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Multivariate mathematical morphology based on fuzzy extremum estimation

机译：基于模糊极值估计的多元数学形态学

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摘要

The existing lexicographical ordering approaches respect the total ordering properties, thus making this approach a very robust solution for multivariate ordering. However, different marginal components derived from various representations of a colour image will lead to different results of multivariate ordering. Moreover, the output of lexicographical ordering only depends on the first component leading to the followed components taking no effect. To address these issues, three new marginal components are obtained by means of quaternion decomposition, and they are employed by fuzzy lexicographical ordering, and thus a new fuzzy extremum estimation algorithm (FEEA) based on quaternion decomposition is proposed in this study. The novel multivariate mathematical morphological operators are also defined according to FEEA. Comparing with the existing solutions, experimental results show that the proposed FEEA performs better results on multivariate extremum estimation, and the presented multivariate mathematical operators can be easily handled and can provide better results on multivariate image filtering.
机译：现有的字典顺序排序方法尊重总排序属性，因此使该方法成为用于多变量排序的非常可靠的解决方案。但是，从彩色图像的各种表示派生的不同边缘分量将导致多元排序的不同结果。此外，词典顺序的输出仅取决于第一个组件，导致随后的组件不起作用。为了解决这些问题，通过四元数分解获得了三个新的边际成分，并将它们用于模糊字典序，从而提出了一种新的基于四元数分解的模糊极值估计算法（FEEA）。还根据FEEA定义了新颖的多元数学形态学算子。与现有解决方案相比，实验结果表明，所提出的FEEA算法在多元极值估计上具有更好的结果，所提出的多元数学算子易于处理，在多元图像滤波中可以提供更好的结果。

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