# New region force for variational models in image segmentation and high dimensional data clustering

## TL;DR

This paper introduces a novel region force term for the Potts model, enhancing multi-phase image segmentation and data clustering by leveraging Bernoulli distribution-based likelihoods, with effective optimization methods and competitive results.

## Contribution

It proposes a new region force function based on Bernoulli likelihoods for variational models, improving segmentation and clustering performance.

## Key findings

- Competitive performance on benchmark problems
- Effective optimization via primal-dual and augmented Lagrangian methods
- Applicable to both image segmentation and data clustering

## Abstract

We propose an effective framework for multi-phase image segmentation and semi-supervised data clustering by introducing a novel region force term into the Potts model. Assume the probability that a pixel or a data point belongs to each class is known a priori. We show that the corresponding indicator function obeys the Bernoulli distribution and the new region force function can be computed as the negative log-likelihood function under the Bernoulli distribution. We solve the Potts model by the primal-dual hybrid gradient method and the augmented Lagrangian method, which are based on two different dual problems of the same primal problem. Empirical evaluations of the Potts model with the new region force function on benchmark problems show that it is competitive with existing variational methods in both image segmentation and semi-supervised data clustering.