Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness, spectral approaches are traditionally neglected by the scientific community due to their practical issues and underperformance. In this paper, we adopt a sparse graph formulation based on the inclusion of extra nodes to a simple grid graph. While the grid encodes the pixel spatial disposition, the extra nodes account for the pixel color data. Applying the original Normalized Cuts algorithm to this graph leads to a simple and scalable method for spectral image segmentation, with an interpretable solution. Our experiments also demonstrate that our proposed methodology over performs both traditional and modern unsupervised algorithms for segmentation in both real and synthetic data.

翻译：谱聚类是解决分割问题最传统的方法之一。基于归一化割准则，该方法旨在通过图定义的目标函数对图像进行划分。尽管谱方法在数学上具有吸引力，但由于其实际问题和性能不足，科学界传统上对其关注较少。本文提出了一种基于稀疏图的构建方法，通过在简单网格图中引入额外节点实现。网格编码像素的空间分布，而额外节点则表征像素的颜色数据。将原始归一化割算法应用于该图，可得到一种简单且可扩展的谱图像分割方法，其解具有可解释性。实验结果表明，我们提出的方法在真实数据和合成数据上的分割性能均优于传统及现代无监督分割算法。