Nonparametric training of snakes to find indistinct boundaries

We enable highly improved performance of deformable model (snake) segmentation of a known type of object (human bladder) with unclear edges in a cluttered domain (abdominal CT scans). This is accomplished by learning an objective function from ground-truth contours in test images, using a nonparametric estimator of the distributions of chosen image quantities (intensity on the boundary and image gradient perpendicular to it). The Parzen-window estimator is found to reward correct contours much more accurately than a model based on means and covariances. This latter Gaussian model, in turn, performs adequately where a traditional a priori objective function does not. Performance of objective functions is measured by checking the fraction of incorrect contours that score better than ground truth (false positives), and the deviation of plots of shape incorrectness vs. objective function value from the closest strictly increasing function.