Efficient Representation and Sparse Sampling of Head-Related Transfer Functions Using Phase-Correction Based on Ear Alignment

Abstract

With the proliferation of high quality virtual reality systems, the demand for high fidelity spatial audio reproduction has grown. This requires individual head-related transfer functions (HRTFs) with high spatial resolution. Acquiring such HRTFs is not always possible, which motivates the need for sparsely sampled HRTFs. Additionally, real-time applications require compact representation of HRTFs. Recently, spherical-harmonics (SH) has been suggested for efficient interpolation and representation of HRTFs. However, representation of sparse HRTFs with a limited SH order may introduce spatial aliasing and truncation errors, which have a detrimental effect on the reproduced spatial audio. This is because the HRTF is inherently of a high spatial order. One approach to overcome this limitation is to pre-process the HRTF, with the aim of reducing its effective SH order. A recent study showed that order-reduction can be achieved by time-alignment of HRTFs, through numerical estimation of the time delays of the HRTFs. In this paper, a new method for pre-processing HRTFs in order to reduce their effective order is presented. The method uses phase-correction based on ear alignment, by exploiting the dual-centering nature of HRTF measurements. In contrast to time-alignment, the phase-correction is performed parametrically, making it more robust to measurement noise. The SH order reduction and ensuing interpolation errors due to sparse sampling were analyzed for these two methods. Results indicate significant reduction in the effective SH order, where only 100 measurements and order 6 are required to achieve a normalized mean square error below −10 dB compared to a fully-sampled, high-order HRTF.

Applied Methods for Sparse Sampling of Head-Related Transfer Functions

“…The simulated HRTFs consist of a Q = 1730 Lebedev grid and the measured HRTFs consist of a Q = 440 non-standard grid as described in [18]. The entire dataset was ear-aligned by preprocessing [11], using the head width provided per subject. The 90 subjects were divided to two groups: the training set, containing 54 random subjects (60% of the entire dataset), and the test set, containing the remaining 36 subjects.…”

“…Various pre-processing methods were proposed for SH order reduction by concentrating most of the contained energy at low orders [9,10]. The recently developed ear-alignment method was shown to be especially effective [11]. In this method, the HRTF is phase corrected to each of the subject's ears, rather than the center of its head, as the reference location.…”

Measurement of Head-Related Transfer Functions: A Review

“…A lot of studies are interested in the HRTF representation in the spherical harmonic (SH) domain, taking advantage of the spatial continuity and orthonormality of SHs over the sphere. Such a representation shows the suitability for HRTF interpolation/extrapolation [20][21][22][23], binaural rendering [118], etc. Zhang et al [28] compared various spatial sampling schemes (distributions of measurement points) and revealed that the IGLOO schema is the most suitable one when considering the SH transformation, and the required minimum number of HRTF pairs is 2304.…”

“…Measuring high-density HRTF datasets for each individual listener is usually a time-consuming task, especially when considering different source-listener distances. Several studies proposed to interpolate and extrapolate (distance or direction) sparse HRTF sets to obtain a high-density HRTF dataset [17][18][19][20][21][22][23][24][25][26].…”

Implicit HRTF Modeling Using Temporal Convolutional Networks

“…These can be alleviated by forming a continuous, functional representation from sparsely sampled measurements, i.e., expressing the HRTFs mathematically as a continuous function of direction [9]. Methods based on (bi)linear interpolation or cubic spline interpolation [10] that use neighboring HRTFs measurements do not provide sufficiently accurate or high quality HRTFs from sparse measurements, due to the high spatial complexity of the HRTF, especially at high frequencies [11]. Recently more sophisticated methods based on the analysis and decomposition of the entire set of measured HRTFs have been suggested for efficient representation of HRTFs, e.g., using spectral domain [12] and spherical harmonics decomposition [9,13].…”