Discrete Skeletons from Distance Transforms in 2D and 3D

In this chapter we present discrete methods to compute the digital skeleton of shapes in 2D and 3D images. In 2D, the skeleton is a set of curves, while in 3D it is a set of surfaces and curves, the surface skeleton, or a set of curves, the curve skeleton. A general scheme could, in principle, be followed for both 2D and 3D discrete skeletonization. However, we will describe one approach for 2D skeletonization, mainly based on marking, in the distance transform, the shape elements that should be assigned to the skeleton, and another approach for 3D skeletonization, mainly based on iterated element removal. In both cases, the distance transform of the image will play a key role to obtain skeletons reflecting important shape features such as symmetry, elongation, and width.