# Joint reconstruction-segmentation on graphs

arXiv: https://arxiv.org/abs/2208.05834 · HTML: https://mlsanity.com/paper/2208.05834/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 11 Aug 2022.

## Builds on (most cited first, 9 of 9)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates](https://mlsanity.com/paper/2006.11184/) (2020)
- [Calculus of the exponent of Kurdyka-Lojasiewicz inequality and its applications to linear convergence of first-order methods](https://mlsanity.com/paper/1602.02915/) (2016)
- [Task adapted reconstruction for inverse problems](https://mlsanity.com/paper/1809.00948/) (2018)
- [Multiclass Data Segmentation using Diffuse Interface Methods on Graphs](https://mlsanity.com/paper/1302.3913/) (2013)
- [Graph-based Active Learning for Semi-supervised Classification of SAR Data](https://mlsanity.com/paper/2204.00005/) (2022)
- [Convex variational methods for multiclass data segmentation on graphs](https://mlsanity.com/paper/1605.01443/) (2016)
- [NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks](https://mlsanity.com/paper/1808.04580/) (2018)
- [Graph clustering, variational image segmentation methods and Hough transform scale detection for object measurement in images](https://mlsanity.com/paper/1602.08574/) (2016)

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

- [Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation](https://mlsanity.com/paper/2402.01052/) (2024)
- [Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs](https://mlsanity.com/paper/2501.00389/) (2024)

## Abstract (arXiv)

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation, using each to guide the other. However, this work has so far employed relatively simple segmentation methods, such as the Chan--Vese algorithm. In this paper, we present a method for joint reconstruction-segmentation using graph-based segmentation methods, which have been seeing increasing recent interest. Complications arise due to the large size of the matrices involved, and we show how these complications can be managed. We then analyse the convergence properties of our scheme. Finally, we apply this scheme to distorted versions of ``two cows'' images familiar from previous graph-based segmentation literature, first to a highly noised version and second to a blurred version, achieving highly accurate segmentations in both cases. We compare these results to those obtained by sequential reconstruction-segmentation approaches, finding that our method competes with, or even outperforms, those approaches in terms of reconstruction and segmentation accuracy.