A Short- Time Beltrami Kernel for Smoothing Images and Manifolds

Heat Kernel Smoothing of Anatomical Manifolds via Laplace-Beltrami Eigenfunctions

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green’s function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. The Green’s function is then used in explicitly constructing heat kernel smoothing as a series expansion of the eigenfunctions. Unlike many previous ...

Heat Kernel Smoothing Using Laplace-Beltrami Eigenfunctions

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansi...

Efficient Beltrami Flow Using a Short Time Kernel

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Smoothing images via the Beltrami flow in Hilbert space

The Beltrami flow is an effective tool for smoothing images in many computer vision tasks. However, a deep problem that is how to set the right embedding space is not solved in the Beltrami framework. In this paper, we attempt to find a suitable embedding space by a nonlinear map. First, the image space is mapped into a high-dimensional feature space whose dimension may be infinite. Then the Be...