A generalized fuzzy mathematical morphology and its application in robust 2-D and 3-D object representation
A generalized fuzzy mathematical morphology and its application in robust 2-D and 3-D object representation
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DOI：
10.1109/83.869190
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发表时间：
2000-10
期刊：
影响因子：
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通讯作者：
V. Chatzis;I. Pitas
中科院分区：
文献类型：
--
作者：
V. Chatzis;I. Pitas
本文基于模糊包含指标（FII）的新定义，提出了广义模糊数学形态学（GFMM）。FII是一种模糊集，用于度量一个模糊集包含到另一个模糊集中，该模糊集被提议为模糊集。证明了FII服从一组公理，这些公理是任何包含指示符都应服从的已知公理的扩展，并且它们对应于任何数学形态学运算的期望性质。GFMM为形态学操作提供了一个非常强大和灵活的工具。二值和灰度的数学形态可以看作是所提出的GFMM的特殊情况。介绍了二维（2-D）和三维（3-D）对象的鲁棒骨架化和形状分解的应用。仿真实例表明，在大多数情况下，使用GFMM可以比使用二值数学形态学更好地实现从它们的骨架子集中重建目标。此外，使用GFMM进行骨骼化和形状分解可以保留骨骼子集和脊柱的形状和位置。
In this paper, the generalized fuzzy mathematical morphology (GFMM) is proposed, based on a novel definition of the fuzzy inclusion indicator (FII). FII is a fuzzy set used as a measure of the inclusion of a fuzzy set into another, that is proposed to be a fuzzy set. It is proven that the FII obeys a set of axioms, which are proposed to be extensions of the known axioms that any inclusion indicator should obey, and which correspond to the desirable properties of any mathematical morphology operation. The GFMM provides a very powerful and flexible tool for morphological operations. The binary and grayscale mathematical morphologies can be considered as special cases of the proposed GFMM. An application for robust skeletonization and shape decomposition of two-dimensional (2-D) and three-dimensional (3-D) objects is presented. Simulation examples show that the object reconstruction from their skeletal subsets that can be achieved by using the GFMM is better than by using the binary mathematical morphology in most cases. Furthermore, the use of the GFMM for skeletonization and shape decomposition preserves the shape and the location of the skeletal subsets and spines.