On a generalization of Blaschke's Rolling Theorem and the smoothing of surfaces
Guenther Walther · Mathematical Methods in the Applied Sciences · 1999
A generalization of Blaschke's Rolling Theorem for not necessarily convex sets is proved that exhibits an intimate connection between a generalized notion of convexity, various concepts in mathematical morphology and image processing, and a certain smoothness condition. As a consequence a geometric characterization of Serra's regular model is obtained and various problems in image processing arisng from the smoothing of surfaces with Sternberg's rolling ball algorithm are addressed. Copyright © 1999 John Wiley & Sons, Ltd.