A Relevant Distance Criterion for Interpolation of Head-Related Transfer Functions

In binaural synthesis, in order to realize more precise and accurate spatial sound, it would be desirable to measure a large number of the head-related transfer functions (HRTFs) in various directions. To reduce the size of the HRTFs, interpolation is often employed, where the HRTF for any direction can be obtained by a limited number of the representative HRTFs. In this paper, it is determined which distortion measure for interpolation of the HRTFs in the horizontal plane is most suitable for predicting audible differences in sound location. Four kinds of HRTF sets, measured using three human heads and one mannequin (KEMAR), were prepared for this study. Using various objective distortion criteria, the differences between interpolated and measured HRTFs were computed. These were then related to the results from the listening tests through receiver operator characteristic (ROC) curves. The results of the present study indicated that for the HRTF sets measured from three human heads, the best predictor of performance was obtained using the distortion measurement computed from the mel-cepstral coefficients, whereas the distortion measurement associated with interaural time delay predicted audible differences in sound location reasonably well for the KEMAR HRTF set. A feasibility test was conducted to verify the usefulness of the selected distortion measurement.

I. Introduction

In binaural synthesis, virtual sound sources are implemented with locations relative to the listener. This is done by convolving an anechoic signal with a pair of head-related transfer functions (HRTFs) and presenting the resulting signals through equalized headphones [1], [2]. The HRTF is the directional-dependent acoustical transfer function from a sound source to a listener's eardrum. Usually, the HRTFs are obtained from their corresponding head-related impulse responses (HRIRs) measured under controlled conditions on a spherical surface with a constant radius for only a predefined set of elevation and azimuth angles. In order to represent all possible directions of the sound source with respect to the listener, HRTFs measured from all possible directions should be prepared. The need for HRTFs measured from various directions becomes more important when we address the problem of moving sound sources where we need to switch between different HRTFs, or when the perceived direction of the sound changes due to the listener's head movements. This means that enough memory space for storing the large HRTF database would be desirable for the reproduction of more realistic sounds. However, the audio systems embedded in handheld devices have limitations on CPU power and memory size. In these applications, an efficient compression of the HRTF database can lead to a higher quality binaural synthesis given the limited system memory.