Sectored snakes: Evaluating learned-energy segmentations

We describe how to teach deformable models to maximize image segmentation correctness based on user-specified criteria, and we present a method for evaluating which criteria work best. We present sectored snakes, a formulation that demonstrably improves upon regular snakes. A traditional deformable model ("snake" in 2D) fails to find an object's boundary when the strongest nearby image edges are not the ones sought. But models can be trained to respond to other image features instead by learning their probability distributions. The implementor must then decide on which of many image qualities to teach the model. To this end, we show how to evaluate the efficacy of any resulting deformable model, given a sampling of ground truth, a model of the range of shapes tried during optimization, and a measure of shape closeness. In the domain of abdominal CT images, we demonstrate such evaluation on a simple "sectoring" of a snake, in which intensity and perpendicular gradient are observed over equal-length segments. This specific set of qualities shows a measured improvement over an objective function that is uniform around the shape, and it follows naturally from examination of the latter's failures due to images variations around the organ boundary.