Skip to content. | Skip to navigation


Sections
Document Actions

Lessig Seminar

What Seminar
When 2012-06-25
from 16:00 to 17:00
Where Seminar room 115, 1st floor, Rogowski building, Schinkelstr. 2
Contact Name Janssen
Contact Email
Add event to calendar vCal
iCal

Modern Foundations of Light Transport Simulation

Dr. Christian Lessig
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.

« September 2016 »
Su Mo Tu We Th Fr Sa
123
4567 8910
11121314151617
18192021222324
25262728 2930
Upcoming Events
Steering Committee GRS, Schinkelstr. 2a, room 101,
2016-09-28
Cid EURS Course Room 115, AICES, Rogowski,
2016-11-03
McClarren EURS Course Room 115, AICES, Rogowski,
2016-11-11
Upcoming events…
News
AICES 10-Year Anniversary 2016-09-06
Advisory Board Meeting 2016 2016-09-06
AICES Fellow Markus Krauss Has Passed his Doctoral Exam 2016-09-06
Marek Behr held a Plenary Lecture at the World Congress on Computational Mechanics in Korea 2016-09-06
Former AICES Fellow Markus Bachmayr gets a W2-Proffessorship in Bonn 2016-09-05
More news…