Heat Kernels for Non-Rigid Shape Retrieval: Sparse Representation and Efficient Classification

One of the major goals of computer vision and machine intelligence is the development of flexible and efficient methods for shape representation. This paper presents an approach for shape retrieval based on sparse representation of scale-invariant heat kernel. We use the Laplace-Beltrami eigen functions to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales, combined with the normalized eigen values of the Lap lace-Beltrami operator. Sparse representation is used to reduce the dimensionality of the calculated descriptor. The proposed descriptor is used for classification via the collaborative representation-based classification with regularized least square algorithm. We compare our approach to two well-known approaches on two different data sets: the nonrigid world data set and the SHREC 2011. The results have indeed confirmed the improved performance of the proposed approach, yet reducing the time and space complicity of the shape retrieval problem.