The morphological skeleton defined by a conventional structuring element is not necessarily connected We propose a double structuring element method for producing morphological skeletons of a discrete binary image. The introduced main and sub-structuring elements control the size and orientation of the skeleton, where the substructuring element is a subset of the main structuring element. The resultant skeleton contains the entire skeleton by a single structuring element, which significantly improves connectivity. Furthermore, we show that the morpholgical skeleton by double structuring elements is the intersection of the two skeletons produced by the main structuring element and the divided two subsets of the original substructuring one. Connected skeletons can be obtained by successive application of the theorem starting with a small subset of the substructuring element. Original image can be reconstructed by the substructuring element as well as the main structuring one.
We will also discuss another properties of the method and clarify the relation to conventional morphological skeleton.
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