Entropic hashing of 3D objects using Laplace-Beltrami operator

In this paper, we present a hashing technique for 3D models using spectral graph theory and entropic spanning trees. The main idea is to partition a 3D triangle mesh into an ensemble of sub- meshes, then apply eigen-decomposition to the Laplace-Beltrami matrix of each sub-mesh, followed by computing the hash value of each sub-mesh. This hash value is defined in terms of spectral coefficients and Tsallis entropy estimate. The experimental results on a variety of 3D models demonstrate the effectiveness of the proposed technique in terms of robustness against the most common attacks including Gaussian noise, mesh smoothing, mesh compression, scaling, rotation as well as combinations of these attacks.