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Inferring the Structure of Extremal Trace Points

Points on a surface that mark occlusion boundaries, concave discontinuities in orientation, or negative curvatures whose magnitudes are local maxima, are important features with respect to the partitioning of a surface into regions corresponding to different parts and/or objects. We refer to such points as extremal trace points because their loci often form contours that partition a surface according to intuitive notions of part and object. The emphasis of this research, however, is not the identification of such points, but rather how part and object boundaries are inferred from their local structure. Our related work in surface reconstruction addresses the issues of trace point identification and making their local structure explicit. We have been investigating two different strategies in this regard. The first is a classical approach based on energy minimizing splines (so-called ``snakes''), where the task is to infer the 3-D space curve that best fits a particular cluster of trace points subject to constraints imposed by their local structure. Excellent part decompositions have been obtained using this approach, but at great computational expense due to the difficulty of the interpolation problem, especially when points are sparse. This concern has led to a second strategy that approaches the interpolation problem differently, using a scale space representation of the surface based on local continuity of curvature. One of the attributes of this scale space is that it implicitly represents the possible loci of extremal trace points. By combining this with the actual trace points recovered through surface reconstruction, i.e. by insisting on a consistent interpretation between the two, we have made significant gains in both locating part boundaries and reducing the complexity of the procedures involved.
A. Lejeune, F.P. Ferrie

Thierry Baron
Mon Nov 13 10:43:02 EST 1995