direction of evolution. Experimental results show how the approach is accurate in segmenting different types of 2-D and 3-D data sets including medical images.