Nonlocal Operators with Applications to Image Processing

We propose the use of nonlocal operators to define new types of flows and functionals for image processing and elsewhere. A main advantage over classical PDE-based algorithms is the ability to handle better textures and repetitive structures. This topic can be viewed as an extension of spectral graph theory and the diffusion geometry framework to functional analysis and PDE-like evolutions. Some possible applications and numerical examples are given, as is a general framework for approximating Hamilton–Jacobi equations on arbitrary grids in high demensions, e.g., for control theory.