When the Hough transform is applied to identify an instance of a given model, the output is typically a histogram of votes cast by a set of image features into a parameter space. The next step is to threshold the histogram of counts to hypothesize a given match. The question is “What is a reasonable choice of the threshold?” In a standard implementation of the Hough transform, the threshold is selected heuristically, e.g., some fraction of the highest cell count. Setting the threshold too low can give rise to a false alarm of a given shape(Type I error). On the other hand, setting the threshold too high can result in mis-detection of a given shape(Type II error). In this paper, we derive two conditional probability functions of cell counts in the accumulator array of the generalized Hough transform(GHough), that can be used to select a scientific threshold at the peak detection stage of the Ghough.