Multilayer Joint Segmentation Using MRF and Graph Cuts

The problem of jointly segmenting objects, according to a set of labels (of cardinalityL), from a set of images (of cardinalityK) to produceKindividual segmentations plus one joint segmentation, can be cast as a Markov random field model. Coupling terms in the considered energy function enforce the consistency between the individual segmentations and the joint segmentation. However, neither optimality on the minimizer (at least for particular cases), nor the sensitivity of the parameters, nor the robustness of this approach against standard ones has been clearly discussed before. This paper focuses on the case whereL>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L>1$$\end{document},K>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K>1$$\end{document}and the segmentation problem is handled using graph cuts. Noticeably, some properties of the considered energy function are demonstrated, such as global optimality whenL=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L=2$$\end{document}andK>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K>1$$\end{document}, the link with majority voting and the link with naive Bayes segmentation. Experiments on synthetic and real images depict superior segmentation performance and better robustness against noisy observations.