The richness of natural images makes the quest for optimal representations in image
processing and computer vision challenging. The latter observation has not prevented the …

This paper systematically studies the well-known Mexican hat wavelet (MHW) on manifold
geometry, including its derivation, properties, transforms, and applications. The MHW is …

This paper gives a survey of methods for the construction of space–frequency concentrated
frames on Riemannian manifolds with bounded curvature, and the applications of these …

We present a novel kernel regression framework for smoothing scalar surface data using the
Laplace–Beltrami eigenfunctions. Starting with the heat kernel constructed from the …

This tutorial reference serves as a coherent overview of various statistical and mathematical
approaches used in brain network analysis, where modeling the complex structures and …

This paper introduces a general principle for constructing multiscale kernels on surface
meshes, and presents a construction of the multiscale pre‐biharmonic and multiscale …

In this paper, we present a powerful spectral shape descriptor for shape analysis, named
Anisotropic Spectral Manifold Wavelet Descriptor (ASMWD). We proposed a novel manifold …

The spectral graph wavelet transform (SGWT) has recently been developed to compute
wavelet transforms of functions defined on non-Euclidean spaces such as graphs. By …

Abstract 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 …

Basis functions provide a simple and effective way to interpolate signals on a surface with an
arbitrary dimension, topology, and discretisation. However, the definition of local and shape …