Scale space vector fields for symmetry detection

This paper describes a vectorial representation that can be used to assess the symmetry of objects in 2D images. The method exploits the calculus of v ector fields. Commencing from the gradient field extracted from filtered gr ey-scale images we construct a vector potential. Our image representation i s based on the distribution of tangential gradient vectors residing on the image plane. By embedding the image plane in an augmented S-dimensional spa ce, we compute the vector potential by performing volume integration over t he distribution of edge tangents. The associated vector field is computed b y taking the curl of the vector potential. The auxiliary spatial dimension provides a natural scale-space sampling of the generating edge-tangent dist ribution; as the height above the image plane is increased, so the volume o ver which averaging is effected also increases. We extract edge and symmetr y lines through a topographic analysis of the vector-field at various heigh ts above the image plane. Symmetry axes are lines of where the curl of the vector potential vanishes; at edges the divergence of the vector potential vanishes. (C) 1999 Elsevier Science B.V. All rights reserved.