A ridge-following algorithm for finding the skeleton of a fuzzy image

A typical method for finding the skeleton of a grayscale image is to threshold the image, then thin the result with one of several binary thinning algorithms. This process loses information in the intensity dimension by reducing all intensities to either one of two values. The loss of intensity information causes the skeleton of non-uniform grayscale images to be centrally located within the thresholded image, but may not lie along the maximum intensity ridge-line. In this paper we propose a method that avoids thresholding; instead we transform the grayscale image into a fuzzy set and use the degree of membership in the underlying object to find the skeleton along the maximum intensity ridge-line. Topographical labeling methods find a ridge-line by topographically labeling pixels; the ride-line is the union of peak, ridge and saddle-point pixels. These methods require preprocessing, or postprocessing, to find connected single pixel skeletons. We show the results of our algorithm on images varying in uniformity from a Gaussian-smoothed binary rectangle to a scanned image of a grayscale object. We compare results with the threshold-and-thin, and topographical labeling methods.