Confocal ellipse-based distance and confocal elliptical field for polygonal shapes

The paper introduces a novel confocal ellipse-based distance (CED), that is based on the properties of the confocal ellipses. This distance is used to produce a confocal elliptical field (CEF). The Euclidean Distance Transform (EDT) of a single point (called seed) generates a distance field of concentric circles. The sum of two such distance fields of two distinct seed points produces a distance field of confocal ellipses. This fact enables to adapt CED and CEF to the discrete case, referred to as CED­DT and CEF-DT. The properties of the CEF and CEF-DT make them useful for skeletonization, in particular for efficient removal of the spurious branches.