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

Abstract

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.

Auditory Spatial Perception: Auditory Localization

“…The resulting localization cue is frequently referred to as the interaural envelope difference (IED). In a similar fashion, the IID cues have been found to be important for the localization of low frequency sounds in the case of near-field sound sources Shinn-Cunningham et al, 2000). See section 2.1.5 for more information on the differences in the localization of far-and near-field sound sources.…”

Influence of aging on human sound localization

“…BB and limBB stimuli activated all known spatial channels (ITD, IID, and elevation-dependent spectral cues). LP targets provided ITDs but no usable IIDs as the target array was located sufficiently far (Ͼ1 m away) from listeners (Brungart and Rabinowitz 1999;Shinn-Cunningham et al 2000). HP, limHP, and uHP targets selectively emphasized IID and spectral cues and were broad enough in bandwidth to preclude utilization of envelope ITD cues in free-field localization (Macpherson and Middlebrooks 2002;McFadden and Pasanen 1976).…”

Three-dimensional Sound Source Localization Using Inter-channel Time Difference Trajectory

“…For the sources with azimuth angles within − θ R , 0 , the propagation to the rotating microphone corresponds to case 3. The transition from case 1 to case 2 occurs when the rotating microphone passes θ b and the subsequent transition from case 2 to case 1 occurs at π + θ b , where θ b is defined in equation (14). For the sources with azimuth angles within 0, + θ R , the transition from case 1 to case 2 occurs at θ b and the consecutive transition from case 2 to case 1 occurs…”

“…Except for circumstances in which directional microphones are used, if only two microphones are used and their locations do not change with time, 3-D SSL is not possible, because front-back confusion occurs due to the existence of many directions sharing the same localization cues, even for a single SSL [13,14]. This is called the cone-of-confusion in 3-D space.…”