I recently got a new book to read, From Gestalt Theory to Image Analysis, A Probabilistic Approach by Desolneux, Moisan, and Morel. I’ve heard of Gestalt before – apparently it’s a psychology theory of the mind. There is also an image analysis angle as Gestalt is a German word for “form” or “shape”. In the introduction the book presents are few Gestalt principles and gives them a mathematical interpretation. One principle I found especially relevant.

Werthheimer’s contrast invariance principle: Image interpretation does not depend on actual values of the gray levels, but only their relative values.

As the book further explains, the principle comes from the fact that one shouldn’t expect or rely on precise measurements of intensity. Once again this is our example:

The second part of the principle suggests that one should look at the level sets of the gray scale function, as well as sub- and supra-level sets. In the blurred image above, the circle is still recognizable regardless of the low contrast. Which should be picked to evaluate the size of the circle is ambiguous however.

So far, so good. Unfortunately, next the authors concentrate on supra-level (or “upper level”) sets exclusively. This is a common approach. The result is that you recognize only light objects on dark background. To see dark on light will take an extra step (invert colors). Meanwhile the case of objects with holes (or dark spots on light objects) becomes really messy. Our algorithm builds the hierarchy of dark and- light objects in one sweep (see Topology graph).

The book isn’t really about Werthheimer’s principle but another one (more of a definition).

Helmholtz principle: Gestalts are sets of points whose (geometric regular) special arrangements could not occur in noise.

This should be interesting…