The probabilistic framework of W.E. Grimson and D.P. Huttenlocher (1990, 1991) is adapted to evaluate analytically the probability of false alarm attached to a simple recognition algorithm, the PS-Matcher. The model is extended to anisotropic distributions image edge orientations. It provides a natural criterion for selecting automatically the major threshold in edge detection, namely, the gradient magnitude threshold, as a function of the scene complexity. The model provides a probabilistic justification to select the most reliable peak in the Hough accumulator. This analytic quantitative evaluation appears to be extremely important to discriminate between correct and wrong hypotheses, especially in the presence of clutter edges.>