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Keywords = PSLG construction

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12 pages, 8071 KiB  
Article
Unbiased Finite Element Mesh Delaunay Constrained Triangulation Applied to 2D Images with High Morphological Complexity Using Mathematical Morphology Tools Part 2: Labeled Images
by F. N’Guyen, T. Kanit and A. Imad
Computation 2025, 13(2), 57; https://doi.org/10.3390/computation13020057 - 19 Feb 2025
Viewed by 526
Abstract
We propose a method for generating a constrained Delaunay triangulation CDT applied to labeled 2D images with high morphological complexity. In the previous paper, Part 1, we established an unbiased planar straight-line graph (PLSG) on image objects of any morphological complexity, using mathematical [...] Read more.
We propose a method for generating a constrained Delaunay triangulation CDT applied to labeled 2D images with high morphological complexity. In the previous paper, Part 1, we established an unbiased planar straight-line graph (PLSG) on image objects of any morphological complexity, using mathematical morphology tools. In the case of labeled images of this paper, the PSLG is defined by the set of local PSLG pieces for each adjacent label. The global PSLG of each label must respect the injective nature of Jordan’s curve. Full article
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21 pages, 8652 KiB  
Article
Unbiased Finite Element Mesh Delaunay Constrained Triangulation Applied to 2D Images with High Morphological Complexity Using Mathematical Morphology Tools Part 1: Binary Images
by Franck N’Guyen, Toufik Kanit and Abdellatif Imad
Computation 2025, 13(2), 52; https://doi.org/10.3390/computation13020052 - 13 Feb 2025
Viewed by 648
Abstract
We propose a method for establishing a Constrained Delaunay Triangulation CDT applied to 2D binary images of high morphological complexity. A prerequisite for CDT is the unbiased definition of the Planar Straight-Line Graph PSLG, which must respect the injective nature of Jordan’s Curve [...] Read more.
We propose a method for establishing a Constrained Delaunay Triangulation CDT applied to 2D binary images of high morphological complexity. A prerequisite for CDT is the unbiased definition of the Planar Straight-Line Graph PSLG, which must respect the injective nature of Jordan’s Curve whatever the topology of the image objects. Mathematical morphology provides tools for extracting the image contour, on which points will be judiciously placed at particular points to construct the vector path of the PSLG. Finally, these tools will enable us to implement a judicious pointing process in the image to guarantee the relative equivalence of triangles. The deterministic and rigorous procedure detailed in this article will be generalized in a second article, Part 2, to the case of labeled images for which the definition of the PSLG is more complex to define, since the contour of objects in the image is defined by the set of contours of adjacent objects. Full article
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