Mathematical Morphology: A Modern Approach in Image Processing Based on Algebra and Geometry
Mathematical Morphology: A Modern Approach in Image Processing Based on Algebra and Geometry
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DOI：
10.1137/1037001
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发表时间：
1995-03
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影响因子：
--
通讯作者：
H. Heijmans
中科院分区：
文献类型：
--
作者：
H. Heijmans
数学形态学是一种基于集合理论、几何和拓扑概念的图像变换和图像泛函理论。这种方法对分析图像的几何结构特别有用。本文的主要目的是对与该领域相关的基本哲学和数学理论给出一个印象。讨论了以下主题：数学形态学概论；完备格的推广；形态学滤波器及其迭代构建形态学的几何方面（例如，凸性、距离、测地线算子、粒度、度量膨胀、距离变换、成本函数）；并将二值算子扩展到灰度图像。
Mathematical morphology is a theory of image transformations and image functionals which is based on set-theoretical, geometrical, and topological concepts. The methodology is particularly useful for the analysis of the geometrical structure in an image. The main goal of this paper is to give an impression of the underlying philosophy and the mathematical theories which are relevant to this field. The following topics are discussed: introduction to mathematical morphology; generalization to complete lattices; morphological filters and their construction by iteration; geometrical aspects of morphology (e.g., convexity, distance, geodesic operators, granulometries, metric dilations, distance transform, cost functions); and extension of binary operators to grey-scale images.