Binaural independence indices and the edges of auditory images

The edge model is uniquely consistent with spatial hearing when spatial cues are broadly distributed over time, prompting auditory images or their edges to ‘split apart’.

Below, we consider four models of spatial hearing: 1) edge, 2) maximal, 3) inter-hemispheric channel, and 4) acoustic cross-correlation, as binaural independence indices are varied.

• • An independence index of 0 indicates that the same noise-bursts are played in the left and right ears, prompting spatial cues to recur over time.
• • An independence index of 1 indicates that the noise-bursts are statistically independent (dichotic), prompting broad distributions of spatial cues over time.
• • Intermediate independence indices are described by the equations: L = a∙(1-index)+b∙(index) and R = a∙(1-index)+c∙(index), where a, b, and c are statistically independent noises and the resulting left and right noise-bursts (L and R) are scaled to have amplitudes equal to those of a, b, and c.

Listen to examples of varying binaural independence  here or test yourself in an online psychoacoustic experiment.

notes:

• • The exact independence index at which half-maximal representations become distinct, under the edge model, depends on many factors, including the shapes of auditory filters and the shapes of neurons selective of interaural phase differences. 
• • An independence indices of 3 corresponds to a cross-correlation value of ~0.5.
• • Half-maximal and maximal representations were averaged over a 5 sec. noise-burst.
• • Large individual differences are typical in psychoacoustic experiments exploring binaural independence. So much so that some subjects may always report hearing two edges or images while other subjects may never report more than one. How much of this is due differences in spatial perception as opposed to other decision criteria remains unclear.
• • Open-ear headphones may increase binaural independence across all sounds and therefore prompt slightly different results when compared to closed-ear headphones or earphones.
• • Listeners may not hear two images or two edges when sounds are short (< 200 ms). This is because recurring spatial cues available during the onsets of short sounds contribute more to spatial hearing than cues available during short ongoing segments, when non-zero independence indices cause spatial cues to fluctuate.
• • Binaural independence indices corresponding to scaled and summed noise-bursts, differ from those achieved by scaling and summing phase and frequency values obtained using the Fourier transformation.

 A few citations:

• • Blauert J, Lindemann W. (1986) Spatial mapping of intracranial auditory events for various degrees of interaural coherence. J Acoust Soc Am.
• • Hall DA, Barrett DJK, Akeroyd MA, Summerfield AQ. (2005) Cortical representations of temporal structure in sound. J Neurophysiol.
• • Nelson BS, Donovan JM, Takahashi TT (2015) A Neural Model of Auditory Space Compatible with Human Perception under Simulated Echoic Conditions. PLoS One.