AKA the Leopold Szondi Test.

A projective-type psychology test invented by Leopold Szondi (AKA Lipót Szondi) (1893-1986). Szondi believed that many personality traits were genetic, and furthermore that you could link specific traits to specific physical appearances. He also believed in genotropism, the idea that people with similar genetics would be attracted to each other.

Putting these together, he developed a test in which subjects were shown 48 photographs of various people, and asked which two they liked best, and which two they liked least. Unbeknownst to the subject, these photographs were all of 'mental patients' -- homosexuals, sadists, epileptics, paranoiac, etc. The photographs you chose told what types of drives were dominant in your personality.

Szondi was testing for what he believed were the eight basic types of disorders, paired in sets of opposites: homosexual and sadist, epileptic and hysteric, catatonic and paranoid schizophrenic, depressive and manic. These were the complete set of driving forces behind human personality; the pictures were of people who represented extreme and 'pure' examples of these drives.

The Szondi test was big in the 50s and 60s, but has decreased significantly in popularity since then. It is still holding out, just barely, and more in Europe than America. Recently Jaakko G. Borg published Szondi's Personality Theory in The Year 2000, in which he attempts to put forth a quantitative scoring system, and measure its effectiveness with experiments using identical twins (genetic determinism is still an important part of the theory behind the test). He finds that this new modified Szondi test is quite efficient when compared to other projective tests.

This site has more information, and this site shows some of the pictures used.

I do not mean to suggest that this theory is anything other than nonsense.
I just like to report on weird things.