On the amount of data required for reliable recognition

Many recognition procedures rely on the consistency of a subset of data features with an hypothesis, as the sufficient evidence to the presence of the corresponding object. We analyze here the recognition and localization tasks using a probabilistic model and provide expressions for the sufficient size of such data subsets, that, if consistent, guarantee the validity of the hypotheses with arbitrary confidence. We focus on 2D objects and the affine transformation class, and provide, for the first time, an integrated model, which takes into account the shape of the objects involved, the accuracy of the data collected, the clutter present in the scene, the class of the transformations involved, the accuracy of the localization, and the confidence we would like to have in our hypotheses