Shape Representation and Clustering Based on Laplacian Spectrum

The spectrum of a graph has been widely used to characterize the properties of a graph and extract information from its structure. In this paper, we investigate the performance of Laplacian spectrum and multidimensional scaling (MDS) as shape recognition and clustering. Firstly, we extract boundary points to characterize the shape and to construct the Laplacian matrix. Secondly, the structural information about graph is described by using the eigenvalues of the Laplacian matrix. Finally, the given shapes are projected onto the low-dimensional space by performing MDS. Meanwhile, the clustering is achieved via analyzing the distribution of shapes. Comparative experiments on the public data sets demonstrate the validation of the proposed algorithm.