Joint Projective Invariants for Distributed Camera Networks

A novel method is presented for distributed matching across different viewpoints. The fundamental perspective invariants for curves in the real projective space are the volume cross-ratios. Probabilistic analysis of projective invariants shows that they are not unique and therefore not discriminative. However, a curve in m-dimensional Euclidean space is completely prescribed by the signature manifold of joint invariants generated by taking all possible combinations of n points on the projective curve where n is at least m + 2. Furthermore, submanifolds given by the projection of the signature manifold also represent the curve uniquely. Sections of the sub-manifolds that admit large enough variation of cross ratios are found to be sufficient, statistically, for matching of curves. Such sectional signatures allow fast computation and matching of features while keeping the descriptors compact. These features are computed independently at cameras with different viewpoints and shared, thereby achieving the matching of objects in the image. Experimental results with simulated as well as real data are provided.