Approximating Condorcet Ordering for Vector-Valued Mathematical Morphology

doi:10.1007/978-3-032-09544-2_32

Approximating Condorcet Ordering for Vector-Valued Mathematical Morphology

2026-01-01

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Marcos Eduardo Valle *

S

Santiago Velasco-Forero

DOI：10.1007/978-3-032-09544-2_32

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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.

Keywords:

Vector-valued mathematical morphology multivariate ordering

Condorcet ordering

neural networks

Approximating Condorcet Ordering for Vector-Valued Mathematical Morphology

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