LJKPhD Students Seminar

On Thursday October 25 2018 at 15h00 in Room 106  IMAG Building

Seminary of Mr Jocelyn MEYRON (Laboratoire Jean Kuntzmann)

Semidiscrete optimal transport and applications to nonimaging optics

Summary

In this seminar, we show how optimal transport theory can be used
to build a common framework to solve many optical component design problems.
In a first part, we present optimal transport, its main formulations and the
motivations behind it. We then describe in more details the socalled
semidiscrete setting where the target measure is supported on a point cloud
and explain the main numerical method we will use namely the damped Newton's
algorithm. We then look at a particular case where the source measure is
supported on a triangulation in R^3 and show the convergence with linear speed
of the damped Newton's method. The convergence is a direct consequence of the
regularity and strict motonicity of the Kantorovich functional. We also mention
some applications such as optimal quantization of a probability density over a
surface or remeshing.
In a second part, we describe the relation between optimal transport and optical
component design. In particular, we show how we can recast such problems into a
nonlinear system of equations that is a discretization of the socalled
MongeAmpĂ¨re equation. This formulation allows us to develop a generic,
parameterfree and efficient algorithm. We finish by showing numerous simulated and
fabricated examples.
