Characterization of a 2D Face–Recognition Method based on Landmarks Position

This work is focused on the theoretical–statistical characterization of an authentication procedure for human faces that uses few face–landmarks coordinates anyway extracted from 2D face images with neutral facial–expression. The measurement uncertainty of landmarks position is due to noise sources present both in the acquisition system and in the features extraction process. This uncertainty affects the reliability of the recognition method that is expressed in terms of probability of true recognition (PTR) and false recognition (PFR). The authentication problem is approached by using a threshold method based on the Likelihood Ratio Test (LRT). It is an optimal detection technique, as according to the Neymann–Pearson (NP) theorem, that guarantees the minimum achievable PFR for a target PTR independently of the algorithm used for extracting features. In particular, this paper provides a theoretical criterion for determining the threshold value that a–priori guarantees the desired PTR from the knowledge of both measurements uncertainty and number of the used landmarks. Moreover, a given PFR value is assured on the basis of the target likeness degree to be discriminated between the probe and the gallery landmarks. Theoretical results are validated by means of Monte– Carlo simulations and are effectively applied also to experimental data of the Bosphorous database.