Extending the presentations in Thirion (1995, 1996), we
propose an original viewpoint for image-to-image matching,
also based on an analogy with thermodynamic concepts (see
Figure 1). Having two images to match, the main idea
is to consider the object boundaries in one image as semipermeable
membranes and to let the other image, considered
as a deformable grid model, diffuse through these interfaces,
by the action of effectors situated within the membranes.
We illustrate this concept by an analogy with Maxwell’s
demons and we contrast it with more conventional viewpoints
such as deformable models based on attraction. As we will
see, diffusing models rely mainly on the notion of polarity
(inside–outside), while attraction relies on the notion of
distance, but mixed models can be devised, and we will also
see how to translate the diffusing model concept into the
concept of attraction, with an intermediate step corresponding
to optical flow methods.