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Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory

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2 Author(s)
Lee R. Nackman ; Department of Computer Science, University of North Carolina, Chapel Hill, NC 27514; Computer-Aided Design and Analysis Project at the Manufacturing Research Center, IBM Thomas J. Watson Research Center, Yorktown, Heights, NY 10598. ; Stephen M. Pizer

Blum's two-dimensional shape description method based on the symmetric axis transform (SAT) is generalized to three dimensions. The method uniquely decomposes an object into a collection of sub-objects each drawn from three separate, but not completely independent, primitive sets defined in the paper: width primitives, based on radius function properties; axis primitives, based on symmetric axis curvatures; and boundary primitives, based on boundary surface curvatures. Width primitives are themselves comprised of two components: slope districts and curvature districts. Visualizing the radius function as if it were the height function of some mountainous terrain, each slope district corresponds to a mountain face together with the valley below it. Curvature districts further partition each slope district into regions that are locally convex, concave, or saddle-like. Similarly, axis (boundary) primitives are regions of the symmetric surface where the symmetric surface (boundary surfaces) are locally convex, concave, or saddle-like. Relations among the primitive sets are discussed.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:PAMI-7 ,  Issue: 2 )