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Performance in noise of a diffusion-based shape descriptor

A diffusion-like process, analogous to the thermodynamic diffusion of heat or of gas molecules, is used to describe the shape of two- or three-dimensional objects. It is effective at identifying extrema of curvature as would be used to segment the boundary, and also at characterizing the types of line segments that lie between the extrema. Both of those operations are essential for qualitative descriptions of images, as would be required by an approach based on geometrical icons (geons). The region need not be convex. The descriptor is invariant to several common transformations, including rotation. It can be implemented easily on parallel machines, does not pose problems with the definition of slope, and appears to be capable of dealing with the matching of partially occluded objects. The descriptor's performance is essentially independent of user-supplied parameters. It is shown that noise does not affect the accuracy of identification of the extrema -- a simple stopping rule for the process ensures that the structural parts of the boundary are preserved while the noise is suppressed. The procedure is compared and contrasted to scale-based boundary-description methods.