Nonlinear Diffusion Scale-Spaces

Abstract

Although Gaussian scale-space is the canonical way to define a linear scale evolution, people may regard some of its properties as less desirable under certain conditions:

• (a) Semantically useful information is eliminated in the same way as noise. Since the Gaussian scale-space is completely uncommitted, one cannot incorporate image-driven information in order to bias the scale-space evolution towards a desired task, for instance edge detection.

• (b) Linear diffusion filtering dislocates edges when moving from finer to coarser scales, see e.g. Witkin (Witkin, 1983). So structures which are identified at a coarse scale have to be traced back to the original image (Witkin, 1983; Bergholm, 1987). In practice, this correspondence problem can be difficult to handle and may give rise to instabilities.