Shortest Length Total Orders Do Not Minimize Irregularity in Vector-Valued Mathematical Morphology
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911747871342592 |
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| author | Francisco, Samuel Valle, Marcos Eduardo |
| author_facet | Francisco, Samuel Valle, Marcos Eduardo |
| contents | Mathematical morphology is a theory concerned with non-linear operators for image processing and analysis. The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations. Because vectors can be ordered in many ways, finding appropriate ordering schemes is a major challenge in mathematical morphology for vector-valued images, such as color and hyperspectral images. In this context, the irregularity issue plays a key role in designing effective morphological operators. Briefly, the irregularity follows from a disparity between the ordering scheme and a metric in the value set. Determining an ordering scheme using a metric provide reasonable approaches to vector-valued mathematical morphology. Because total orderings correspond to paths on the value space, one attempt to reduce the irregularity of morphological operators would be defining a total order based on the shortest length path. However, this paper shows that the total ordering associated with the shortest length path does not necessarily imply minimizing the irregularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17356 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shortest Length Total Orders Do Not Minimize Irregularity in Vector-Valued Mathematical Morphology Francisco, Samuel Valle, Marcos Eduardo Computer Vision and Pattern Recognition Mathematical morphology is a theory concerned with non-linear operators for image processing and analysis. The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations. Because vectors can be ordered in many ways, finding appropriate ordering schemes is a major challenge in mathematical morphology for vector-valued images, such as color and hyperspectral images. In this context, the irregularity issue plays a key role in designing effective morphological operators. Briefly, the irregularity follows from a disparity between the ordering scheme and a metric in the value set. Determining an ordering scheme using a metric provide reasonable approaches to vector-valued mathematical morphology. Because total orderings correspond to paths on the value space, one attempt to reduce the irregularity of morphological operators would be defining a total order based on the shortest length path. However, this paper shows that the total ordering associated with the shortest length path does not necessarily imply minimizing the irregularity. |
| title | Shortest Length Total Orders Do Not Minimize Irregularity in Vector-Valued Mathematical Morphology |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2306.17356 |