On PDE-based, Variational and Neural Distance Function Approximations

Fast and accurate estimation of the distance to a surface (distance to a curve in 2D) is important in various areas including redistancing or reinitialization for level-set methods, wall distance models in turbulence modeling, heterogeneous material modeling in computational mechanics, medial axis transform and Chamfer distance in imaging, FEM extensions, robot navigation and mapping, and computer graphics applications. Recently PDE-based, variational, and neural approximation techniques have become the main tools for delivering fast and accurate distance function approximation. In this talk, I will give a brief and informal overview of recent advances in developing computationally inexpensive and reliable distance function approximations.