Objective measure for sound localization based on head-related transfer functions

Head-related transfer functions (HRTFs) are widely used in the study of the human auditory system. It is known that HRTFs contain spatial cues allowing individuals to localize sounds. Inter-aural phase and level differences, and high-frequency magnitude variations, are among the most common cues. While these cues require detailed analysis of specific HRTFs, in the current paper a new measure is proposed, based on the distribution of the singular values of the HRTF matrix, effectively representing the amount of information contained in the HRTFs as a function of frequency and arrival direction. This measure is generic, encompassing all cues in a single quantity. First, the validity of the proposed measure is justified theoretically. Then, the proposed measure is validated against empirically known results of human localization in the horizontal and median planes. The comparison is performed by taking into account two different aspects: (1) whether the information contained in the HRTFs is monaural or binaural, and (2) the variation of the minimum audible angle (MAA) and other localization measures as a function of azimuth and elevation. The results show that the proposed measure is in good agreement with the established theory of human sound localization and can be used as a predictor of the potential performance of human sound localization and of human-like systems such as humanoid robots.