Are human faces unique? A metric approach to finding single individuals without duplicates in large samples

To explore singularity, the ANSUR database which contains anthropometric measurements of 3982 individuals was used. Eight facial metric traits were used to search for duplicates. With the addition of each trait, the chances of finding a duplicate were reduced until singularity was achieved. Singularity was consistently achieved at a combination of the maximum of seven traits. The larger the traits in dimension, the faster singularity was achieved. By exploring how singularity is achieved in subsamples of 200, 500, etc. it has been determined that about one trait needs to be added when the size of the target population increases by 1000 individuals. With the combination of four facial dimensions, it is possible to achieve a probability of finding a duplicate of the order of 10−7, while, the combination of 8 traits reduces probability to the order of 10−14, that is less than one in a trillion.