Geometric Partial Differential Equations and Image Analysis

Thursday, September 14, 2000 - 9:30am - 10:30am
Keller 3-180
Guillermo Sapiro (University of Minnesota, Twin Cities)
This short tutorial is an introduction to the use of Geometric Partial Differential Equations (PDE's) in image processing and computer vision. This relatively new research area brings a number of new concepts into the field, providing among other things a very fundamental and formal approach to image processing. State-of-the-art practical results in problems like image segmentation, stereo, image enhancement, distance computations, and object tracking have been obtained with algorithms based on PDE formulations. We develop the PDE approach, starting with curves and surfaces deforming with intrinsic velocities, passing through surfaces moving with image-based velocities, and escalating all the way to the use of PDE's for families of images. A large number of applications are presented, including image segmentation, shape analysis, image enhancement, stereo, and tracking. Some basic connections between PDE's among themself as well as to other more classical approaches to image processing will be discussed. This tutorial will be a useful resource for researchers and practitioners. It is intended to provide information for people investigation new solutions to image processing problems as well as for people searching for existent advanced solutions. Basic knowledge in mathematics and image processing is needed to enjoy this tutorial in an optimal form.