Segmentation-free skeletonization of gray-scale images via PDEs

A simple approach to compute the skeletons of gray-scale images using partial differential equations is presented. The proposed scheme works directly on the gray-scale images, without the necessity of pre-segmentation (binarization), or the addition of shock capturing schemes. This is accomplished by deforming the given image according to a family of modified continuous-scale erosion/dilation equations. With the scheme here proposed, the skeleton of multiple objects can be simultaneously computed. Examples on synthetic and real images are provided.