Joint Reconstruction-Segmentation on Graphs

Joint Reconstruction-Segmentation on Graphs

Budd, Jeremy M. (Universität Bonn)
van Gennip, Y. (TU Delft Mathematical Physics)
Latz, Jonas (Heriot-Watt University)
Parisotto, Simone (University of Cambridge)
Schonlieb, Carola Bibiane (University of Cambridge)

2023

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 analyze 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.

Ginzburg-Landau functional
graph-based learn-ing
image reconstruction
image segmentation
joint reconstruction-segmentation
Merriman-Bence-Osher scheme
total variation regularization

http://resolver.tudelft.nl/uuid:d0907459-9dec-4d2e-97cb-1759b3367e87

https://doi.org/10.1137/22M151546X

2024-01-01

1936-4954

SIAM Journal on Imaging Sciences (online), 16 (2), 911-947

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2023 Jeremy M. Budd, Y. van Gennip, Jonas Latz, Simone Parisotto, Carola Bibiane Schonlieb