The problem of jointly segmenting objects, according to a set of labels (of cardinality L), from a set of images (of cardinality K) to produce K individual 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 where \(L>1\), \(K>1\) and the segmentation problem is handled using graph cuts. Noticeably, some properties of the considered energy function are demonstrated, such as global optimality when \(L=2\) and \(K>1\), 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.

中文翻译：

---

使用MRF和图割的多层关节分割

根据一组标签（基数L）从一组图像（基数K）联合分割对象以产生K个单独的分割和一个联合分割的问题，可以作为马尔可夫随机场模型进行转换。所考虑的能量函数中的耦合项会增强各个细分与联合细分之间的一致性。但是，既没有明确讨论最小化器的最优性（至少对于特定情况而言），也不是参数的敏感性，也不是该方法相对于标准方法的鲁棒性。本文重点讨论\（L> 1 \），\（K> 1 \）并使用图割来解决分割问题。值得注意的是，证明了所考虑的能量函数的一些性质，例如\（L = 2 \）和\（K> 1 \）时的全局最优性，具有多数表决权的链接和具有朴素贝叶斯分割的链接。在合成图像和真实图像上进行的实验显示了出色的分割性能和针对嘈杂观测的更好的鲁棒性。