Concepts of Binary Morphological Operations Dilation and Erosion on the Triangular Grid

Abdalla, Mohsen; Nagy, Benedek

doi:10.1007/978-3-319-54609-4_7

Cited by 2 publications

(3 citation statements)

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“…Note that the dilation and erosion above are done by the neighborhood used in this paper. In paper [1] similar operations are defined in a more general manner, instead of a fixed neighbourhood, various structural elements were used with various constraints. Allowing only vectors that translate the grid to itself, the strict approach is defined.…”

Section: Pattern Recovery By Combining Bs-automatamentioning

confidence: 99%

“…Morphological operations dilation and erosion are considered for the triangular grid in a more general and mathematical approach in [1,2]. Our aim here was to show how cellular automata can be applied in mathematical morphology and other related image processing tasks on the triangular grid.…”

Section: Literature Reviewmentioning

confidence: 99%

“…This is an important difference from the square and hexagonal lattices. In mathematical morphology, dilation and erosion are based on local translations, various approaches to extend their definitions to the triangular grid was shown recently in [1]. This paper is also motivated by the reason of lack of morphological operations described and analysed on the triangular grid.…”

Section: Introductionmentioning

confidence: 99%

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Cellular Automata Approach to Mathematical Morphology in the Triangular Grid

Saadat¹,

Nagy²

2018

ACTA POLYTECH HUNG

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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.

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Section: Pattern Recovery By Combining Bs-automatamentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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