Point cloud segmentation through spectral clustering

Spectral clustering is a powerful technique in data analysis. We extend the spectral clustering method to point cloud segmentation. By connecting each point with its neighbors and assigning the edge a weight that describes the similarity, the point cloud can be represented as a graph. Then segmentation problem can be turned into a graph min-cut problem, which is NP hard. If we cut this graph into p parts, spectral clustering provides a relaxed solution in space R^n×p. A novel approach is presented to find the neighbors of a point in the point cloud, which is adaptive to the sampling density of point cloud and is more accurate than the k-nearest neighbors on close-by surface sheets. A bilateral filter is used to guarantee that only the close points with similar normal directions having high weights. By removing redundant eigenvectors from the spectral domain, the segmentation solution is found in a lower dimensional space. We prove that this method is theoretically reasonable and experimental results show the efficiency.