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.