Chapter 1 PROJECTIVE JOINT INVARIANTS FOR MATCHING CURVES IN CAMERA NETWORKS

A novel method is presented for distributed matching of curves across widely varying viewpoints. The fundamental projective joint-invariants for curves in the real projective space are the volume cross-ratios. A curve in m-dimensional projective space is represented by a signature manifold comprising n-point projective joint invariants, where n is at least m + 2. The signature manifold can be used to establish equivalence of two curves in projective space. However, without correspondence information, matching signature manifolds is a computational challenge. Our approach in this chapter is to first establish best possible correspondence between two curves using sections of the invariant signature manifold and then perform a simple test for equivalence. This allows fast computation and matching while keeping the descriptors compact. The correspondence and equivalence of curves is established independently at each camera node. Experimental results with simulated as well as real data are provided.