Applied Math Seminar
Spring Quarter 2003
3:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

Friday, April 11, 2003


Luminita Vese
UCLA

PDE based image processing: an overview and some new results


Abstract:

In this talk, I will present three applications of nonlinear partial differential equations to image processing. A common technique is to derive the PDE models from energy minimization formulations. Here, the starting energy minimization problems will be: the Mumford-Shah problem for image segmentation, the total variation model of Rudin-Osher-Fatemi for image restoration, and the problem of harmonic maps. New results and new formulations based on these classical image analysis models will be presented, using the level set method of Osher-Sethian for curve evolution, and recent results of Meyer on oscillatory functions. The illustrated applications are:
1. A multi-phase level set method for image segmentation and object detection
2. Image decomposition models into cartoon plus texture
3. A new formulation for processing of directional data
The mathematical formulations, as well as experimental results, will be presented.

Seminar Main Page