We here consider deformation on simple minimal 4-connected path, and its possible deformations inside this set of paths. Elementary deformations are :

1) the flip of a corner,

2) the removal of a bump

3) the creation of a bump on a flat part

We also define the energy of such a path by the euclidean length of its minimum length polygon considering that the bounds are given by the borders obtained when moving a unit square along the contour.

Eventually the optimization scheme is either to take the deformation that bring the lower energy (requires to compute all of them), or to take the first one diminishing the energy (depends on how the deformations are listed, but does nice computational saving).

One of the most important properties is that all deformations diminishing the energy converge toward a minimal energy stable state. This property will be explained in a draft for the DGCI'09 conference.

Future works will focus on formulations of classical energy terms and the use with topological maps of these deformable model.