{"ID":2873396,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.06577","arxiv_id":"2509.06577","title":"Approximating Condorcet Ordering for Vector-valued Mathematical Morphology","abstract":"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.","short_abstract":"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 fo...","url_abs":"https://arxiv.org/abs/2509.06577","url_pdf":"https://arxiv.org/pdf/2509.06577v1","authors":"[\"Marcos Eduardo Valle\",\"Santiago Velasco-Forero\",\"Joao Batista Florindo\",\"Gustavo Jesus Angulo\"]","published":"2025-09-08T11:47:11Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"cs.LG\",\"cs.NE\"]","methods":"[]","has_code":false}