A description of the diamond grid for topological and combinatorial analysis

Abstract

We define a new topological (combinatorial) coordinate system for all cells (voxels, faces, edges and vertices) in the diamond grid. Topological relations between cells (incidence and adjacency relations) can easily be retrieved from the coordinate values, through simple integer operations. This makes the coordinate system apt for implementation in various applications, such as morphological and topological operations in image processing and shape analysis. We present an application to boundary tracking and computation of the Euler characteristic.