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Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning
October 1994 (vol. 16 no. 10)
pp. 1028-1032

The problems of 3-D digital topology preservation under binary transformations and 3-D object thinning are considered in this correspondence. First, the authors establish the conditions under which transformation of an object voxel to a non-object voxel, or its inverse does not affect the image topology. An efficient algorithm to detect a simple point has been proposed on the basis of those conditions. In this connection, some other interesting properties of 3-D digital geometry are also discussed. Using these properties and the simple point detection algorithm, the authors have proposed an algorithm to generate a surface-skeleton so that the topology of the original image is preserved, the shape of the image is maintained as much as possible, and the results are less affected by noise.

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Index Terms:
computational geometry; image processing; topology; 3-D simple points; 3-D digital topology preservation; binary transformations; 3-D object thinning; object voxel; nonobject voxel; 3-D digital geometry; point detection algorithm; surface-skeleton
P.K. Saha, B.B. Chaudhuri, "Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 10, pp. 1028-1032, Oct. 1994, doi:10.1109/34.329007
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