ABSTRACT
In this chapter we present several variational models for the decomposition of an image f into a cartoon component u and a texture component v, inspired by ideas proposed by Meyer [236]. This topic has been of much interest in recent years. The models discussed here can be seen as extensions and generalizations of those presented in Chapter 3, now applied to the separation of cartoon from texture. The cartoon component u should be a simplified version of the image f and can be seen as a piecewise-smooth image made of homogeneous regions with sharp boundaries. Such cartoon component u can be modeled by a function in the space BV of functions of bounded variation, or in its closed subspace, SBV. The texture component v should contain the small oscillatory features of the image f and can be represented by a function (or distribution) belonging to a larger or rougher space, such as Lp or a dual space of distributions. However, when the oscillatory component v belongs to a dual space of distributions, difficulties arise in the numerical computation of the decomposition. This chapter presents an overview of existing cartoon+texture models in variational form and a simpler one, together with experimental results.
