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 ${\displaystyle B}$.

Let ${\displaystyle \{nB\}}$, ${\displaystyle n=0,1,\ldots }$, be a family of shapes, where B is a structuring element,

The variable n is called the size of the structuring element.

Lantuéjoul's formula has been discretized as follows. For a discrete binary image ${\displaystyle X\subset \mathbb {Z} ^{2}}$, the skeleton S(X) is the union of the skeleton subsets ${\displaystyle \{S_{n}(X)\}}$, ${\displaystyle n=0,1,\ldots ,N}$, where:

The original shape X can be reconstructed from the set of skeleton subsets ${\displaystyle \{S_{n}(X)\}}$ as follows: