Understanding the Impact of Evaluation Metrics in Kinetic Models for Consensus-Based Segmentation

In this article, we extend a recently introduced kinetic model for consensus-based
segmentation of images. In particular, we will interpret the set of pixels of a 2D image
as an interacting particle system that evolves in time in view of a consensus-type process
obtained by interactions between pixels and external noise. Thanks to a kinetic formulation
of the introduced model, we derive the large time solution of the model. We will show
that the parameters defining the segmentation task can be chosen from a plurality of loss
functions that characterize the evaluation metrics.