SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1367-1385, January 2020.
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 $\mathbb R^n$, 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.

中文翻译：

---

三角网格上的数学形态：严格方法

SIAM影像科学杂志，第13卷，第3期，第1367-1385页，2020年1月。
数学形态为图像分析提供了各种工具。膨胀和腐蚀这两个基本操作是基于在给定结构元素（网格的另一幅图像）的帮助下进行平移的。与$ \ mathbb R ^ n $的离散子组相反，三角形网格在平移下不闭合；因此，我们对结构元素进行了限制。即，我们仅允许那些trixel（三角形像素）位于表示矢量的结构元素中，以使网格在这些矢量的平移下闭合。我们证明严格的膨胀和侵蚀都具有良好的性能。通过严格的膨胀和腐蚀相结合，也定义了严格的开闭。