Creaseness from level set extrinsic curvature

Creases are a type of ridge/valley-like structures of a d dimensional image, characterized by local conditions. As creases tend to be at the center of anisotropic grey-level shapes, creaseness can be considered as a type of medialness. Among the several crease definitions, one of the most important is based on the extrema of the level set curvatures. In 2-d it is used the curvature of the level curves of the image landscape, however, the way it is usually computed produces a discontinuous creaseness measure. The same problem arises in 3-d with its straightforward extension and with other related creaseness measures. In this paper, we first present an alternative method of computing the level curve curvature that avoids the discontinuities. Next, we propose the Mean curvature of the level surfaces as creaseness measure of 3-d images, computed by the same method. Finally, we propose a natural extension of our first alternative method in order to enhance the creaseness measure.