Estimating correspondence between multiple cameras using joint invariants

The joint invariants of the projective group PSL(3,R) on R², the five-point volume cross-ratios, are studied to address the problem of correspondence in a camera network. The distribution of cross-ratios over the unit square as well as in a small local-neighbourhood of a reference point are found to have a heavy tail. No cross ratio value is unique but the collection of five point cross ratios generated by taking all possible combination of five points completely prescribes the curve. Sections of the signature submanifold that admit large enough variation of cross ratios are found to be sufficient in providing correspondence across wide perspectives. Such invariant signatures may be collected independently at cameras with different viewpoints and shared, thereby achieving the registration of objects in the image. Experimental results with license plate database are provided.