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solutions are no longer valid on these collision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:
By Huseyin Tek and Benjamin B. Kimia