Signed Distance Function - Definition

Definition

If (X, d) is a metric space, the signed distance function f is defined by

f(x)=
\begin{cases} d(x, \Omega^c) & \mbox{ if } x\in\Omega \\ -d(x, \Omega)& \mbox{ if } x\in\Omega^c
\end{cases}

where

and 'inf' denotes the infimum.


Algorithms for calculating the signed distance function include the efficient fast marching method and the more general but slower level set method.

Signed distance functions are applied for example in computer vision.

Read more about this topic:  Signed Distance Function

Famous quotes containing the word definition:

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.
    William James (1842–1910)