Learning prototypical shapes for object categories

We describe a method to compute the prototypical shapes for object categories using the shock graph representation. Given a set of category exemplars, we determine a prototypical shape for this category by estimating the Karcher mean of the shock graphs of the exemplar shapes. The method is described in three steps. First, we derive an iterative method to average N points in an abstract continuous metric space with well-defined geodesics and well-defined mid-point of geodesics. Second, we show how two shapes can be averaged by finding the mid-point of the geodesic induced by the edit-distance shock graph matching. Third, the above two steps are combined with a gradient descent step to compute the average of a set of N exemplar shapes. We evaluate each of the three steps with experiments using standard shape datasets.