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.

Modeling the direction-continuous time-of-arrival in head-related transfer functions.

Head-related transfer functions (HRTFs) describe the filtering of the incoming sound by the torso, head, and pinna. As a consequence of the propagation path from the source to the ear, each HRTF contains a direction-dependent, broadband time-of-arrival (TOA). TOAs are usually estimated independently for each direction from HRTFs, a method prone to artifacts and limited by the spatial sampling. In this study, a continuous-direction TOA model combined with an outlier-removal algorithm is proposed. The model is based on a simplified geometric representation of the listener, and his/her arbitrary position within the HRTF measurement. The outlier-removal procedure uses the extreme studentized deviation test to remove implausible TOAs. The model was evaluated for numerically calculated HRTFs of sphere, torso, and pinna under various conditions. The accuracy of estimated parameters was within the resolution given by the sampling rate. Applied to acoustically measured HRTFs of 172 listeners, the estimated parameters were consistent with realistic listener geometry. The outlier removal further improved the goodness-of-fit, particularly for some problematic fits. The comparison with a simpler model that fixed the listener position to the center of the measurement geometry showed a clear advantage of listener position as an additional free model parameter.