Title: Partial Differential Equations In Image Processing
Time: 4:00pm, July 5 (Thursday)
Venue: Meeting room 210, 2ndfloor, Democratic Building
Abstract of report: In this talk, I will give an introduction of basic PDE concepts and methods as well as an overview of applications to image processing. In particular, I will discuss PDE models for image segmentation and present an advanced PDE method (Distance Regularized Level Set Evolution), developed recently for image segmentation.
Professor Gui Changfeng is a Dan Parman Endowed Professor of University of Texas at San Antonion, chair professor under the Chang Jiang Scholars Program of the Ministry of Education, expert under the Thousand Talents Plan, and AMS fellow.
Area of research:
Nonlinear partial differential equations, applied mathematics and image processing.
Graduated from Peking University with abachelor degree in mathematics in 1984;
Graduated from Peking University with a master degree in 1987;
Graduated from University of Minnesota with a doctor degree in 1991;
Research Achievement Award of the Pacific Institute for the Mathematical Sciences (PIMS);
CRM Aisensdadt Prize;
IEEE Best Paper Award;
NSFC overseas cooperation fund (Joint Research Fund for Overseas Chinese);
50+ publications on such world-leading academic journals as Annals of Mathematics, Communications on Pure and Applied Mathematics;
Validations of the De Giorgi’s conjecture in dimension 2 and the Gibbons conjecture in dimension 3 with Professor Nassif Ghoussoub; their achievements has great effect on the study of the related problems.
Discovery of the general Liouville nature of the first-category second-order elliptic partial differentiator and establishment of the internal relations between such nature and the De Giorg conjecture; this project has proposed a new way regarding the symmetry research of the overall solution to nonlinear partial differential equations;
Validations of the Gibbons conjecture in all dimensions with Martin Barlow and Rich Bass; this project has furthered the understanding of the general Liouville nature of the second-order elliptic partial differentiator and revealed the relations between such nature and the random process. The discovery of this new type of Liouville’s theorem is pioneering in the research field of analytical mathematics. Such new theorem and method has a significant influence on the research of the partial differential equations theory and random mathematics.
Other remarkable achievements in the research of multi-peak solutions to the nonlinear Neumann problems and Schrödinger equation.