Scale-invariant Mexican Hat wavelet descriptor for non-rigid shape similarity measurement

The Mexican Hat wavelet (MHW) is strictly derived from the heat kernel by taking its negative first-order derivative with respect to time t. As a solution to the heat equation that the heat kernel has a clear initial condition, the Laplace-Beltrami operator. Although the MHW descriptor can effectively characterize the model information, but it has poor robustness to the model with scale transformation, and the feature description performance is affected to some extent. Following a popular mathematical method, in this paper, we bases on the MHW to study scaling invariance and proposes a new shape descriptor, the scale-invariant Mexican Hat wavelet (SIMHW), which by logarithmic sampling and Fourier transform that obtains the expression of SIMHW in Fourier domain. The experimental results show that SIMHW has finer information description ability and stronger recognition ability, and has better robustness to various non-rigid transformations. It can correctly calculate the similarity between 3D shapes and realize the effective shape retrieval.