Energy formulations of medical image segmentations

The first phase of a radiological revolution is already well underway. New medical imaging modalities produce rich, evocative imagery, and there is a large body of evidence suggesting that a quantitative analysis of this imagery would provide much more telling diagnostic information than is currently extracted qualitatively in mainstream medicine. However, quantitative analyses of these images require some type of unified geometrical description of the anatomy, which is only possible once boundaries between anatomical structures have been segmented. But current state of the art segmentation for medical imagery is still largely an inaccurate, highly repetitive, costly procedure for specially trained technicians, which makes quantitative image analysis unrealistic for large-scale projects. Automated and semi-automated segmentation methods, however, are faster, cheaper, and more repeatable alternatives.; One route to more automated medical image segmentation is via energy minimization methods. The goal in energy minimization approaches is to define a segmentation energy which concisely captures the quantitative properties of desirable segmentations—the segmentation is the set of edges and regions which minimize the energy. The comparative advantage of using energy formulations of the segmentation problem compared to competing methods, such as edge detection and active surface methods, is the flexibility of the energy definition and resulting higher-quality segmentations. However, energy methods for medical image segmentation often suffer intractable optimization problems associated with their solution, so although theoretically attractive, they have posed problems in practice.; We have implemented an efficient method to segment medical imagery via robust segmentation methods based on energy minimization approaches. We have developed efficient means for medical image segmentation based on two variants of a segmentation energy with important geometrical (arclength minimizing edge processes, e.g.), and theoretical (scale space, shock-forming, e.g.) properties. We make broad contributions to each of two different energy formulations of the medical image segmentation problem. Specifically, we present novel and efficient approaches to minimizing two segmentation energies related to the well-known Mumford-Shah energy. Most importantly, by using advanced optimization techniques (half-quadratic minimization and Kalman filter-based techniques) we present for both energies an efficient method to both segment the medical images as well as compute useful sensitivity measures on the associated segmentations. In particular, our method finds segmentations for even small images more than 1000 times faster than competing techniques and finds segmentation sensitivity metrics for a medical image with n pixels in O( n) computational complexity rather than the O( n3) computational complexity associated with competing methods. We also show data fusion examples which use the sensitivity metrics we compute to combine information from multi-channel MR brain imagery. Our work in finding tractable solutions and associated sensitivity metrics to the segmentation problem is a fundamental first step toward any completely automated medical image segmentation task.