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Lessig Seminar
| What | Seminar |
|---|---|
| When |
2012-06-25 16:00
2012-06-25 17:00
2012-06-25 from 16:00 to 17:00 |
| Where | Seminar room 115, 1st floor, Rogowski building, Schinkelstr. 2 |
| Contact Name | Janssen |
| Contact Email | janssen@aices.rwth-aachen.de |
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Modern Foundations of Light Transport Simulation
Dynamic Graphics Project, California Institute of Technology
Abstract:
Light transport, sometimes also referred to as radiative transfer,
describes the propagation of visible light energy in macroscopic
environments. While applications range from medical imaging over
computer graphics to astrophysics, to this date the foundations of the
theory remain phenomenological. Utilizing recent results from various
communities, we develop the physical and mathematical structure of
light transport from Maxwell's equations by studying a lifted
representation of electromagnetic theory on the cotangent bundle. At
the short wavelength limit, this yields a Hamiltonian description on
six-dimensional phase space, with the classical formulation over the
space of "positions and directions" resulting from a reduction to the
five-dimensional cosphere bundle. We establish the connection between
light transport and geometrical optics by a non-canonical Legendre
transform, and we derive classical concepts from radiometry, such as
radiance and irradiance, by considering measurements of the light
energy density. We also show that in idealized environments light
transport is a Lie-Poisson system for the group of symplectic
diffeomorphisms, unveiling a tantalizing similarity between light
transport and fluid dynamics.
Using Stone's theorem, we also derive a functional analytic
description of light transport. This bridges the gap to existing
formulations in the literature and naturally leads to computational
questions. We then address one of the central challenges for light
transport simulation in everyday environments with scattering
surfaces: how are efficient computations possible when the light
energy density can only be evaluated pointwise? Using biorthogonal and
possibly overcomplete bases formed by reproducing kernel functions, we
develop a comprehensive theory for computational techniques that are
restricted to pointwise information, subsuming for example sampling
theorems, interpolation formulas, quadrature rules, density estimation
schemes, and Monte Carlo integration. The use of overcomplete
representations makes us thereby robust to imperfect information, as
is often unavoidable in practical applications, and numerical
optimization of the sampling locations leads to close to optimal
techniques, providing performance which considerably improves over the
state of the art in the literature.
AICES Fellow Sonia Vivas Has Passed Her Doctoral Exam
Steering Committee