Local matching of surfaces using a boundary-centered radial decomposition

The local matching problem on surfaces is: Given a pair of oriented surfaces in 3-space, find subsurfaces that are identical or complementary in shape. A heuristic solution is presented that is intended for use on complex surfaces (as opposed to such things as cubes and cylinders). The method proceeds as follows: (1) Find a small set of points--called "critical points"--on the two surfaces with the property that if p is a critical point and p matches q, then q is also a critical point. The critical points are taken to be local extrema of curvature, either Gaussian or mean. (2) Construct a rotation invariant representation around each critical point by intersecting the surface with spheres of standard radius centered around the critical point. For each of the resulting curves, compute a "distance contour" function equal to the distance from a point on the curve to the center of gravity of the curve as a function of arc length (normalized so that the domain of the function is the interval 0,1 ). Call the set of contours for a given critical point a "distance profile." (3) Match distance profiles by computing a "correlation" between corresponding distance contours. (4) Use maximal compatible subsets of the set of matching profiles to induce a transformation that maps corresponding critical points together, then use a cellular spatial partitioning technique to find all points on each surface that are within a tolerance of the other surface. This method has been implemented using surfaces represented by polygonal networks as input. It has been successfully applied to synthetically produced surfaces. Applications include scene analysis, molecular docking (fitting) and assembly of three dimensional jigsaw puzzles.

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