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Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory
February 1985 (vol. 7 no. 2)
pp. 187-202
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.
Stephen M. Pizer, Departments of Computer Science and Radiology, University of North Carolina, Chapel Hill, NC 27514.
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.
Citation:
Lee R. Nackman, Stephen M. Pizer, "Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 7, no. 2, pp. 187-202, Feb. 1985, doi:10.1109/TPAMI.1985.4767643
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