I was reading about optimization for an ill-posed problem in computer vision and came across the explanation below about optimization on Wikipedia. What I don't understand is, why do they call this optimization "Energy minimization" in Computer Vision?
An optimization problem can be represented in the following way:
Given: a function $f: A \to R$ from some set $A$ to the real numbers
Sought: an element $x_0$ in $A$ such that $f(x_0) ≤ f(x)$ for all $x$ in $A$ ("minimization") or such that $f(x_0) ≥ f(x)$ for all $x$ in $A$ ("maximization").
Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming, but still in use for example in linear programming – see History below). Many real-world and theoretical problems may be modeled in this general framework. Problems formulated using this technique in the fields of physics and computer vision may refer to the technique as energy minimization, speaking of the value of the function $f$ as representing the energy of the system being modeled.