Multiscale 2D medial axes and 3D surface skeletons by the image foresting transform

Skeletons are simplified shape representations with many applications involving image processing, analysis, and visualization. A fundamental problem in shape skeletonization is the sensitivity of the skeletons to small perturbations of the input shape, which leads to the appearance of spurious branches. By assigning an importance metric to every skeleton point, one encodes the scale of the shape details. Subsequently, simplified skeletons can be obtained by simply thresholding at continuous values of that metric. Such a multiscale regularization procedure should ideally produce one-spel-wide skeletons in all scales. In this chapter, we present a new method based on the image foresting transform framework, which achieves this result for medial axes of 2D shapes and for surface skeletons of 3D shapes. Our approach relies on simple and efficient algorithms, faster than several methods based on the same importance metric, simpler than others, far less sensitive to numerical noise than a recent one, and attains similar quality of centeredness, smoothness, thinness, and ease to simplify the skeleton. Such a conclusion is substantiated with a comparative analysis on a wide set of 2D and 3D real-word shapes against its multiscale counterparts.