Semi-local projective invariants for the recognition of smooth plane curves

TLDR: The strengths and weaknesses of a number of semi-local methods for describing plane, non-algebraic curves in a projectively invariant fashion are compared on the basis of the same images and edge data.

Abstract: Recently, several methods have been proposed for describing plane, non-algebraic curves in a projectively invariant fashion. These curve representations are invariant under changes in viewpoint and therefore ideally suited for recognition. We report the results of a study where the strengths and weaknesses of a number of semi-local methods are compared on the basis of the same images and edge data. All the methods define a distinguished or canonical projective frame for the curve segment which is used for projective normalisation. In this canonical frame the curve has a viewpoint invariant signature. Measurements on the signature are invariants. All the methods presented are designed to work on real images where extracted data will not be ideal, and parts of curves will be missing because of poor contrast or occlusion. We compare the stability and discrimination of the signatures and invariants over a number of example curves and viewpoints. The paper concludes with a discussion of how the various methods can be integrated within a recognition system.