In this paper, basic concepts of digital binary morphological operations, i.e., dilation and erosion are investigated on a triangular grid. Every triangle pixel is addressed by a unique coordinate triplet with sum zero (even pixels) or one (odd pixels). Even and odd pixels have different orientations. The triangular grid is not a lattice, that is, not every translation with a grid vector maps the grid to itself. Therefore, to extend the morphological operations to the triangular grid is not straightforward. We introduce three types of definition for both of dilation and erosion. Various examples and properties of the considered dilation and erosion are analyzed on the triangular grid.
CITATION STYLE
Abdalla, M., & Nagy, B. (2017). Concepts of binary morphological operations dilation and erosion on the triangular grid. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10149 LNCS, pp. 89–104). Springer Verlag. https://doi.org/10.1007/978-3-319-54609-4_7
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