Morphological skeleton

In digital image processing, morphological skeleton is a skeleton (or medial axis) representation of a shape or binary image, computed by means of morphological operators.

Morphological skeletons are of two kinds:

In (Lantuéjoul 1977), Lantuéjoul derived the following morphological formula for the skeleton of a continuous binary image ${\displaystyle X\subset \mathbb {R} ^{2}}$:

where ${\displaystyle \ominus }$ and ${\displaystyle \circ }$ are the morphological erosion and opening, respectively, ${\displaystyle \rho B}$ is an open ball of radius ${\displaystyle \rho }$, and ${\displaystyle {\overline {B}}}$ is the closure of ${\displaystyle B}$.

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