Surface definition for branching, contour-defined objects

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.

REFERENCES

• 1: H. Fuchs , Z. M. Kedem , S. P. Uselton, Optimal surface reconstruction from planar contours, Communications of the ACM, v.20 n.10, p.693-702, Oct. 1977 [doi>10.1145/359842.359846]
• 2: Kedem Z. M., and H. Fuchs, 'Finding several minimum cost paths in directed acyclic graphs', University of Texas at Dallas technical report No. 13, January 1977.
• 3: Ugo Montanari, Continuous Skeletons from Digitized Images, Journal of the ACM (JACM), v.16 n.4, p.534-549, Oct. 1969 [doi>10.1145/321541.321543]
• 4: Catmull E., and J. Clark, 'Recursively generated B-spline surfaces on arbitrary topological meshes', COMPUT. AIDED DES., 10:6, November 1978.