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 we show how to instead learn, from training data, the relation between the shape and any image feature, as the probability distribution (PDF) of a function of image and shape.
An important but neglected task for the implementor has always been to select image qualities to guide a model. Because success depends on the relation of objective function (PDF) output to shape correctness, it is evaluated using a sampling of ground truth, a random model of the range of shapes tried during optimization, and chamfer distance as a measure of shape closeness. The test results are evaluated for incidence of ``false positives'' (scoring better than ground truth) versus closeness, and for monotonicity using correlation coefficient, and using a new measure which we introduce.
We demonstrate such evaluation on a simple ``sectoring'' of a snake, in which intensity and perpendicular gradient are learned separately 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 consistent image nonuniformity around the organ boundary.
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Samuel D. Fenster
Department of Computer Science
Columbia University