Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing

 Luminita Vese

Department of Mathematics
UCLA

Abstract:  This talk is devoted to the decomposition of a given (possibly textured) image $f$ into a sum of two components $u+v$, where $u$ is a function of bounded variation (a simplified version of $f$) while $v$ is an oscillating function, representing texture or noise. To model the textured component $v$, we use a space of oscillatory functions, defined by duality, instead of the standard $L^2$ norm. The obtained algorithm is very simple, making use of differential equations and is easily solved in practice. Finally, I will present various numerical results on real textured images, showing the obtained decomposition $u+v$. I will also illustrate how the proposed method can be used for image restoration, texture discrimination and texture segmentation.