A new approach to computing the Euler characteristic
In this paper we describe a new approach to computing the Euler characteristic of a three dimensional digital image. Our approach is based on computing the change in numbers of black components, tunnels and cavities in 3  3  3 neighborhood of an object (black) point due to its deletion. The existing algorithms to computing the Euler characteristic of a 3D digital image are based on counting the numbers of all k-dimensional elements (0 ? k ? 3) in a polyhedral representation of the image. Our approach can be modified for (6,26), (18,6), (6,18) and other connectivity relations of grid points. A parallel implementation of the algorithm is described using the concept of sub-fields.
euler characteristic tunnels 3d digital topology betti numbers binary transformation sub-fields