论文标题
最大代数中的矩阵表示信号和图像处理的形态学辅助
Morphological adjunctions represented by matrices in max-plus algebra for signal and image processing
论文作者
论文摘要
在离散的信号和图像处理中，可以将许多扩张和侵蚀写成矩阵上矩阵的最大加值和最小乘积。先前的研究考虑了对称，无限的完整晶格的操作员，例如完整的实际线路的笛卡尔力量。本文重点介绍了封闭的高管的附加条件，这是用于代表数字信号和图像的完整晶格。我们表明，这将代表矩阵的限制为双重0，我们表征了它们可以代表的辅助。定义的运算符的图形解释自然来自由矩阵编码的邻接关系以及最大频谱解释。
In discrete signal and image processing, many dilations and erosions can be written as the max-plus and min-plus product of a matrix on a vector. Previous studies considered operators on symmetrical, unbounded complete lattices, such as Cartesian powers of the completed real line. This paper focuses on adjunctions on closed hypercubes, which are the complete lattices used in practice to represent digital signals and images. We show that this constrains the representing matrices to be doubly-0-astic and we characterise the adjunctions that can be represented by them. A graph interpretation of the defined operators naturally arises from the adjacency relationship encoded by the matrices, as well as a max-plus spectral interpretation.
