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 which 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 choice of parameters defining the segmentation task can be chosen from a plurality of loss functions characterising the evaluation metrics.