pHarmonic Map Heat Flows and Applications to Color Image Denoising 【2012.11.2 10:00am,Z311】 
【大 中 小】【打印】【关闭】 
20121031
Colloquia & Seminars
Speaker

Prof. Xiaobing H. Feng,Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, U.S.A.

Title

pHarmonic Map Heat Flows and Applications to Color Image Denoising

Time

2012.11.2 10:00am

Venue

Z311

Abstract

Color images can be described mathematically by $3$dimensional vectorvalued image functions. The three components of a vectorvalued image function represent respectively the compositions/intensity of three primary colors, namely, red (R), green (G), and blue (B). An interesting and intensely studied question is how to extend the successful PDE and variational methods for gray image processing to color image processing. Apparently, there is no unique way for achieving the goal. Moreover, as the trivial adaptation of the methods for gray image processing to color image processing by treating the RGB channels independently would give unsatisfactory results in general, more advanced and sophisticated approaches and methods must be developed for color image processing.
In this talk I shall first introduce a variational and PDE method for color image denoising based on the chromaticity and brightness decomposition. The method consists of the standard TV (total variation) model for denoising the brightness and a cTV (color TV) model for denoising chromaticity. The cTV models then lead to very interesting variational and PDE problems of pharmonic maps, linear growth maps, and their corresponding heat flows. I shall then give an overview of recent developments in heat flows for linear growth maps into the unit sphere, in particular, I shall discuss a newly developed BV (bounded variation) weak solution theory for the 1harmonic map heat flow. Finally, I shall come beck to applications of these geometric flows to color image denoising based on the chromaticity and brightness decomposition. I shall also present some numerical methods and computer simulations for the proposed color image denoising models.

Affiliation



