We describe how to teach deformable models to maximize image segmentation correctness based on user-specified criteria, and present a method for evaluating which criteria work best. 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 image variations around the organ boundary.

We review our work on how to teach deformable models to maximize image segmentation correctness based on user-specified criteria. We then present new variants and applications of learned snakes, modeled by four different probability density functions (PDFs), at three scales, and in the two medical domains of abdominal CT slices and echocardiograms. We review and extend our method for evaluating which criteria work best. Success depends on the relation of objective function (the PDF) output to shape correctness. This relationship for all the above learned snake variants and domains, is evaluated on perturbed ground truth shapes in three ways: by the incidence of "false positives" of randomized shapes; by the monotonicity of the objective function versus shape closeness to ground truth, as given by a correlation coefficient; and by the distance of this relationship to the nearest monotonically increasing function, a new performance measure which we introduce. We demonstrate such evaluations on traditional snakes, and on snakes for which image intensity and perpendicular gradient are learned separately, and with their covariances, and with separate learning over equal-length "sectors". Optimal blur appears to depend on domain. Both sectoring and the use of covariance markedly improve results in abdominal CT images, where nearby image landmarks (i.e. organs) stabilize learning. Results on echocardiograms, however, are less striking, although the use of covariance does show improvements; this appears to be due to the non-Gaussian distribution of image features in this domain.

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.