Abstract

In data and image analysis, the data sets are often modelled as a graph in which the nodes represent the data points and the edges encode some relationship between the nodes, relevant to the task at hand. In recent years, people have studied classical continuum PDE models used in image analysis, formulated on graphs, to be applicable to data analysis problems.

These studies show interesting connections between continuum results and the analogous problems on graphs. In this talk we will focus on mean curvature. In the continuum world this concept is of great geometric importance. For example, it shows up as the first variation of the total variation functional. We will discuss the concept of curvature on graphs and, starting from our continuum intuition, discuss its relation to the Allen-Cahn equation and threshold dynamics (Merriman-Bence-Osher) scheme on graphs.