Relations as Images


Boolean matrices constitute an immediate representation of black and white images, with 1 and 0 representing the black and white pixels, respectively. We give relational expressions for calculating two morphological operations on images, namely dilation and erosion. These operations have been implemented under RelView and we compare the performance of RelView with that of Matlab and Mathematica, which have a package for computing various morphological operations. Heijmans et al. have defined dilation and erosion for undirected graphs with vertices weighted by grey-level values. Graphs generalise images by allowing irregular “grids”. We propose a definition of dilation and erosion for nonweighted directed graphs (i.e., relations) along the same lines. These operations have been implemented under RelView too.

In 16th International Conference on Relational and Algebraic Methods in Computer Science.