# A Multiscale Kinetic Framework for Image Segmentation: From Particle Systems to Continuum Models

arXiv: https://arxiv.org/abs/2605.28619 · HTML: https://mlsanity.com/paper/2605.28619/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 13 of 13)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [A Review Paper: Noise Models in Digital Image Processing](https://mlsanity.com/paper/1505.03489/) (2015)
- [A consensus-based global optimization method for high dimensional machine learning problems](https://mlsanity.com/paper/1909.09249/) (2019)
- [Polarized consensus-based dynamics for optimization and sampling](https://mlsanity.com/paper/2211.05238/) (2022)
- [Boltzmann type control of opinion consensus through leaders](https://mlsanity.com/paper/1405.0736/) (2014)
- [CBX: Python and Julia packages for consensus-based interacting particle methods](https://mlsanity.com/paper/2403.14470/) (2024)
- [Kinetic description of optimal control problems and applications to opinion consensus](https://mlsanity.com/paper/1401.7798/) (2014)
- [Opinion dynamics over complex networks: kinetic modeling and numerical methods](https://mlsanity.com/paper/1604.00421/) (2016)
- [Unsupervised Image Segmentation using the Deffuant-Weisbuch Model from Social Dynamics](https://mlsanity.com/paper/1604.04393/) (2016)
- [A kinetic approach to consensus-based segmentation of biomedical images](https://mlsanity.com/paper/2211.05226/) (2022)
- [Understanding the Impact of Evaluation Metrics in Kinetic Models for Consensus-based Segmentation](https://mlsanity.com/paper/2412.03458/) (2024)
- [Agent-Based Optimal Control for Image Processing](https://mlsanity.com/paper/2510.16154/) (2025)

## Abstract (arXiv)

In this work, we present a multiscale kinetic framework for consensus-based image segmentation. By interpreting an image as a system of interacting particles, each pixel is characterised by its spatial position and an internal feature encoding color information. We introduce a coupled interaction scheme governing the evolution of particles in both position and feature spaces, from which we derive a kinetic formulation for the particle density in the space-feature domain combining transport, aggregation, and diffusion effects. Furthermore, through a suitable scaling, we obtain a first-order macroscopic model describing the evolution of the fraction of pixels carrying information on the fraction of pixels having a certain feature. Based on this reduced-complexity model, we present a data-oriented approach where we make use of particle-based optimisation techniques for the accurate segmentation of images. Numerical tests show the effectiveness of the proposed framework and its robustness under different noise conditions.