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.

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