The accuracy and the reliability of 2-D object localization in pictures are investigated. The notion of normal (small) and anomalous (large) errors is introduced, and the formulas for the variance of normal errors and the probability of anomalous errors of localization are derived. In addition the structure of an optimal localization device is established for localization of an object in the presence of additive Gaussian noise. The lower bound is estimated for the signal energy per bit of measurement information. The probability of anomalous localization errors in the presence of multiple outside objects is determined, and an upper permissible bound for the intensity of the additive noise is estimated. The problem of design of the optimal filters for reliable localization of an object on a cluttered background is formulated and solved.