Treffer: A spatially continuous max-flow and min-cut framework for binary labeling problems.

We propose and investigate novel max-flow models in the spatially continuous setting, with or without i priori defined supervised constraints, under a comparative study of graph based max-flow/min-cut. We show that the continuous max-flow models correspond to their respective continuous min-cut models as primal and dual problems. In this respect, basic conceptions and terminologies from discrete max-flow/min-cut are revisited under a new variational perspective. We prove that the associated nonconvex partitioning problems, unsupervised or supervised, can be solved globally and exactly via the proposed convex continuous max-flow and min-cut models. Moreover, we derive novel fast max-flow based algorithms whose convergence can be guaranteed by standard optimization theories. Experiments on image segmentation, both unsupervised and supervised, show that our continuous max-flow based algorithms outperform previous approaches in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Copyright of Numerische Mathematik is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)