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:

Skeleton by openings

Lantuéjoul's formula

Continuous images

In (Lantuéjoul 1977), Lantuéjoul derived the following morphological formula for the skeleton of a continuous binary image : where \ominus and \circ are the morphological erosion and opening, respectively, \rho B is an open ball of radius \rho, and \overline B is the closure of B.

Discrete images

Let {nB},, 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, the skeleton S(X) is the union of the skeleton subsets {S_n(X)}, , where:

Reconstruction from the skeleton

The original shape X can be reconstructed from the set of skeleton subsets {S_n(X)} as follows: Partial reconstructions can also be performed, leading to opened versions of the original shape:

The skeleton as the centers of the maximal disks

Let nB_z be the translated version of nB to the point z, that is,. A shape nB_z centered at z is called a maximal disk in a set A when: Each skeleton subset S_n(X) consists of the centers of all maximal disks of size n.

Performing Morphological Skeletonization on Images

Morphological Skeletonization can be considered as a controlled erosion process. This involves shrinking the image until the area of interest is 1 pixel wide. This can allow quick and accurate image processing on an otherwise large and memory intensive operation. A great example of using skeletonization on an image is processing fingerprints. This can be quickly accomplished using bwmorph; a built-in Matlab function which will implement the Skeletonization Morphology technique to the image. The image to the right shows the extent of what skeleton morphology can accomplish. Given a partial image, it is possible to extract a much fuller picture. Properly pre-processing the image with a simple Auto Threshold grayscale to binary converter will give the skeletonization function an easier time thinning. The higher contrast ratio will allow the lines to joined in a more accurate manner. Allowing to properly reconstruct the fingerprint. skelIm = bwmorph(orIm,'skel',Inf); %Function used to generate Skeletonization Images