Physically and Statistically Based Deformable Models for Medical Image Analysis

Medical imaging continues to permeate the practice of medicine, but automated yet accurate segmentation and labeling of anatomical structures continues to be a major obstacle to computerized medical image analysis. Deformable models, with their roots in estimation theory, optimization, and physics-based dynamical systems, represent a powerful approach to the general problem of medical image segmentation. This chapter presents an introduction to deformable models, beginning with the classical Active Contour Models (ACMs), or snakes, and focusing on explicit, physics-based methods. Snakes are useful for segmenting amorphous shapes when little or no prior knowledge about shape and motion is available. Many extensions of snakes incorporate such additional knowledge. An example presented in this chapter is the use of optical flow forces to incorporate knowledge of shape dynamics and guide the snake deformations to track the leading edge of an injected contrast agent in an echocardiographic image sequence. Active Shape Models (ASMs), or smart snakes, is a powerful method for incorporating statistical models of shape variability in the segmentation process. ASMs and ACMs offer different advantages, and, as such, a method combining both is presented. Statistical knowledge about shape dynamics is useful for segmenting and tracking objects with distinctive motion patterns (such as a beating heart). An extension of the ASM to model knowledge of spatiotemporal constraints is presented.