Classification of Rational Lemniscates in the Complex Plane

Abstract

Generalizing the work of Ebenfelt, Khavinson, and Shapiro, this study sought to find a means of classifying shapes in the complex plane by using "fingerprints" of shapes. These fingerprints are constructed to have useful properties, in that shapes will have the same fingerprint even when they are scaled in size or translated. Such a property is useful in applications such as computer imaging, where often images are zoomed or taken from a different angle, but would like to be able to identify the shapes within the image in a consistent manner.