• # What is skeletonization?

In many pattern recognition applications the input patterns to be analyzed are essentially "line-link".In other words, they consist of components which are essentially strokes and the relevant perceptual information is contained not in the thickness of the pieces but in their relative position to the other strokes of the pattern.

Consider the binary digital character "I" below.

A "line-link" pattern consisting of three strokes.

It consists basically of three strokes or line-link pieces(two horizontal and one vertical)connected in a certain manner. The thickness of the strokes is irrelevant to the recognition problem.What is important is the topology of how the three pieces are connected together. In such situations it is convenient to simplify the input as much as possible in order to make the topological analysis as simple as possible. One approach which is quite powerful and popular is to create a version of the pattern that is as thin as possible. For example, it would be nice to represent the pattern above as the one-pixel thick black pattern as illustrated bellow.

The skeleton of the pattern,i.e.,the thinnest representation of the original pattern that preserves the topology.

Methods to accomplish this are called thinning or skeletonization techniquesand the resulting patterns are usually referred to as skeletons.

• # Requirements to be met by a skeleton

There are some general requirements that should be met by a skeleton. let P denote a (line-link) binary pattern,i.e.,the set of "black" pixels in a digital picture represented as a square array.

• Thinness : The skeleton of P is required to consist of thin lines.
• Position : The skeleton should lie along the center of P .
• Connectivity : The skeleton should have the same connectivity (topology) as the original pattern.
• stability : Once a skeleton (or part of it) is obtained, say after n passes, it should not be eroded away by subsequent passes.

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