Simplicity of a 3D simple point after its neighbors are deleted
Cherng-Min Ma · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
A binary image contains object points and background points. Many operations on 2D and 3D images are required to preserve connectivity, that is, every object of the resulting image after the application of the operation preserves the same connectivity of the corresponding object in the original image. Normally, such operations can only delete `simple' object points. The simplicity of an object point can be determined by verifying its immediate neighborhood, i.e., a 3 X 3 neighborhood for the 2D case, or a 3 X 3 X 3 neighborhood for the 3D case, respectively. This verification for the 2D case is not difficult. However, it is not very easy for the 3D case since the number of different configurations of the 3D immediate neighborhood of a point is rather large. This paper studies some properties of this 3D problem and reduce it to a 2D problem.