# Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities

## TL;DR

This paper introduces a novel biconvex variational model for segmenting 3D images with intensity inhomogeneities, combining total variation and multiplicative modeling to improve accuracy in challenging imaging conditions.

## Contribution

The paper proposes a new biconvex variational model with a specialized optimization method for effective 3D image segmentation under intensity inhomogeneities.

## Key findings

- Demonstrates superior segmentation performance on 3D FIB tomography images.
- Shows convergence of the proposed optimization algorithm.
- Achieves robust results in handling intensity inhomogeneities.

## Abstract

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. Our method assumes that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of our biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled by our model. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images which was indeed the motivation of our work.