Wavelets and Digital Geometry Processing

Friday, June 6, 2003 - 2:30pm - 3:20pm
Keller 3-180
Wim Sweldens (Alcatel-Lucent Technologies Bell Laboratories)
Over the last 50 years we have seen a tremendous evolution in digital signal processing. As computers become more and more powerful they are able to deal with ever increasing amounts of digitized media. So far we have witnessed three waves: audio (1D), images (2D), and video (3D). Each wave of digitization comes with its own need for algorithms and sets off a new branch of digital signal processing. Today a forth wave in digital signal processing is emerging: digital geometry processing. New technology exist for quickly and accurately acquiring 3D geometry of objects: A sub-millimeter digitization of Michelangelo's David for example consists of over one billion samples. While audio, images, and video are defined on Euclidean geometry and therefore often used Fourier based algorithms, this no longer works for digital geometry. We will describe new multiresolution and wavelet based geometry representations and show how they are used to build a digital geometry processing toolbox, including denoising, filtering, editing, morphing, and compression.