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.
翻译:实际图像分割任务涉及从噪音、扭曲和(或)不完整的观测中重建的图像。 解决这些任务的最近方法是用这种分离来联合进行这种重建,使用每种方式来指导另一种方式。 但是,迄今为止,这项工作采用了相对简单的分割方法,如Chan-Vese算法。 在本文中,我们提出了一个使用基于图形的分割方法进行联合重建分割的方法,这些方法最近引起了越来越多的兴趣。由于所涉及的矩阵体规模很大,产生了一些问题,我们说明了如何处理这些复杂问题。然后我们分析了我们计划的融合特性。最后,我们用这个方法来分析从先前基于图形的分割文献中熟悉的“两头牛”图像的扭曲版本,先是高度注解的版本,第二是模糊版本,在两种情况下都实现了高度准确的分割。我们把这些结果与通过按顺序重组划分方法获得的结果进行比较,发现我们的方法在重建和分割准确性方面与这些方法相冲突,甚至有悖。