Total Variation Applications in Computer Vision

TL;DR

This paper provides an overview of total variation regularization in computer vision, explaining its mathematical basis, applications, and how it preserves edges in images while controlling noise.

Contribution

It offers a comprehensive review of TV regularization methods, their mathematical foundations, and practical applications in image processing.

Findings

TV regularization effectively preserves edges in images.

The scalar parameter mbda controls the regularization strength.

Various practical implementations of TV regularization are discussed.

Abstract

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.