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arXiv · 2605.28619

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

Horacio Tettamanti·Giulia Guicciardi·Mattia Zanella
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Abstract

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.

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Horacio Tettamanti, Giulia Guicciardi, Mattia Zanella. 2026-05-27. A Multiscale Kinetic Framework for Image Segmentation: From Particle Systems to Continuum Models. https://arxiv.org/abs/2605.28619

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