Cellular Automata Approach to Mathematical Morphology in the Triangular Grid

Abstract

Cellular automata are parallel computing devices working on a discrete timescale. In the paper, each cell of the triangular grid has a state from the binary set (i.e., we have a binary pattern, an image, on the grid), and the state in the next time instant depends only on the actual state of the cell itself and the states of its side-neighbor cells. We illustrate their use in image synthesis, e.g., generating snowflakes, and in image analysis: some of our automata are connected to image processing operations, e.g., dilation and erosion. Computation of Hausdorff distance of two binary images on the triangular grid is also presented. In image processing, and especially in mathematical morphology, operations are local operations, and thus, cellular automata are apt to use. On the other side, the triangular grid is not a point lattice, thus the definition of translation based image operations is not always straightforward.