Heat Kernel Smoothing in Irregular Image Domains

We review heat kernel smoothing techniques for denoising and regressing data in irregularly shaped domains embedded in Euclidean spaces. This is a problem often encountered in functional data analysis and medical imaging. In this chapter, we present a unified mathematical framework based on the eigenfunctions of the Laplace-Beltrami operators defined on irregular domains. Numerical implementation issues will be addressed as well. Various examples will be presented. We also present few new theoretical results on the properties of heat kernel smoothing.