We describe a method based on the Hough transform to compute a set of parameters that completely describe line segments. By complete, we mean the description includes the endpoints of each segment as well as the number of points along the segment, and, assuming a noise model N, the parameter(s) of N. The method involves fitting a surface locally to the Hough array, where the variables of the fit are the parameters we are looking for. In addition to providing a complete description for each segment, the computed estimates of p and 9 are better than the resolution of the Hough array H(p, 9) so that a relatively low resolution H may be used.