On sampling planar curves

In this paper we address the problem of sampling and perfect reconstruction of closed planar curves belonging to a certain class. We successively study the following problems: (1) identifying the class of curves yielding perfect reconstruction from their samples and establishing efficient class identification procedures, (2) sampling and reconstruction algorithms, (3) applicability of general sampling methods to curves not satisfying the proposed model constraints. We propose a theoretically efficient and numerically implementable solution and illustrate its effectiveness with a number of examples.