PSYCHOLOGICAL SCIENCE Commentary A PICTURE IS WORTH A THOUSAND WORDS: REPLY TO "ON THE DIFFICULTY OF AVERAGING FACES"

acteristics of our technique of mathematically averaging faces to produce an attractive composite face (Langlois & Roggman, 1990). He claims that our procedure compro-mises the "... ability to recover either morphologically normal faces or mental prototypes of faces " and com-promises "the ability to recover optimum structure " of faces. The problems he cites are: (1) averaging the gray values of a matrix of the whole face rather than averaging spatial locations of anatomically defined features; (2) us-ing two-dimensional rather than three~dimensionalrepre-sentations offaces; and (3) using a "mean " as a measure of central tendency rather than using a true "optimum value " or some other measure of central tendency. AVERAGING GRAY VALUES Pittenger's complaint about our averaging technique is based on two incorrect assumptions. The first assump-tion is that the gray-level representation of a face does not preserve the shapes and locations of anatomical fea-tures. In general terms, if this assumption were true, one would be unable to tell if a person had a big nose or a small nose from a black-and-white photograph of the face of that person, because a photograph is simply a gray-level representation of its subject. ' In particular, the av-eraging procedure we used for merging faces was analo-gous to, although more precise than, a multiple-exposure· photograph of several faces. Common spatial locations of dark pixels became darker and common spatial locations of light pixels became lighter. Thus, by averaging the matrices of gray values we, in effect, created a frequency map, similar to a contour map in which contrast informa-tion is preserved. Such a spatial distribution of image contours certainly preserves the "shapes and locations of anatomical features, " as it is..well known that depth, shape, and location are easily perceived from shading, contrast, andcontour information (e.g., Acton & Bovik