# Joint Image Reconstruction and Segmentation Using the Potts Model

arXiv: https://arxiv.org/abs/1405.5850 · HTML: https://mlsanity.com/paper/1405.5850/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2014.

## Built on by (most cited first, 8 of 8)

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- [Feature reconstruction from incomplete tomographic data without detour](https://mlsanity.com/paper/2202.10724/) (2022)
- [Structure Unbiased Adversarial Model for Medical Image Segmentation](https://mlsanity.com/paper/2205.12857/) (2022)
- [TPG-INR: Target Prior-Guided Implicit 3D CT Reconstruction for Enhanced Sparse-view Imaging](https://mlsanity.com/paper/2511.18806/) (2025)
- [Plasticine: A Traceable Diffusion Model for Medical Image Translation](https://mlsanity.com/paper/2512.18455/) (2025)
- [CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification](https://mlsanity.com/paper/2607.03145/) (2026)

## Abstract (arXiv)

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from 7 angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data.