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

arXiv: https://arxiv.org/abs/1704.08218 · HTML: https://mlsanity.com/paper/1704.08218/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2017.

## Built on by (most cited first, 3 of 3)

- [PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks](https://mlsanity.com/paper/2307.09039/) (2023)
- [Double-well Net for Image Segmentation](https://mlsanity.com/paper/2401.00456/) (2023)
- [A Registration-Based Star-Shape Segmentation Model and Fast Algorithms](https://mlsanity.com/paper/2508.07721/) (2025)

## Abstract (arXiv)

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.