Projective and illumination invariant representation of disjoint shapes

We describe a projectively invariant representation of disjoint contour groups, which is suitable for shape-based retrieval from an image database. It consists of simultaneous polar reparametrization of multiple curves where an invariant point is used as the origin. For each ray orientation, a cross-ratio of its intersections with other curves is taken as a value associated to the radius. With respect to other methods, this representation is less reliant on single curve properties, both for the construction of the projective basis and for calculating the signature. It is, therefore, more robust to contour gaps and image noise and is better suited to describing complex planar shapes defined by multiple disjoint curves. Moreover, we show that illumination invariance fits well within the proposed framework and can easily be introduced in the representation in order to make it more appropriate for shape-based retrieval. Experiments are reported on a database of real trademarks.