Mathematical Morphology on the Triangular Grid: The Strict Approach

Mathematical morphology provides various tools for image analysis. The two basic operations, dilation and erosion, are based on translations with the help of a given structural element (another image of the grid). In contrast to the case of discrete subgroups of R-n, the triangular grid is not closed under translations; therefore, we use a restriction for the structural elements. Namely, we allow only those trixels (triangle pixels) to be in the structural elements which represent vectors such that the grid is closed under translations by these vectors. We prove that both strict dilation and erosion have nice properties. Strict opening and closing have also been defined by combining strict dilation and erosion.