  The objectives of this chapter are: (i) to introduce a concise overview of
regularization; (ii) to define and to explain the role of a particular type of
regularization called total variation norm (TV-norm) in computer vision tasks;
(iii) to set up a brief discussion on the mathematical background of TV
methods; and (iv) to establish a relationship between models and a few existing
methods to solve problems cast as TV-norm. For the most part, image-processing
algorithms blur the edges of the estimated images, however TV regularization
preserves the edges with no prior information on the observed and the original
images. The regularization scalar parameter {\lambda} controls the amount of
regularization allowed and it is an essential to obtain a high-quality
regularized output. A wide-ranging review of several ways to put into practice
TV regularization as well as its advantages and limitations are discussed.
