Heat Kernel Approximation on Kendall Shape Space

Spectral Approximation of the Free-Space Heat Kernel

Many problems in applied mathematics, physics, and engineering require the solution of the heat equation in unbounded domains. Integral equation methods are particularly appropriate in this setting for several reasons: they are unconditionally stable, they are insensitive to the complexity of the geometry, and they do not require the artificial truncation of the computational domain as do finit...

Volumetric heat Kernel: Padé-Chebyshev approximation, convergence, and computation

This paper proposes an accurate and computationally efficient solver of the heat equation (∂t +D)F(·, t) = 0, F(·,0) = f , on a volumetric domain, through the (r,r)-degree Padé-Chebyshev rational approximation of the exponential representation F(·, t) = exp( tD) f of the solution. To this end, the heat diffusion problem is converted to a set of r differential equations, which involve only the L...

Shape-Based Transfer Function Design Using Heat Kernel

Transfer functions have been designed based on size, texture, density, gradient and other parameters. However, design of good transfer functions based on shape still remains a challenge as it is not trivial to define shape. Heat diffusion is a process governed by the heat kernel that provides a means to obtain the shape information from the volume data and can be used in the transfer function d...

The heat kernel on R

Heat kernel analysis on graphs

In this thesis we aim to develop a framework for graph characterization by combining the methods from spectral graph theory and manifold learning theory. The algorithms are applied to graph clustering, graph matching and object recognition. Spectral graph theory has been widely applied in areas such as image recognition, image segmentation, motion tracking, image matching and etc. The heat kern...