Tori of confusion: binaural localization cues for sources within reach of a listener

To a first-order approximation, binaural localization cues are ambiguous: many source locations give rise to nearly the same interaural differences. For sources more than a meter away, binaural localization cues are approximately equal for any source on a cone centered on the interaural axis (i.e., the well-known "cone of confusion"). The current paper analyzes simple geometric approximations of a head to gain insight into localization performance for nearby sources. If the head is treated as a rigid, perfect sphere, interaural intensity differences (IIDs) can be broken down into two main components. One component depends on the head shadow and is constant along the cone of confusion (and covaries with the interaural time difference, or ITD). The other component depends only on the relative path lengths from the source to the two ears and is roughly constant for a sphere centered on the interaural axis. This second factor is large enough to be perceptible only when sources are within one or two meters of the listener. Results are not dramatically different if one assumes that the ears are separated by 160 deg along the surface of the sphere (rather than diametrically opposite one another). Thus for nearby sources, binaural information should allow listeners to locate sources within a volume around a circle centered on the interaural axis on a "torus of confusion." The volume of the torus of confusion increases as the source approaches the median plane, degenerating to a volume around the median plane in the limit.