Head-related Transfer Functions Dataset Research Articles

Reconstruction of individualized near-field head-related transfer functions from a small set of far-field data based on tensor decomposition

Head-related transfer functions (HRTFs) are essential for virtual auditory display. Generally, near-field HRTFs vary with source direction, distance, frequency, and individual. The huge dimensionality of data makes the measurement or calculation of individualized near-field HRTFs difficult. In the present work, a method to estimate individualized near-field HRTFs with high directional and distance resolution from a small set of directional measured or calculated data at a far-field distance is proposed. Based on tensor decomposition, the near-field HRTFs are decomposed into a weighted combination of direction-, distance-, frequency-, and a few of individual-related modes. The universal direction-, distance-, and frequency-modes as well as the weights are evaluated from a baseline near-field HRTFs dataset. For an arbitrary new individual outside the baseline dataset, the individual modes are estimated from a small set of directional measured or calculated of far-field HRTFs, and then the individualized near-field HRTFs with high directional resolution are estimated. An example of analysis indicates that 15 individual modes account for more than 98 % individual-related energy variation of HRTFs; and near-field HRTFs with high directional resolution can be estimated from far-field data of 30 directional measurements or calculations. Two psychoacoustic experiments validate the proposed method.

Estimation of the Optimal Spherical Harmonics Order for the Interpolation of Head-Related Transfer Functions Sampled on Sparse Irregular Grids

Conventional individual head-related transfer function (HRTF) measurements are demanding in terms of measurement time and equipment. For more flexibility, free body movement (FBM) measurement systems provide an easy-to-use way to measure full-spherical HRTF datasets with less effort. However, having no fixed measurement installation implies that the HRTFs are not sampled on a predefined regular grid but rely on the individual movements of the subject. Furthermore, depending on the measurement effort, a rather small number of measurements can be expected, ranging, for example, from 50 to 150 sampling points. Spherical harmonics (SH) interpolation has been extensively studied recently as one method to obtain full-spherical datasets from such sparse measurements, but previous studies primarily focused on regular full-spherical sampling grids. For irregular grids, it remains unclear up to which spatial order meaningful SH coefficients can be calculated and how the resulting interpolation error compares to regular grids. This study investigates SH interpolation of selected irregular grids obtained from HRTF measurements with an FBM system. Intending to derive general constraints for SH interpolation of irregular grids, the study analyzes how the variation of the SH order affects the interpolation results. Moreover, the study demonstrates the importance of Tikhonov regularization for SH interpolation, which is popular for solving ill-posed numerical problems associated with such irregular grids. As a key result, the study shows that the optimal SH order that minimizes the interpolation error depends mainly on the grid and the regularization strength but is almost independent of the selected HRTF set. Based on these results, the study proposes to determine the optimal SH order by minimizing the interpolation error of a reference HRTF set sampled on the sparse and irregular FBM grid. Finally, the study verifies the proposed method for estimating the optimal SH order by comparing interpolation results of irregular and equivalent regular grids, showing that the differences are small when the SH interpolation is optimally parameterized.

Auto-detection of Spectral Notches of Head-related Transfer Function using Wavelet Multi-resolution Analysis

The spectral features of pressure characterized by the human outer ear, head, and torso are vital for sound localization in humans, especially for sound above 5 kHz. Many studies have shown that spectral notches contribute significantly as cues for this purpose. These spectral notches and their center frequencies depend on the shape and geometry of each individual, so their characteristics are different between individuals. We used wavelet multi-resolution analysis to automatically detect the center frequencies of spectral notches in head-related transfer functions (HRTFs). Auto-detection of these notches at certain locations for an individual helps in using suitable, complete, 3D HRTFs from HRTF datasets that have similar notch characteristics for an individual. Symlet and Daubechies wavelets were successfully used at different decomposition levels for this purpose. Symlet2 gives the best performance in terms of the auto-detection sensitivity.

Estimation of Spectral Notches From Pinna Meshes: Insights From a Simple Computational Model

While previous research on spatial sound perception investigated the physical mechanisms producing the most relevant elevation cues, how spectral notches are generated and related to the individual morphology of the human pinna is still a topic of debate. Correctly modeling these important elevation cues, and in particular the lowest frequency notches, is an essential step for individualizing Head-Related Transfer Functions (HRTFs). In this paper we propose a simple computational model able to predict the center frequencies of pinna notches from ear meshes. We apply such a model to a highly controlled HRTF dataset built with the specific purpose of understanding the contribution of the pinna to the HRTF. Results show that the computational model is able to approximate the lowest frequency notch with improved accuracy with respect to other state-of-the-art methods. By contrast, the model fails to predict higher-order pinna notches correctly. The proposed approximation supplements understanding of the morphology involved in generating spectral notches in experimental HRTFs.

Low-Order Spherical Harmonic HRTF Restoration Using a Neural Network Approach

Spherical harmonic (SH) interpolation is a commonly used method to spatially up-sample sparse head related transfer function (HRTF) datasets to denser HRTF datasets. However, depending on the number of sparse HRTF measurements and SH order, this process can introduce distortions into high frequency representations of the HRTFs. This paper investigates whether it is possible to restore some of the distorted high frequency HRTF components using machine learning algorithms. A combination of convolutional auto-encoder (CAE) and denoising auto-encoder (DAE) models is proposed to restore the high frequency distortion in SH-interpolated HRTFs. Results were evaluated using both perceptual spectral difference (PSD) and localisation prediction models, both of which demonstrated significant improvement after the restoration process.

Measurement of Head-Related Transfer Functions: A Review

A head-related transfer function (HRTF) describes an acoustic transfer function between a point sound source in the free-field and a defined position in the listener’s ear canal, and plays an essential role in creating immersive virtual acoustic environments (VAEs) reproduced over headphones or loudspeakers. HRTFs are highly individual, and depend on directions and distances (near-field HRTFs). However, the measurement of high-density HRTF datasets is usually time-consuming, especially for human subjects. Over the years, various novel measurement setups and methods have been proposed for the fast acquisition of individual HRTFs while maintaining high measurement accuracy. This review paper provides an overview of various HRTF measurement systems and some insights into trends in individual HRTF measurements.

Fully perceptual-based 3D spatial sound individualization with an adaptive variational autoencoder

To realize 3D spatial sound rendering with a two-channel headphone, one needs head-related transfer functions (HRTFs) tailored for a specific user. However, measurement of HRTFs requires a tedious and expensive procedure. To address this, we propose a fully perceptual-based HRTF fitting method for individual users using machine learning techniques. The user only needs to answer pairwise comparisons of test signals presented by the system during calibration. This reduces the efforts necessary for the user to obtain individualized HRTFs. Technically, we present a novel adaptive variational AutoEncoder with a convolutional neural network. In the training, this AutoEncoder analyzes publicly available HRTFs dataset and identifies factors that depend on the individuality of users in a nonlinear space. In calibration, the AutoEncoder generates high-quality HRTFs fitted to a specific user by blending the factors. We validate the feasibilities of our method through several quantitative experiments and a user study.

A Parallel Approach to HRTF Approximation and Interpolation Based on a Parametric Filter Model

Spatial audio-rendering techniques using head-related transfer functions (HRTFs) are currently used in many different contexts such as immersive teleconferencing systems, gaming, or 3-D audio reproduction. Since all these applications usually involve real-time constraints, efficient processing structures for HRTF modeling and interpolation are necessary for providing real-time binaural audio solutions. This letter presents a parametric parallel model that allows us to perform HRTF filtering and interpolation efficiently from an input HRTF dataset. The resulting model, which is an adaptation from a recently proposed modeling technique, not only reduces the size of HRTF datasets significantly, but also allows for simplified interpolation and real-time computation over parallel processors. In order to discuss the suitability of this new model, an implementation over a graphic processing unit is presented.

Head-Related Transfer Function Selection Using Neural Networks

AbstractIn binaural audio systems, for an optimal virtual acoustic space a set of head-related transfer functions (HRTFs) should be used that closely matches the listener’s ones. This study aims to select the most appropriate HRTF dataset from a large database for users without the need for extensive listening tests. Currently, there is no way to reliably reduce the number of datasets to a smaller, more manageable number without risking discarding potentially good matches. A neural network that estimates the appropriateness of HRTF datasets based on input vectors of anthropometric measurements is proposed. The shapes and sizes of listeners’ heads and pinnas were measured using digital photography; the measured anthropometric parameters form the feature vectors used by the neural network. A graphical user interface (GUI) was developed for participants to listen to music transformed using different HRTFs and to evaluate the fitness of each HRTF dataset. The listening scores recorded were the target outputs used to train the neural networks. The aim was to learn a mapping between anthropometric parameters and listener’s perception scores. Experimental validations were performed on 30 subjects. It is demonstrated that the proposed system produces a much more reliable HRTF selection than previously used methods.

Headphone-based immersive audio for virtual reality headsets

In this paper, we propose a binaural system for virtual auditory space synthesis and reproduction. We introduce a subjective listening test for head-related transfer function (HRTF) customization and real-time implementation of ambisonic surround sound over headphones. In this test, a listener first selects the closest-matching HRTF dataset from an existing database. The selected HRTF dataset must fulfill the criteria of front-back discrimination and up-down discrimination. Secondly, the selected HRTF dataset is utilized to build a binaural ambisonic system composed of an encoder for synthesizing multiple sound sources, an image-source model for listening-room simulation, an ambisonic rotator responding to head motion in three axes, and a binaural ambisonic decoder. Additionally, we propose a system optimization technique that minimizes computational cost and enhances audio quality. Finally, we present both subjective and objective measurements of the perceived audio quality that were conducted to validate this approach. The audio quality assessment examined the frequency hearing impairment, localization error, and localization blur. The proposed system is especially suitable for mixing and rendering immersive sound in virtual reality.

Design theory for binaural synthesis: Combining microphone array recordings and head-related transfer function datasets

Design theory for binaural synthesis: Combining microphone array recordings and head-related transfer function datasets

Design theory for binaural synthesis: Combining microphone array recordings and head-related transfer function datasets

Design theory for binaural synthesis: Combining microphone array recordings and head-related transfer function datasets

A high-resolution head-related transfer function dataset and 3D ear model database

Binaural reproduction techniques, which use head-related transfer functions (HRTFs), become more and more popular. Human localization performance using binaural synthesis is, however, often poor due to non-individual HRTFs. To investigate the physical relationship between the ear geometry and the directional HRTFs, the ears and the HRTF datasets of 48 subjects are measured. The detailed ear models are obtained from magnetic resonance imaging scans of the subjects. Two rough scans series of the head and a detailed horizontal scan series, which covers both ears, are taken. The 3D model meshes, which are generated from the MRI scans, allow a very precise determination of anthropometric dimensions which can be used for the individualization of the HRTFs. Additionally, the relationship between the anthropometric dimensions and monaural cues of the HRTFs is studied by the boundary element method. These simulations show which parts of the pinna are involved in case of resonances or destructive interferences.

Empirical Determination of Frequency Representation in Spherical Harmonics-Based HRTF Functional Modeling

This paper considers a functional modeling of a head-related transfer function (HRTF) where the spatial-portion is constrained to be expanded using spherical harmonics and the frequency-portion is expanded in terms of standard closed-form orthonormal functions, which may be user selected. We derive an objective evaluation metric to compare the relative energy efficiencies of candidate functional models using empirical HRTF database measurements and robust estimation techniques. Among four sets of closed-form orthonormal functions the complex exponentials are identified as the most efficient to represent the frequency-portion in the spherical harmonics-based HRTF functional model. The proposed model is evaluated across three HRTF data sets: 1) CIPIC database, 2) the MIT KEMAR (Knowles Electronics Mannequin for Acoustics Research) database, and 3) the ANU KEMAR database.

A spatial compression technique for head-related transfer function interpolation and complexity estimation.

A head-related transfer function (HRTF) model employing Legendre polynomials (LPs) is evaluated as an HRTF spatial complexity indicator and interpolation technique in the azimuth plane. LPs are a set of orthogonal functions derived on the sphere which can be used to compress an HRTF dataset by transforming it into a lower dimensional space. The LP compression technique was applied to various HRTF datasets, both real and synthetic, to determine how much different HRTFs can be compressed with respect to their structural complexity and their spatial resolution. The spatial complexity of different datasets was evaluated quantitatively by defining an HRTF spatial complexity index, which considers the rate of change in HRTF power spectrum with respect to spatial position. The results indicate that the compression realized by the LP technique is largely independent of the number of spatial samples in the HRTF dataset, while compressibility tracks the HRTF spatial complexity index so that more LP coefficients are needed to represent an HRTF dataset with a larger complexity index. The slope of the complexity index with respect to sub-sampling density can be used as a predictor for high interpolation error.

Recovery of individual head-related transfer functions from a small set of measurements

Head-related transfer functions (HRTFs) vary with individuals, and in practice, measuring HRTFs with high directional resolution for each individual is tiresome. Based on a basis functions representation of HRTFs, the present work proposes a method for recovering individual HRTFs from a small set of measurements. The HRTFs are represented by a combination of a small set of spatial basis functions (SBFs) with frequency- and individual-dependent weights. The SBFs are derived by applying spatial principal component analysis to a baseline HRTF dataset with high directional resolution. The individual weights for any subject outside the dataset are estimated from measurements at a few source directions, and then the HRTFs with high directional resolution are recovered by combining the SBFs and the individual weights. In an illustrative case, the SBFs derived from a baseline dataset that includes 20 subjects are used to recover the HRTF magnitudes for six subjects outside the baseline dataset. Results show that individual HRTF magnitudes can be recovered from measurements at 73 directions with a mean signal-to-distortion ratio of 19 dB. The proposed method is also applicable to recovering head-related impulse responses. The results of psychoacoustic experiments indicate that in most cases the recovered and measured HRTFs are indistinguishable.

Efficient Continuous HRTF Model Using Data Independent Basis Functions: Experimentally Guided Approach

This paper introduces a continuous functional model for head-related transfer functions (HRTFs) in the horizontal auditory scene. The approach uses a separable representation consisting of a Fourier-Bessel series expansion for the spectral components and a conventional Fourier series expansion for the spatial components. Being independent of the data, these two sets of basis functions remain unchanged for all subjects and measurement setups. Hence, the model can transform an individualized HRTF to a subject specific set of coefficients. A continuous functional model is also developed in the time domain. We show the efficient model performance in approximating experimental measurements by using the HRTF measurements from a KEMAR manikin and the synthetic data from the spherical head model. The statistical results are determined from a 50-subject HRTF data set. We also corroborate the predictive capability of the proposed model. The model has near optimal performance, which can be ascertained by comparison with the standard principle component analysis (PCA) and discrete Karhunen-Loeve expansion (KLE) methods at the measurement points and for a given number of parameters.

The Effect of Head-Related Transfer Function Measurement Methodology on Localization Performance in Spatial Audio Interfaces

Four head-related transfer function (HRTF) data sets were compared to determine the effect of HRTF measurement methodology on the localization of spatialized auditory stimuli. Spatial audio interfaces typically require HRTF data sets to generate the spatialized auditory stimuli. HRTF measurement is accomplished using a variety of techniques that can require several nearly arbitrary decisions about methodology. The effects of these choices upon the resulting spatial audio interface are unclear. Sixteen participants completed a sound localization task that included real-world, broadband stimuli spatialized at eight locations on the horizontal plane. Four different HRTF data sets were utilized to spatialize the stimuli: two publicly available HRTF data sets and two data sets obtained using different in-house measurement systems. All HRTFs were obtained from the Knowles Electronics Mannequin for Acoustics Research. Unsigned localization error and proportion of front/back reversals did not differ significantly across HRTF data sets. Poorest accuracy was observed in locations near the medial (front/back) axis of the listener, mainly because of the relatively large proportions of reversals at these locations. This study suggests that the particular generalized HRTF data set chosen for spatialization is of minimal importance to the localizability of the resulting stimuli. This result will inform the design of many spatial audio interfaces that are based upon generalized HRTFs, including wayfaring devices, communication systems, and virtual reality systems.

A new HRTF decomposition and the corresponding algorithm for sound spatialization

Binaural simulations make extensive use of head-related transfer functions (HRTF), so spatializers have to deal with large amounts of data and long computing times to interpolate the HRTF database over the whole space. A better understanding of human auditory localization could lead to a better simulation of localization cues and allow the database and the computing time to be minimized. Principal component analysis on HRTFs, reported by D. J. Kistler and F. L. Wightman [J. Acoust. Soc. Am. 91, 1637–1647 (1992)], gave only second-order decorrelated base vectors. In order to find simple vectors (bandpass or low-pass), an independent component analysis has been computed for upper-hemisphere preprocessed HRTFs (reported in by M. Emerit et al. [Proc. 15th ICA, Trondheim, Norway, (1995) pp. 437–440]). New analyses have been done on a new HRTF data set, on different representations (time, magnitude alone and with phase). These analyses give a small number of base vectors, which can be used to reconstruct any HRTF, with a correlation coefficient near 1, and allow a new spatialization method using 3 IIR filters, derived from independent impulse responses, to be conceived. Source signals are filtered by each of these filters, and linear combination of the results gives the spatialized signal.