Scale-space vector fields for feature analysis

This paper describes a vectorial representation that can be used to assess the symmetry of objects in 2D images. The method exploits a magneto-static analogy. Commencing from the gradient-field extracted from filtered grey-scale images we construct a vector-potential. Our magneto-static analogy is that tangential gradient vectors represent the elements of a current distribution on the image plane. By embedding the image plane in an augmented 3-dimensional space, we compute the vector potential by performing volume integration over the current distribution. The associated magnetic field is computed by taking the curl of the vector-potential. The auxiliary spatial dimension provides a natural scale-space sampling of the generating current distribution; as the height above the image plane is increased, so the volume over which averaging is effected also increases. We extract edge and symmetry lines through a topographic analysis of the vector-field at various heights above the image plane. Symmetry axes are lines where the curl of the vector-potential vanishes; at edges the divergence of the vector-potential vanishes.