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 traditional spectral algorithms for segmentation.

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，它旨在利用由图定义的代价函数对图像进行分割。尽管谱方法在数学上具有吸引力，但由于其实际应用中的问题和性能欠佳，传统上被科学界所忽视。本文采用一种基于向简单网格图添加额外节点的稀疏图构建方法。其中，网格编码了像素的空间排列，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光谱图像分割方法，且其解具有可解释性。我们的实验也证明，所提出的方法在分割性能上优于传统谱算法。