A Pseudo-Distance Map for the Segmentation-Free Skeletonization of Gray-Scale Images

In this paper, we introduce a new tool, called a pseudodistance map (PDM), for extracting skeletons from grayscale images without region segmentation or edge detection. Given an edge-strength function (ESF) of a gray-scale image, the PDM is computed from the ESF using the partial differential equations we propose. The PDM can be thought of as a relaxed version of a Euclidean distance map. Therefore, its ridges correspond to the skeleton of the original gray-scale image and it provides information on the approximate width of skeletonized structures. Since the PDM is directly computed from the ESF without thresholding it, the skeletonization result is generally robust and less noisy. We tested our method using a variety of synthetic and real images. The experimental results show that our method works well on such images.