Joint Reconstruction-Segmentation on Graphs

Jeremy M. Budd, Yves van Gennip, Jonas Latz, Simone Parisotto, Carola-Bibiane Schönlieb

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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.
Original languageEnglish
Pages (from-to)911-947
Number of pages37
JournalSIAM Journal on Imaging Sciences
Issue number2
Early online date7 Jun 2023
Publication statusPublished - Jun 2023


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

ASJC Scopus subject areas

  • Applied Mathematics
  • General Mathematics


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