Editing Color histogram (section)

==Intensity histogram of continuous data==

The idea of an intensity histogram can be generalized to continuous data, for example audio signals represented by real functions or images represented by functions with two-dimensional [[Function domain|domain]].

Let <math>f \in L^1(\mathbb{R}^n)</math> (see [[Lp space|Lebesgue space]]), then the cumulative histogram operator <math>H</math> can be defined by:
:<math>H(f)(y) = \mu\{x : f(x)\le y\}</math>.
<math>\mu</math> is the [[Lebesgue measure]] of sets.
<math>H(f)</math> in turn is a [[real function]].
The (non-cumulative) histogram is defined as its [[derivative]].
:<math>h(f) = H(f)'</math>.