In model-based recognition, ad hoc techniques are used to decide if a match of data to model is correct. Generally an empirically determined threshold is placed on the fraction of model features that must be matched. We rigorously derive conditions under which to accept a match, relating the probability of a random match to the fraction of model features accounted for, as a function of the number of model features, number of image features and the sensor noise. We analyze some existing recognition systems and show that our method yields results comparable with experimental data.