Set Of Head-related Transfer Functions Research Articles

Efficient Approximation of Head-Related Transfer Functions in Subbands for Accurate Sound Localization

Head-related transfer functions (HRTFs) describe the acoustic filtering of incoming sounds by the human morphology and are essential for listeners to localize sound sources in virtual auditory displays. Since rendering complex virtual scenes is computationally demanding, we propose four algorithms for efficiently representing HRTFs in subbands, i.e., as an analysis filterbank (FB) followed by a transfer matrix and a synthesis FB. All four algorithms use sparse approximation procedures to minimize the computational complexity while maintaining perceptually relevant HRTF properties. The first two algorithms separately optimize the complexity of the transfer matrix associated to each HRTF for fixed FBs. The other two algorithms jointly optimize the FBs and transfer matrices for complete HRTF sets by two variants. The first variant aims at minimizing the complexity of the transfer matrices, while the second one does it for the FBs. Numerical experiments investigate the latency-complexity trade-off and show that the proposed methods offer significant computational savings when compared with other available approaches. Psychoacoustic localization experiments were modeled and conducted to find a reasonable approximation tolerance so that no significant localization performance degradation was introduced by the subband representation.

Use of k-means clustering analysis to select representative head related transfer functions for use in subjective studies

A head related transfer function (HRTF) must be applied when creating auralizations; however, the HRTFs of individual subjects are not typically known in advance. Often, an overall ‘average’ HRTF is used instead. The purpose of this study was to develop a listening test to identify a ‘matched’ (best) and ‘unmatched’ (worst) HRTF for specific subjects, which could be applied to customize auralizations for individual participants. The method of k-means clustering was used to identify eight representative HRTFs from the CIPIC database. HRTFs from 45 subjects’ left and right ears in four directions were clustered, which resulted in 56 cluster centers (possible representative HRTFs). A comparative analysis was conducted to determine an appropriate set of HRTFs. These HRTFs were then convolved with pink noise bursts at 00 elevation and various azimuths to sound like the bursts were rotating around a subject’s head. A paired comparison test was used where listeners selected the ‘most natural’ sounding HRTF signal. ‘Most natural’ was described as coming from the correct directions and located outside the head. The results from the clustering analysis and listening test will be presented, along with a subjective study that incorporated the HRTF listening test. [Work was supported by NSF Grant 1302741.]

Spatially continuous model of the broadband time-of-arrival in the head-related transfer functions

Head-related transfer functions (HRTFs) describe the filtering of the incoming sound by the human anatomy. They contain the so-called broadband time-of-arrivals (TOAs), which interaural differences yield the well-known interaural time differences used to estimate the lateral position of sound sources by the human auditory system. The TOAs are essential for a time-synchronous binaural rendering of multiple virtual sound sources or for interpolation of the timing information in an existing HRTF set. Estimation of the TOA is usually done separately for each spatial direction and is thus prone to errors and directional outliers. A method for a robust estimation of spatially continuous TOA function from a set of listener-specific HRTFs is presented. The method relies on a geometric model of the HRTF-measurement setup represented by parameters like head position, radius, and ear position. The model parameters were fit to HRTFs of a sphere numerically calculated under various conditions, and to measured HRTFs of 160 listeners. The resulting model parameters and TOA functions corresponded well with the measurement geometry and manually derived TOAs, respectively. The model parameters were further compared to those resulting from a simplified model which assumes the listener being in the center of the HRTF-measurement setup, demonstrating the impact of the usually neglected aspect of listener position on the HRTF timing quality.

Consistency among the head-related transfer functions from different measurements

Empirical measurement is a common approach to obtaining head-related transfer functions (HRTFs). Due to differences in experimental conditions and possible errors, some deviations exist among the data from different measurements even for the same subject. This work aims to evaluate deviations of HRTFs from different measurements. Five sets of KEMAR HRTFs from three groups including MIT-media Lab, CIPIC Interface Lab, and our lab are used. A free-field equalization is applied to the original data so as to eliminate the influence caused by the difference in the response of electro-acoustic measuring chain. The deviations among HRTF magnitudes for different measurements are specified by spectral distortion. Results indicate that the magnitude deviation increases with increasing frequency and reaches more than 10 dB above the frequency of 6 kHz. Salient deviations often occur in contralateral source directions or in ipsilateral source directions near the frequency of pinna-related notch. Nevertheless, most deviations can be effectively reduced after an auditory filter smoothing. This work suggests that the inconsistency in measured HRTF data and its impact on auditory perception should be taken into account when comparing and standardizing HRTFs from different measurements. [Work supported by National Nature Science Fund of China Grant No. 11004064]

Sound localization in individualized and non-individualized crosstalk cancellation systems

The sound-source localization provided by a crosstalk cancellation (CTC) system depends on the head-related transfer functions (HRTFs) used for the CTC filter calculation. In this study, the horizontal- and sagittal-plane localization performance was investigated in humans listening to individualized matched, individualized but mismatched, and non-individualized CTC systems. The systems were simulated via headphones in a binaural virtual environment with two virtual loudspeakers spatialized in front of the listener. The individualized mismatched system was based on two different sets of listener-individual HRTFs. Both sets provided similar binaural localization performance in terms of quadrant, polar, and lateral errors. The individualized matched systems provided performance similar to that from the binaural listening. For the individualized mismatched systems, the performance deteriorated, and for the non-individualized mismatched systems (based on HRTFs from other listeners), the performance deteriorated even more. The direction-dependent analysis showed that mismatch and lack of individualization yielded a substantially degraded performance for targets placed outside of the loudspeaker span and behind the listeners, showing relevance of individualized CTC systems for those targets. Further, channel separation was calculated for different frequency ranges and is discussed in the light of its use as a predictor for the localization performance provided by a CTC system.

Estimation of parameters of a head-related transfer function customization model

Head-Related Transfer Functions (HRTFs) are special digital filters used to create the effect of three-dimensional (3D) virtual sound source placement over headphones. The two most common methods of obtaining HRTFs are to either individually measure the HRTFs on specialized equipment (individualized HRTFs) or to create a set of generic HRTFs by measuring them on a mannequin with average anatomical features (generic HRTFs). Individualized HRTFs required specialized equipment that is not readily available to the general public. Additionally, it is known that HRTFs are heavily dependent on our anatomical features. As a result, generic HRTFs produce significant localization errors. A multi-linear model is now available which uses simple anthropometric measurements of the intended user's anatomy to generate customized HRTFs. These customized HRTFs can be generated without specialized equipment and have improved spatialization over generic HRTFs. However, the anthropometric measurements, which are used as parameters for the customization model, are currently collected manually. In the present work, computer vision techniques are used to automatically estimate a portion of the anthropometric measurements of the human pinnae. Analysis of the estimation technique's performance will also be conducted.

Similarity and cluster analysis on magnitudes of individual head-related transfer functions

Although head-related transfer functions (HRTFs) vary with individuals, non-individualized HRTFs are typically employed in virtual auditory display (VAD) due to the difficulty in measuring individual HRTFs. Similarity among the HRTFs of different individuals allows for customizing a matched set of HRTFs for a user from an existing database and thereby improving performance of VADs. The first step of HRTF customization is evaluation of the similarities among individual HRTFs. In the present work, based on a HRTF database of 52 Chinese subjects, the similarities are evaluated by calculating the directional-mean of normalized cross-correlation coefficient (MCC) of HRTF magnitudes between each pair of subjects and then applying cluster analysis to the resultant MCC. The results indicate that MCC depends on subject pair with values ranging from 0.934 to 0.562 (mean 0.842) and from 0.948 to 0.635 (mean 0.863) for the left and right ear, respectively. HRTF magnitudes for most subjects can be classified into six to eight clusters and represented by the corresponding cluster centers. Some singleton clusters are also observed on a few subjects, which reflect the diversity in HRTFs and should be careful in practice. Psychoacoustic experiment also validates above analyses.

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.

Obtaining Binaural Room Impulse Responses From B-Format Impulse Responses Using Frequency-Dependent Coherence Matching

Measuring binaural room impulse responses (BRIRs) for different rooms and different persons is a costly and time-consuming task. In this paper, we propose a method that allows to compute BRIRs from a B-format room impulse response (B-format RIR) and a set of head-related transfer functions (HRTFs). This enables to measure the room-related properties and head-related properties of BRIRs separately, reducing the amount of measurements necessary for obtaining BRIRs for different rooms and different persons to one B-format RIR measurement per room and one HRTF set per person. The BRIRs are modeled by applying an HRTF to the direct sound part of the B-format RIR and using a linear combination of the reflections part of the B-format RIR. The linear combination is determined such that the spectral and frequency-dependent interaural coherence cues match those of corresponding directly measured BRIRs. A subjective test indicates that the computed BRIRs are perceptually very similar to corresponding directly measured BRIRs.

A hybrid compression method for head-related transfer functions

The paper proposes a hybrid compression method to resolve the storage problem of a large number of head-related transfer functions (HRTFs). First, each HRTF is approximated by a minimum-phase HRTF and an all pass filter whose group delay equals the interaural time delay (ITD). Second, principal component analysis is applied to the entire HRTF set to derive several basis functions, with a weight vector set defining the contribution of the basis functions to each HRTF. Third, the weight set is vector quantized with the designed codebook. At last, the ITD is curved surface fitted with a cosine series bivariate polynomial. As a result, the HRTF can be reconstructed from the basis functions, codebook indexes, and ITD polynomial coefficients. Simulation results reveal that the proposed method may reduce the data size greatly with similar reconstruction precision comparing with the principal component analysis method.

Binaural Localization Based on Weighted Wiener Gain Improved by Incremental Source Attenuation

This paper addresses the problem of direction-of-arrival (DOA) estimation both in azimuthal and elevation angle from binaural sound that is processed with a head-related transfer function (HRTF). Previously, we proposed a weighted Wiener gain (WWG) method for two-dimensional DOA estimation with two-directional microphones. However, for signals processed with HRTFs, peaks in the spatial spectra of WWG indicating true sources can mingle with spurious peaks. To resolve this situation, we propose to apply incremental source attenuation (ISA) in combination with WWG. In fact, ISA reduces spectral components originating from specified sound sources and thereby improves the localization accuracy of the next targeted source in the proposed incremental estimation procedure. We conduct computer simulations using directional microphones and four HRTF sets corresponding to four individuals. The proposed method is compared to two DOA estimation methods that are equivalent to two generalized cross-correlation functions and two high-resolution methods of multiple signal classification (MUSIC) and minimum variance method. For comparison purposes, we introduce binary coherence detection (BCD) to high-resolution methods for emphasizing valid spectral components for localization in multiple source conditions. Evaluation results demonstrate that, although MUSIC with BCD yield comparable performance to that of WWG in conditions where single speech source exists, WWG with ISA surpasses the other methods in conditions including two or three speech sources.

Estimation of individualized head-related transfer function based on principal component analysis

In binaural reproduction providing spatial sound by means of convolving sound sources and head-related transfer functions (HRTFs), it is important to approximate the listener’s own HRTFs with a high degree of accuracy. HRTF measurement, however, typically requires a great deal of labor, time, and expense. In this paper, a method for estimating such individualized HRTFs that uses principal component analysis (PCA) is introduced. In this method, the orthogonal bases of a set of HRTFs are computed and partially measured HRTFs are interpolated from the weighted sum of the bases. The validity of the method was verified in objective and subjective experiments in which the required approximation accuracy of HRTFs was evaluated.

Binaural Rendering in MPEG Surround

This paper describes novel methods for evoking a multichannel audio experience over stereo headphones. In contrast to the conventional convolution-based approach where, for example, five input channels are filtered using ten head-related transfer functions, the current approach is based on a parametric representation of the multichannel signal, along with either a parametric representation of the head-related transfer functions or a reduced set of head-related transfer functions. An audio scene with multiple virtual sound sources is represented by a mono or a stereo downmix signal of all sound source signals, accompanied by certain statistical (spatial) properties. These statistical properties of the sound sources are either combined with statistical properties of head-related transfer functions to estimate that represent the perceptually relevant aspects of the auditory scene or used to create a limited set of combined head-related transfer functions that can be applied directly on the downmix signal. Subsequently, a binaural rendering stage reinstates the statistical properties of the sound sources by applying the estimated binaural parameters or the reduced set of combined head-related transfer functions directly on the downmix. If combined with parametric multichannel audio coders such as MPEG Surround, the proposed methods are advantageous over conventional methods in terms of perceived quality and computational complexity.

HRTF compression via principal components analysis and vector quantization

The computation burden and the huge memory size of the head-related transfer function (HRTF) database challenge the practical application of 3D sound system. This paper therefore proposes a novel method which employs principal components analysis and vector quantization jointly to reduce the size of HRTF set in 3D sound system. Numerical experiment results demonstrate that the proposed method can save the storage space greatly with little localization performance degradation.

Classification head‐related transfer functions for an individualization procedure by a tournament‐style listening‐test

Individualization of head‐related transfer functions (HRTFs) is necessary for high‐accuracy sound image localization in three‐dimensional spatial rendering by virtual auditory displays (VADs). However, measurement of HRTFs for each listener for all sound‐source directions requires a special measuring apparatus and a long measurement time with a listener’s physical load. The authors have therefore proposed an individualization method of HRTFs called Determination method of OptimuM Impulse‐response by Sound Orientation (DOMISO), in which the best set of HRTFs is selected using a tournament‐style listening test without any measurement. In DOMISO, our HRTF corpus, including more than 120 sets of measured HRTFs, is used. In this study, a classification method of these HRIRs is examined to select good seeds for the tournament. First, relationships among various parameters of HRTFs and individualization results by DOMISO are analyzed using multiple‐correlation analysis. Second, using promising parameters, all sets of HRTFs in the corpus are classified as a structured tree. Third, using results of classification, listening tests by DOMISO procedure are performed using these HTRFs. Finally, a listening test of sound image localization is conducted with the individualized HRTFs to examine the effectiveness of the classification.

Evaluating the principal spectral components positioning a virtual sound source on a cone of confusion

Although many studies have attempted to identify spectral cues to sound-source direction for the entire sphere of possible incidence angles, few studies have focused their attention on directional hearing for virtual sources positioned on cones of confusion. These regions of space, defined by relatively constant interaural time and intensity differences, provide an ideal subset of incidence angles for testing the importance of the spectral cues to direction allowing for up/down and front/rear distinctions between sources at constant angular distance from the median plane. In this study, head-related transfer functions (HRTFs) measured on a well-lateralized cone of confusion were decomposed into principal spectral components putatively responsible for positioning a virtual sound source, and their related angle-dependent scores that describe the relative contribution of each shape to the total spectral variation. The findings can be summarized as follows: For the set of ipsilateral HRTFs the most significant set of scores shows sinusoidal variation with angle, and could potentially encode a front-back cue, though with the extrema rotated by about 30 deg. The most significant score from an analysis of interaural spectral differences seems to capture a head-shadowing effect which is most extreme in the lower rear.

Virtual acoustic prototyping

In this paper the re-creation of 3-D sound fields so the full psycho-acoustic impact of sound sources can be assessed before the manufacture of a product or environment is examined. Using head related transfer functions (HRTFs) coupled with a head tracked set of headphones the sound field at the left and right ears of a listener can be re-created for a set of sound sources. However, the HRTFs require that sources have a defined location and this is not the typical output from numerical codes which describe the sound field as a set of distributed modes. In this paper a method of creating a set of equivalent sources is described such that the standard set of HRTFs can be applied in real time. A structural-acoustic model of a cylinder driving an enclosed acoustic field will be used as an example. It will be shown that equivalent sources can be used to recreate all of the reverberation of the enclosed space. An efficient singular value decomposition technique allows the large number of sources required to be simulated in real time. An introduction to the requirements necessary for 3-D virtual prototyping using high frequency Statistical Energy Analysis models will be presented. [Work supported by AuSim and NASA.]

Explaining individual differences in head-related transfer functions

The fidelity of virtual auditory images is degraded by differences between the listener’s head-related transfer functions (HRTFs) and the HRTFs used to synthesize the virtual images. Middlebrooks (this meeting) argues that simple frequency scaling accounts for many of these individual differences. In an attempt to understand more fully both the capabilities and limitations of frequency scaling, the HRTFs from 100 individuals were analyzed. The difference between each pair of HRTFs was expressed as a single number, the average of the squared dB differences at 40 log-spaced frequencies from 0.12 to 12 kHz. A multidimensional scaling analysis (ALSCAL) was performed on the resulting difference matrix. A two-dimensional solution accounted for over 80% of the total variance. The frequency scaling factor needed for the optimal fit of each individual’s HRTF set to the HRTF set at the center of the 2-D solution was then determined. The correlation between the optimal frequency scalar and the coordinate of each HRTF set on one dimension of the scaling solution was over 0.95. Attempts to reveal a physical basis for the second dimension have been less successful. [Work supported by NIH, NASA, and ONR.]

Adapting head-related transfer functions to individual listeners

A highly efficient data reduction scheme will be described that captures the interindividual variability, present in head-related transfer functions (HRTFs), in only a limited number of parameters. The techniques used are principal component analysis and least-squares fitting of orthogonal spherical functions. The distortions introduced by the data reduction were evaluated using a distance measure based on the dB differences between HRTFs within 1/6 octaves. The distance measure correlates strongly with results of listening tests in which original HRTFs were compared with HRTFs reconstructed from the compressed data. Adaptation of HRTFs to an individual can be performed by reconstructing a set of HRTFs using estimated parameter values. Two methods for estimating these values will be discussed: prediction based on anthropometrical data and optimization using a simple listening test.

Design and Control of Shared Conferencing Environments for Audio Telecommunication Using Individually Measured HRTFs

A technique is presented for dynamically invoking a set of head-related transfer functions (HRTFs) and scaling gain, driven by a dynamic map in a graphic window. With such an interface, users may configure a virtual conferencing environment, manipulating virtual positions of teleconferees. The design of a personal headphone teleconferencing prototype is proposed, integrating spatialized sound presentation with individualized HRTF measurement using a bifunctional transducer. According to judgment tests, the use of individualized HRTFs instead of dummy-head HRTFs can reduce front-back sound image confusion.