Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning

Abstract

The problems of 3-D digital topology preservation under binary transformations and 3-D object thinning are considered in this correspondence. At first, we 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, we have proposed an algorithm to generate 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. © 1994 IEEE.