# Approximating Condorcet Ordering for Vector-valued Mathematical Morphology

arXiv: https://arxiv.org/abs/2509.06577 · HTML: https://mlsanity.com/paper/2509.06577/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 24 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 1 of 1)

- [Soft Condorcet Optimization for Ranking of General Agents](https://mlsanity.com/paper/2411.00119/) (2024)

## Abstract (arXiv)

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.