Geometric diffusion as a classifier

Geometric diffusion of quantum trajectories

A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. ...

Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scale...

Some Geometric Aspects in Diffusion Theory

Adaptive Surfaces Fairing by Geometric Diffusion

In triangulated surface meshes, there are often very noticeable size variances (the vertices are distributed unevenly). The presented noise of such surface meshes is therefore composite of vast frequencies. In this chapter, we solve a diffusion partial differential equation numerically for noise removal of arbitrary triangular manifolds using an adaptive time discretization. The proposed approa...

Diffusion of Geometric Affinity for Surface Integration

A combinatorial method is used to reconstruct a surface by integrating a field of surface normals. An affinity function is defined over pairs of adjacent locations. This function is based on the surface’s principal curvature directions, which are intrinsic and can be estimated from the surface normals. The values of this locally supported function are propagated over the field of surface normal...