Hough transform of special classes of curves

The Hough transform is a standard pattern recognition technique introduced between the 1960s and the 1970s for the detection of straight lines, circles, and ellipses. Here we offer a mathematical foundation, based on algebraic-geometry arguments, of an extension of this approach to the automated recognition of rational cubic, quartic, and elliptic curves. The accuracy of this approach is tested against synthetic data and in the case of experimental observations provided by the NASA Solar Dynamics Observatory mission. © 2013 Society for Industrial and Applied Mathematics.