A generalized morphological skeleton transform using both internal and external skeleton points

• We propose a generalized morphological skeleton transform.
• The new transform uses both the internal and external skeleton points.
• A shape is described in terms of disk components that need to be added and removed.
• The procedures and formulas describing the steps of the transform are developed.
• We have a more powerful framework for modeling shape approximation and reconstruction.

The morphological skeleton transform (MST) is a leading morphological shape representation scheme. In the MST, a given shape is represented as the union of all the maximal disks contained in the shape. The concept of external skeleton points and external maximal disks has been used for shape description and characterization purposes. In this paper, we develop a generalized morphological skeleton transform that combines the concepts of internal and external maximal disks into a unified framework. In this framework, a shape is described in terms of disk components that need to be added as well as disk components that need to be removed. The procedures and formulae describing the extraction of the disk components and the reconstruction of the original shape from these components are developed. The correctness of the procedures and formulae is established. This new framework seems to provide a more powerful and more natural way of modeling the approximation and reconstruction of binary shapes using primitive shape components.