SIAM Journal on Imaging Sciences, Volume 13, Issue 2, Page 651-684, January 2020.
Image segmentation is a fundamental research topic in image processing and computer vision. In recent decades, researchers developed a large number of segmentation algorithms for various applications. Among these algorithms, the normalized cut (Ncut) segmentation method is widely applied due to its good performance. The Ncut segmentation model is an optimization problem whose energy is defined on a specifically designed graph. Thus, the segmentation results of the existing Ncut method are largely dependent on a preconstructed similarity measure on the graph since this measure is usually given empirically by users. This flaw will lead to some undesirable segmentation results. In this paper, we propose an Ncut-based segmentation algorithm by integrating an adaptive similarity measure and spatial regularization. The proposed model combines the Parzen--Rosenblatt window method, nonlocal weights entropy, Ncut energy, and regularizer of phase field in a variational framework. Our method can adaptively update the similarity measure function by estimating some parameters. This adaptive procedure enables the proposed algorithm to find a better similarity measure for classification than the Ncut method. We provide some mathematical interpretation of the proposed adaptive similarity from multiple viewpoints, such as statistics and convex optimization. In addition, the regularizer of phase field can guarantee that the proposed algorithm has a robust performance in the presence of noise, and it can also rectify the similarity measure with a spatial priori. The well-posed theory such as the existence of the minimizer for the proposed model is given in the paper. Compared with some existing segmentation methods such as the traditional Ncut-based model and the classical Chan--Vese model, the numerical experiments show that our method can provide promising segmentation results.

中文翻译：

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基于自适应相似度和空间正则化的归一化裁剪的变分图像分割模型

SIAM影像科学杂志，第13卷，第2期，第651-684页，2020年1月。
图像分割是图像处理和计算机视觉中的基础研究主题。近几十年来，研究人员为各种应用开发了许多分割算法。在这些算法中，归一化割（Ncut）分割方法由于其良好的性能而被广泛应用。Ncut分割模型是一个优化问题，其能量在专门设计的图形上定义。因此，现有的Ncut方法的分割结果在很大程度上取决于图形上预先构造的相似性度量，因为该度量通常由用户凭经验给出。该缺陷将导致一些不希望的分割结果。在本文中，我们通过将自适应相似性度量和空间正则化相结合，提出了一种基于Ncut的分割算法。提出的模型在变分框架中结合了Parzen-Rosenblatt窗方法，非局部权重熵，Ncut能量和相场正则化器。我们的方法可以通过估计一些参数来自适应地更新相似性度量函数。与Ncut方法相比，该自适应过程使所提出的算法能够找到更好的分类相似度度量。我们从统计学和凸优化等多个角度对所提出的自适应相似性进行了数学解释。另外，相位场的正则化器可以确保所提出的算法在存在噪声的情况下具有鲁棒的性能，并且还可以利用空间先验来校正相似性度量。文中给出了很好的理论，如所提出模型的最小化器的存在。