We have developed 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 propagatiion 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When two or more wavefront collides with each other the singularities (shocks) form and analytic solutions are no longer valid on these collision points.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 shockwaves.

Thus, our method is based on the propagation of wavefronts and shockwaves on the discrete domain.

    Discrete Wave Front Propagation:

•                Illustration of sub-pixel propagation

    Shock Propagation:

•               Example1: 2D shape with curvature discontinuities
•               Example2: 2D smooth shape