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

In the forensic sciences it is inferred that human individuals are unique and thus can be reliably identified. The concept of individual uniqueness is claimed to be unprovable because another individual of same characteristics may exist if population size were infinite. It is proposed to replace "unique" with "singular" defined as a situation when only one individual in a specific population has a particular set of characteristics. The likelihood that in a population there will be no duplicate individual with exactly the same set of characteristics can be calculated from datasets of relevant characteristics. 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.