Approximating Condorcet Ordering for Vector-valued Mathematical Morphology
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918137482444800 |
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| author | Valle, Marcos Eduardo Velasco-Forero, Santiago Florindo, Joao Batista Angulo, Gustavo Jesus |
| author_facet | Valle, Marcos Eduardo Velasco-Forero, Santiago Florindo, Joao Batista Angulo, Gustavo Jesus |
| contents | Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and hyperspectral images, there is still no consensus on the most suitable vector ordering for constructing morphological operators. This paper addresses this issue by examining a reduced ordering approximating the Condorcet ranking derived from a set of vector orderings. Inspired by voting problems, the Condorcet ordering ranks elements from most to least voted, with voters representing different orderings. In this paper, we develop a machine learning approach that learns a reduced ordering that approximates the Condorcet ordering. Preliminary computational experiments confirm the effectiveness of learning the reduced mapping to define vector-valued morphological operators for color images. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06577 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximating Condorcet Ordering for Vector-valued Mathematical Morphology Valle, Marcos Eduardo Velasco-Forero, Santiago Florindo, Joao Batista Angulo, Gustavo Jesus Computer Vision and Pattern Recognition Machine Learning Neural and Evolutionary Computing Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and hyperspectral images, there is still no consensus on the most suitable vector ordering for constructing morphological operators. This paper addresses this issue by examining a reduced ordering approximating the Condorcet ranking derived from a set of vector orderings. Inspired by voting problems, the Condorcet ordering ranks elements from most to least voted, with voters representing different orderings. In this paper, we develop a machine learning approach that learns a reduced ordering that approximates the Condorcet ordering. Preliminary computational experiments confirm the effectiveness of learning the reduced mapping to define vector-valued morphological operators for color images. |
| title | Approximating Condorcet Ordering for Vector-valued Mathematical Morphology |
| topic | Computer Vision and Pattern Recognition Machine Learning Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2509.06577 |