A priori mesh grading for the numerical calculation of the head-related transfer functions.

Head-related transfer functions (HRTFs) describe the directional filtering of the incoming sound caused by the morphology of a listener's head and pinnae. When an accurate model of a listener's morphology exists, HRTFs can be calculated numerically with the boundary element method (BEM). However, the general recommendation to model the head and pinnae with at least six elements per wavelength renders the BEM as a time-consuming procedure when calculating HRTFs for the full audible frequency range. In this study, a mesh preprocessing algorithm is proposed, viz., a priori mesh grading, which reduces the computational costs in the HRTF calculation process significantly. The mesh grading algorithm deliberately violates the recommendation of at least six elements per wavelength in certain regions of the head and pinnae and varies the size of elements gradually according to an a priori defined grading function. The evaluation of the algorithm involved HRTFs calculated for various geometric objects including meshes of three human listeners and various grading functions. The numerical accuracy and the predicted sound-localization performance of calculated HRTFs were analyzed. A-priori mesh grading appeared to be suitable for the numerical calculation of HRTFs in the full audible frequency range and outperformed uniform meshes in terms of numerical errors, perception based predictions of sound-localization performance, and computational costs.

Numerical calculation of listener-specific head-related transfer functions and sound localization: Microphone model and mesh discretization.

Head-related transfer functions (HRTFs) can be numerically calculated by applying the boundary element method on the geometry of a listener's head and pinnae. The calculation results are defined by geometrical, numerical, and acoustical parameters like the microphone used in acoustic measurements. The scope of this study was to estimate requirements on the size and position of the microphone model and on the discretization of the boundary geometry as triangular polygon mesh for accurate sound localization. The evaluation involved the analysis of localization errors predicted by a sagittal-plane localization model, the comparison of equivalent head radii estimated by a time-of-arrival model, and the analysis of actual localization errors obtained in a sound-localization experiment. While the average edge length (AEL) of the mesh had a negligible effect on localization performance in the lateral dimension, the localization performance in sagittal planes, however, degraded for larger AELs with the geometrical error as dominant factor. A microphone position at an arbitrary position at the entrance of the ear canal, a microphone size of 1 mm radius, and a mesh with 1 mm AEL yielded a localization performance similar to or better than observed with acoustically measured HRTFs.

Fast multipole boundary element method to calculate head-related transfer functions for a wide frequency range.

Head-related transfer functions (HRTFs) play an important role in spatial sound localization. The boundary element method (BEM) can be applied to calculate HRTFs from non-contact visual scans. Because of high computational complexity, HRTF simulations with BEM for the whole head and pinnae have only been performed for frequencies below 10 kHz. In this study, the fast multipole method (FMM) is coupled with BEM to simulate HRTFs for a wide frequency range. The basic approach of the FMM and its implementation are described. A mesh with over 70 000 elements was used to calculate HRTFs for one subject. With this mesh, the method allowed to calculate HRTFs for frequencies up to 35 kHz. Comparison to acoustically-measured HRTFs has been performed for frequencies up to 16 kHz, showing a good congruence below 7 kHz. Simulations with an additional shoulder mesh improved the congruence in the vertical direction. Reduction in the mesh size by 5% resulted in a substantially-worse representation of spectral cues. The effects of temperature and mesh perturbation were negligible. The FMM appears to be a promising approach for HRTF simulations. Further limitations and potential advantages of the FMM-coupled BEM are discussed.