# Structured Sampling and Recontruction of Illumination for Image Synthesis

Structured Sampling and Reconstruction of Illumination for Image Synthesis
Doctor of Philosophy, 1994
Georgios Drettakis
Graduate Department of Computer Science, University of Toronto
Abstract
An important goal of image synthesis is to achieve accurate, efficient
and consistent sampling and reconstruction of illumination varying over
surfaces in an environment. A new approach is introduced for the
treatment of diffuse polyhedral environments lit by area light sources,
based on the identification of important properties of illumination
structure. The properties of unimodality and curvature of illumination
in unoccluded environments are used to develop a high quality sampling
algorithm which includes error bounds. An efficient algorithm is
presented to partition the scene polygons into a mesh of cells, in
which the visible part of the source has the same topology.
A fast incremental algorithm is presented to calculate the
backprojection, which is an abstract representation of this topology.
The behaviour of illumination in the penumbral regions is carefully
studied, and is shown to be monotonic and well behaved within most of
the mesh cells. An algorithm to reduce the mesh size, and an algorithm
which selects between linear and quadratic interpolants are presented.
The results show that the mesh size and the degrees of the interpolants
can be reduced without significant degradation of image quality. The
preceding algorithms are combined into a complete structured sampling
approach that allows accurate and efficient representation of
illumination using interpolating polynomials for scenes with
occlusion. Images with accurate shadows can be produced from the
structured representation using either ray-casting or polygon rendering
hardware. Finally, it is shown that our methodology generalises easily
to the global illumination problem. An iterative solution to a Galerkin
finite element approach is proposed, and it is shown how the structured
algorithms provide a good initial approximation for the iteration,
enhance efficiency for numerical integration and allow adaptive mesh
modification. The structure-driven global illumination algorithm thus
promises significant improvement over previous higher-order finite
element solutions.

## BibTex references

@PhdThesis{Dre94a, author = "Drettakis, George", title = "Structured Sampling and Recontruction of Illumination for Image Synthesis", school = "University of Toronto", month = "January", year = "1994", note = "CSRI Technical Report 293", url = "http://www-sop.inria.fr/reves/Basilic/1994/Dre94a" }