Symmetry Detection Via Wave Propagation

We present a novel approach for symmetry detection
based on the analytic wave propagation  where the wavefront and its
singularities are explicitly represented. Huygen's construction for
the wave propagation gives the  Eikonal equation. The analytic
solution of this Eikonal equation, which models the constant speed
wavefront propagation is constructed on the places where
waves do not collide with each other. When two or more wavefront
collides with each other the singularities (shocks) form and analytic
solutions are no longer valid on these collision points. We use conservation
laws to detect and model the shocks. Conservation laws states that the
shocks forming from the collision of constant speed waves will move
as {\em shockwaves}. Thus, our method is based on the propagation of wavefronts and
shockwaves on the discrete domain.

    Discrete Wave Front Propagation:

    Shockwave Propagation:
 

By Huseyin Tek and Benjamin B. Kimia