Variational Analysis

Synonyms

Calculus of variations

Related Concepts

Total Variation; Variational Method

Definition

In mathematics, the term variational analysis usually denotes the combination and extension of methods from convex optimization and the classical calculus of variations to a more general theory [5]. However, in computer vision literature, the term is frequently encountered as just a synonym for calculus of variations. This branch of mathematics deals with the minimization of functionals, which are real-valued functions on infinite-dimensional spaces, most frequently spaces of functions.

Background

In the continuous world view, images are modeled as functions on a domain $\Omega\subset{\mathbb R}{n}$. Geometric entities like curves and surfaces are manifolds, which can be described as level sets of functions or by the characteristic functions of their interior region. Consequently, computer vision problems can often successfully be formulated as minimization problems on...