Kinetic Methods for Consensus-Based Segmentation

Speaker: Horacio Tettamanti, Department of Mathematics, University of Pavia, Italy

Abstract: Image Segmentation is a fundamental task in the context of image processing and computer vision that consists of partitioning an image into subsets of pixels that share similar properties so as to facilitate the analysis and interpretation of the visual data. The application of image segmentation methods plays an important role in clinical research by facilitating the study of anatomical structures, highlighting regions of interest, and measuring tissue volume. In this talk Mr. Tettamanti will present a new approach based on Consensus-Based Models for the Image Segmentation task. By considering the pixels of an image as an interacting system where each particle is characterized by its space position and a feature determining the gray level, a virtual interaction between the particles will then determine the asymptotic formation of a finite number of clusters. Hence, a segmentation mask is generated by assigning the mean of their gray levels to each cluster of particles and by applying a binary threshold. Among the various nonlinear compromise terms that have been proposed in the literature, we will consider the Hegselmann–Krause model, where it is supposed that each agent may only interact with other agents that are sufficiently close. Mr. Tettamanti will discuss the various aspects of the model starting from the theoretical structure introducing an extension of the classical opinion formation model and its derivation based on the methods of kinetic theory. Furthermore, he will present the numerical method employed to obtain the stationary state based on the DSMC (Direct Simulation Monte Carlo) method and its computational complexity showing the advantage of this method based on the Nanbu version of the algorithm. We focus on the analysis of brain tumor MRI scans where we look to locate the brain tumor region posing an optimization process where we fit the model parameter to fit the ground truth segmentation mask. I will introduce the different loss functions typically used in the context of biomedical images analysis and the impact on the resulting segmentation mask. Finally, we will mention some future works perspective that are being taken in this direction. This work has been done with the collaboration of Fondazione Mondino.

Biography: Horacio Tettamanti received his Physics degree in 2024 at the University of Buenos Aires where he worked in the resolution of Blow-up type PDEs through the use of Physics Informed Neural Network. In October, 2024 he began his PHD under the supervision of Prof. Mattia Zanella at the University of Pavia and its currently working in various of applications of interacting agent-based systems.

Host: Prof. Michael Multerer