Surface definition for branching, contour-defined objects

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Abstract
Recent work on mapping polygonal surface mosaics onto contour defined objects has resulted in minimum flow algorithms which do a good job of mapping a surface between two single contours. This report extends these algorithms to handle contour defined objects which are highly branched and have holes.For branching contours where n contours in section I are connected to m contours in section i+1, the surfaces are mapped by first concatenating the section I contours into a single large contour using a minimum number of minimum distance links, similarly concatenating the section I+1 contours, then performing the one to one mapping between the resulting composite contours.Capping off a single arbitrarily shaped contour may be done by computing the medial axis transform of the contour, constructing the medial axis contour and mapping a surface from the contour to the medial axis contour.Medial axis transforms of the section I+1 contours may also be projected onto section I and concatenated with the section I contours to handle the mapping of convoluted, highly branched objects. These algorithms have applications to three-dimensional CAT scanner data, topographical map data and object representation for knowledge guided vision systems.

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