Curve matching

This talk is devoted to two related curve matching problems that have numerous applications in computer vision and shape analysis: (1) the equivalence problem of deciding whether or not two plane curves are equivalent under the actions of the projective group and its subgroups; (2) the projection problem of deciding whether a given plane curve is the image of a given space curve under central and parallel projections. I will discuss solutions to these problems based on differential and integral invariants, as well as their approximations. I will emphasize the differences between the smooth and algebraic cases.