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Determining the similarity of two shapes is a significant task in both machine and human vision systems that must recognize or classify objects. The exact properties of human shape similarity judgements are not well understood yet, and this task is particularly difficult in domains where the shapes are not related by rigid transformation. In this paper we identify a number of possibly desirable properties of a shape similarity method, and determine the extent to which these properties can be captured by approaches that compare local properties of the contours of the shapes, through elastic matching. Special attention is devoted to objects that possess articulations, i.e. articulated parts. Elastic matching evaluates the similarity of two shapes as the sum of local deformations needed to change one shape into another. We show that similarities of part structure can be captured by such an approach, without the explicit computation of part structure. This may be of importance, since although parts appear to play a significant role in visual recognition, it is difficult to stably determine part structure. We also show novel results about how one can evaluate smooth and polyhedral shapes with the same method. Finally, we describe shape similarity effects that cannot be handled by current approaches.

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We attempt to unify several approaches to image segmentation in early vision under a common framework. The Bayesian approach is very attractive since: (i) it enables the assumptions used to be explicitly stated in the probability distributions, and (ii) it can be extended to deal with most other problems in early vision. Here, we consider the Markov random field formalism, a special case of the Bayesian approach, in which the probability distributions are specified by an energy function.We show that: (i) our discrete formulations for the energy function is closely related to the continuous formulation; (ii) by using the mean field (MF) theory approach, introduced by Geiger and Girosi [1991], several previous attempts to solve these energy functions are effectively equivalent; (iii) by varying the parameters of the energy functions we can obtain connections to nonlinear diffusion and minimal description length approaches to image segmentation; and (iv) simple modifications to the energy can give a direct relation to robust statistics or can encourage hysteresis and nonmaximum suppression.