Joint reconstruction-segmentation on graphs

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.

arXiv comment33 pages, 20 figures

References in corpus (9)

• Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising
• Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods
• Mean curvature, threshold dynamics, and phase field theory on finite graphs
• Task adapted reconstruction for inverse problems
• Enhancing joint reconstruction and segmentation with non-convex Bregman iteration
• Graph clustering, variational image segmentation methods and Hough transform scale detection for object measurement in images
• Classification and image processing with a semi-discrete scheme for fidelity forced Allen--Cahn on graphs
• NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks
• Graph MBO as a semi-discrete implicit Euler scheme for graph Allen-Cahn flow