# Variational Image Segmentation Model Coupled with Image Restoration Achievements

arXiv: https://arxiv.org/abs/1405.2128 · HTML: https://mlsanity.com/paper/1405.2128/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2014.

## Built on by (most cited first, 2 of 2)

- [Variational volume reconstruction with the Deep Ritz Method](https://mlsanity.com/paper/2508.08309/) (2025)
- [Self2Seg: Single-Image Self-Supervised Joint Segmentation and Denoising](https://mlsanity.com/paper/2309.10511/) (2023)

## Abstract (arXiv)

Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models. Utilizing image restoration aspects, the proposed segmentation model can effectively and robustly tackle high noisy images, blurry images, images with missing pixels, and vector-valued images. In particular, one of the most important segmentation models, the piecewise constant Mumford-Shah model, can be extended easily in this way to segment gray and vector-valued images corrupted for example by noise, blur or missing pixels after coupling a new data fidelity term which comes from image restoration topics. It can be solved efficiently using the alternating minimization algorithm, and we prove the convergence of this algorithm with three variables under mild condition. Experiments on many synthetic and real-world images demonstrate that our method gives better segmentation results in comparison to others state-of-the-art segmentation models especially for blurry images and images with missing pixels values.