Area Exam for Samson Timoner: Wavelets on Surfaces
In fulfillment of the "area exam" doctoral requirements:

Wavelets on Surfaces

It was my job to select and read 3 papers. I selected the following:

"Wavelets on Irregular Point Sets" Trans. R. Soc. 1999
by Daubechies Gusdov, Schroder and Sweldens
"Multiresolution Signal Processing for Meshes" Siggraph 1999
by Igor Guskov, Wim Sweldens, Peter Schroder
"Multiresolution Heirarchies On Unstructured Triangle Meshes" Compu. Geometry: Theory and Applications, 1999
by Kobbelt, Vorsatz, and Seidel

I was unable to find a good paper summarizing all the work concerning wavelets on irregular point sets. The first paper was chosen as the best among several alternatives. See Wim Sweldon's publications below for good references.
The second paper is one of the original implementations of wavelets on triangulated surfaces. A careful look through it shows that they aren't really using wavlets in the strict sense. It is really just multi-resolution processing of meshes. Still, the results are impressive.
The third paper is a different way to approach multi-resolution processing. It forms all levels simultaneously while solving a PDE.

My Work

The summary/critique I wrote.
The current version of my slides. They aren't done yet.

Here are Links with lots of useful information.

Wim Sweldon's (Bell Labs) papers are a great resource for wavelet information as well as digital geometry processing(processing surfaces) papers.

Peter Schroder's (Caltech) papers on multi-resolution modeling(graphics) and papers on multi-resolution simulation are also very interesting and very successful.

Leif Kobbelt's (Lehrstuhl für Informatik) publications cover subdivision, multi-resolution meshes and resampling. His work in "fairing" meshes seems to be referenced everywhere.

Denis Zoris (NYU) has a couple of interesting graphics publications. The smoothness of subdivision is the key in his work. Also, there is the very useful SigGraph course notes on subdividion.

Samson Timoner: samsonaimitedu