Recognition of plane projective symmetry

A novel approach to grouping symmetrical planar curves under a projective transform is described. Symmetric curves are important as a generic model for object recognition where an object class is defined by the set of symmetries that any object in the class obeys. In this paper, a new algorithm is presented for grouping curves based on their correspondence under a plane projectivity. The correspondence between curves is established from an initial correspondence between two pairs of distinguished lines, such as lines tangent to inflection points. This initial correspondence leads to a reduced dimensional form for the projective mapping between the curves and a natural method for establishing correspondence between all points on the curves. A saliency measure is introduced which permits grouping results to be ordered in terms of the degree of symmetry supported by each curve pair. This saliency measure provides a basis for recognition in the case of approximate symmetry.