Representing plane closed curves with Hartley descriptors

We present a new method of synthesis and analysis of closed curves based upon the real Hartley transform. We have already shown elsewhere that periodic functions can be described by Hartley series. We show here that these Hartley series can be used to represent real closed curves with real coefficients. We introduce the real Hartley descriptors in the tangential and the polar representations, as well as in the polygonal representation. We extend the theory to the complex Hartley descriptors in the case of a complex representation. We then study the problem of normalization of these descriptors in the case of polar and complex representations. Finally we present results obtained in the area of classification and pattern recognition