Joint reconstruction-segmentation on graphs

TL;DR

This paper introduces a graph-based joint reconstruction and segmentation method that effectively handles noisy and distorted images, outperforming sequential approaches in accuracy.

Contribution

It presents a novel joint reconstruction-segmentation scheme using graph methods, addressing large matrix challenges and analyzing convergence.

Findings

Achieves highly accurate segmentation on noisy and blurred images.

Outperforms sequential methods in reconstruction and segmentation accuracy.

Demonstrates effective management of large matrix computations.

Abstract

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.