From the Hough Transform to a New Approach for the Detection and Approximation of Elliptical Arcs

The edges of simple geometrical (e.g., manufactured) parts can generally be approximated sufficiently accurately by straight-line segments and elliptical arcs in order, for example, to carry out a dimensional analysis of these parts, such as required by inspection tasks. Hough transforms are robust methods for the detection of straight-line segments but are not directly suitable for the detection of elliptical arcs, for which the processing time and memory space necessary are too important. We present in this paper a new method which allows the determination of the parameters of elliptical arcs (or of ellipses) by use of a two-dimensional discretized parameter space defined similarly to the usual Hough space. This new method allows both the detection and characterization of ellipses whose major and minor axis lengths can be as small as four pixels long or of elliptical arcs with a small angular aperture.