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Brinkmann, Fabian; Lindau, Alexander; Müller-Trapet, Markus; Vorländer, Michael; Weinzierl, Stefan
(2015): Cross-validation of measured and modeled head-related transfer functions. In: Fortschritte der
Akustik - DAGA 2015: 41. Jahrestagung für Akustik, 16. - 19. März 2015 in Nürnberg. Berlin: Deutsche
Gesellschaft für Akustik e.V. pp. 1118–1121.
Fabian Brinkmann, Alexander Lindau, Markus Müller-Trapet, Michael
Vorländer, Stefan Weinzierl
Cross-validation of measured and modeled
head-related transfer functions
Published versionConference paper |
Cross-validation of measured and modeled head-related transfer functions
Fabian Brinkmann1, Alexander Lindau1, Markus M¨uller-Trapet2,
Michael Vorl¨ander2, Stefan Weinzierl1
1Audio Communication Group TU Berlin, Einsteinufer 17c, D-10587 Berlin, Germany.
E-Mail: {fabian.brinkmann, alexander.lindau, stefan.weinzierl}@tu-berlin.de
2Institute of Technical Acoustics, RWTH Aachen University, Kopernikusstr. 5, D-52074 Aachen, Germany.
E-Mail: {mmt, mvo}@akustik.rwth-aachen.de
Abstract
In the current study, we present full-spherical high reso-
lution head-related transfer function (HRTF) datasets of
the head and torso simulator FABIAN including data for
multiple head-above-torso orientations within a typical
horizontal rotation range of ±50 degrees. While the first
dataset was measured acoustically using sequential swept
sines, the second one was modeled numerically using
the boundary-element method accelerated with the fast-
multipole method (FMM-BEM). Comparison of magni-
tude spectra revealed a good agreement at mid and high
frequencies, but increasing differences at frequencies be-
low 200 Hz which could be attributed to the limited fre-
quency range of the measurement loudspeaker. Addi-
tionally, an analysis of times of arrival (TOA) revealed
differences which were presumably caused by mechanical
inaccuracies of the physical measurement setup. Con-
sequently, by using the modeled data as a reference, in
the measured head-related impulse responses (HRIRs),
we corrected TOAs by fractionally delaying, and extrap-
olated the low frequency range.
Introduction
Virtual acoustical environments may be created through
reproduction of measured or modeled binaural signals us-
ing headphones or cross-talk compensated loudspeaker
setups – a method which is called binaural synthesis [1].
It was shown that a plausible acoustical simulation – i.e.,
“a simulation in agreement with the listener’s expecta-
tion towards a corresponding real event” [2, p. 804] –
may be achieved already with non-individual dynamic
binaural synthesis. In this case, head rotations of the lis-
tener are accounted for by real time exchange of binaural
transfer functions which were measured using a dummy
head. When using individual transfer functions and less
critical audio contents such as speech, simulations can
be authentic – i.e., indistinguishable from a given refer-
ence [3].
The potentially high degree of realism and the techni-
cal simplicity of binaural synthesis suggest its usage as
a reference when benchmarking other approaches of spa-
tial audio reproduction such as loudspeaker array based
methods [4] or room acoustic simulation [5]. This in turn
implies that in order to allow for a reliable comparison
between measured and modeled binaural simulations, the
acquisition of binaural transfer functions (binaural room
impulse responses – BRIRs, HRTFs) needs to be thor-
oughly validated as otherwise measurement errors could
bias the results.
Hence, we suggest a thorough cross-validation using
HRTFs both from acoustical measurements, and numer-
ical simulations. This ’two-sided’ validation approach
is founded in inherent restrictions that are related to
both acquisition approaches: In case of measurements,
through inaccuracies in microphone, subject, and loud-
speaker positioning, as well as non-ideal characteristics
of electro-acoustic transducer (e.g. time variance; devia-
tion from omni-directionality [6]) may indroduce errors,
whereas in case of the simulation trade-offs in the dis-
cretization of the subjects’ geometry, and assumptions
about the acoustical surface impedance may give room
for speculations [7].
Head-related transfer function acquisition
HRTFs for the head and torso simulator FABIAN [8]
were acquired for 11950 source position and 11 az-
imuthal head-above-torso orientations (head rotations to
the left and right) covering the typical range of motion of
±50◦[9]. The resolution of source positions (2◦in eleva-
tion; 2◦great circle distance in azimuth, cf. Fig. 1) was
chosen to allow for perceptually transparent HRTF inter-
polation, and aliasing-free high order spherical harmonic
representation. Head-above-torso orientations were mea-
sured in distances of 10◦to assure that artifacts due to
their interpolation remain below the threshold of per-
ception [10]. In the following, we briefly describe the
methods used for measuring and modeling HRTFs.
Measurements
HRTFs were measured in the fully anechoic chamber
of the Acoustics Groups at Carl von Ossietzky Univer-
sity Oldenburg with a lower cut-off frequency of 50 Hz
above which free field conditions may be assumed. The
used Two Arc Source Positioning system (TASP) con-
sisted of two semicircular arcs with a radius of 1.7 m
which could be rotated about the vertical axis. Each arc
was equipped with a Manger MSW bending-wave sound
transducer that could automatically be moved to differ-
ent elevations. Due to mechanical restriction, HRTFs
could not be measured for elevations below −64◦, result-
ing in approximately 5 % of missing data (11345 HRTFs).
FABIAN’s interaural center was aligned to the center of
the measurement system using a cross-line laser and a
laser pointer attached to FABIAN neck joint. Measure-
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Figure 1: Left: Source positions used for HRTF acquisition.
Gray dots denote missing data in measured HRTFs. Right:
Setup for measuring HRTFs.
ments were conducted using sequential swept sines at a
sampling rate of 44.1 kHz. HRTFs were obtained by spec-
tral division of sweeps recorded at FABIAN’s blocked ear
canals and sweeps recorded in the center of the measure-
ment system in the absence of FABIAN. The measure-
ment setup is depicted in Fig. 1, more information can
be found in [11].
Numerical modeling
The numerical HRTF simulation by means of the BEM
required a mesh representation of FABIAN which was
obtained as follows: In a first step, a point cloud repre-
sentation of FABIAN was obtained using a GOM ATOS I
structured light scanner. A point spacing of approxi-
mately 1/100 mm for the head and pinnae, and 1/10 mm
for the torso was achieved by aligning overlapping scans
from multiple viewing directions. FABIAN’s neck, and
torso bottom plate were excluded from the scan because
of their reflecting metallic surfaces. The alignment of
point clouds from different scans was done using refer-
ence points that were marked on FABIAN beforehand
and surface matching as implemented in the ATOS Pro-
fessional software (precision of approx. 1/100 mm).
In the next step, a non-uniform rational basis spline
(NURBS) representation was generated from the point
cloud data using the Geomagix Studio 12 software. Sub-
sequently, the CAD software Rhino was used (a) to de-
sign a cylindrical neck with seamlessly transitions be-
tween head and torso, (b) to close holes in the NURBS
representation, (c) to extend the torso bottom to its orig-
inal size, and (d) to connect the arms to the torso as these
were scanned separately before (cf. Fig. 2, left).
In a last step, Virtual.Lab Acoustics 13.1 was used
for meshing the NURBS data and calculation of com-
plex HRTF spectra at frequencies between 100 Hz and
22.2 kHz with a resolution of 100 Hz. To speed up the
calculation, two triangular meshes with different resolu-
tions were generated: a coarse mesh with edge lengths of
2 mm, 10 mm, and 10 mm for pinnae, head, and torso,
respectively was used for BEM calculations up to 6 kHz,
and a fine mesh with edge lengths of 2 mm, 2 mm, and
5 mm was used for the FMM-BEM above 2 kHz. The
overlapping region between 2 kHz and 6 kHz was used
for verifying that both calculations yielded identical re-
sults. The edge lengths were chosen to fulfil the typical
Figure 2: Left: NURBS represenatation of FABIAN. Light
gray surfaces were manually inserted into the model. Right:
Coarse mesh of FABIAN’s head. Red area denotes micro-
phone position.
requirement of six elements per wavelength in the fre-
quency range under investigation [12]. Simulations were
then carried out by imposing a constant velocity bound-
ary condition on the part of the mesh corresponding to
the microphone at the ear canal entrance of FABIAN.
Otherwise, the mesh was assumed to be sound-hard, i.e.,
with an admittance of zero. The HRTFs were calculated
by dividing the result at the fieldpoints by the analytical
solution of a point source with the same volume veloc-
ity placed in the center of the coordinate system. Finally,
HRIRs with a sampling rate of 44.1 kHz were obtained by
inverse Fourier transform after mirroring the single sided
spectrum considering the symmetry properties of the dis-
crete Fourier transform [13]. The frequency bin at 0 Hz
was set to 1 (0 dB) beforehand. HRIRs for three different
models were calculated: (a) A sound-hard head and torso
model, (b) A head and torso model with an impedance
boundary condition on the torso bottom corresponding
to a porous absorber with a thickness of 30 mm, and (c)
a head, torso, and legs model with legs modeled by a
an elliptical cylinder with the surface impedance of the
porous absorber as in case (b). (cf. Fig. 2, right).
Cross-validation of measured and modeled
head-related transfer functions
Samples of measured and modeled HRIRs/HRTFs for
neutral head-above-torso orientation in the median plane
showed a good first visual agreement (cf. Fig. 3). A
more detailed analysis of spectral and temporal differ-
ences and their implications will be given in the follow-
ing – restricted to HRTFs for neutral head-above-torso
orientation due to page limititations.
Temporal cross-validation
Ideally, TOA should be identical in measured and mod-
eled HRIRs. However, differences in the range of 3 sam-
ples (equaling a displacement of approx. 2.3 cm) were
observed between the two conditions. As the geomet-
rical alignment of the sound sources and FABIANs in-
teraural center was believed to be almost perfect for the
BEM simulation, we used the modeled data as a reference
for correcting the TOA of the measured HRIRs. This
was done separately for the left and right ear HRIRs us-
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Figure 3: Measured (left) and modeled (right) HRIRs (top)
and HRTF magnitude spectra (bottom) in the median plane.
Elevation of 0◦, and 180◦denote sources in the front, and
back. Color denotes magnitude in dB.
ing fractional delaying [14]. The amount of delay τwas
estimated by maximizing the cross-correlation between
pairs of ten times up-sampled measured and modeled
HRIRs, hence τ=argmax
τxy (τ). For the fractional
delay we used Kaiser windowed sinc filters of order 70,
exhibiting negligible magnitude and group delay distor-
tions (<0.1dB;<0.01 samples, ∀f<20 kHz). As a re-
sult the average (and minimum) cross-correlations in our
data increased from 0.7 (-0.18) to 0.94 (0.56). Fig. 4
shows two HRIRs before and after TOA correction.
An analysis across source positions revealed slight
TOA discontinuities in measured data – stemming from
start and end points of the 360◦rotation of the TASP,
and from the two differently mounted measurement loud-
speakers – which were also removed by the fractional de-
lays. The TOA treatment caused changes in the broad
band interaural time difference (ITD) of about ±0.5 sam-
ples (≈11 μs) in the proximity of the horizontal plane.
Differences of about -1.1 to 2.9 samples (≈66 μs) ocurred
for lateral sources where, however, the auditory system
is less sensitive to changes in the ITD [15]. Induced ITD
changeswerethusbelievedtobebelowthethresholdof
perception, and the applied fractional delays were con-
sidered to be perceptually non-critical.
Spectral cross-validation
Spectral differences between measured and modeled
HRTFs were evaluated in 40 auditory filter bands be-
tween 50 Hz and 20 kHz [16]. The results for the three
different FABIAN models (cf. Sec. Numerical model-
ing) were almost identical, and thus the non-rigid sur-
faces models were discarded for simplicity. Results for
the rigid surface model are shown in Fig. 5 for the left
ear HRIRs averaged across source positions. Results
can be discussed with regard to three frequency ranges
showing distinct error pattern: Deviations as seen be-
low 200 Hz are caused by the limited frequency response
of the loudspeaker. Here, the levels of measured HRIRs
are systematically below their modeled counterpart. Be-
tween 200 Hz and 6 kHz the median deviation is approx.
0 20406080100
ï
0
t in samples
HRIR amplitude
Figure 4: Modeled (gray) and measured left ear HRIRs be-
fore (dashed) and after (solid) fractional delaying. For illus-
tration only the HRIR with the lowest cross-correlation before
the alignment is sown.
0 dB, while 90% of the errors are smaller than ±2dB,
and the maximum error remains below ±8 dB. Above 5-
6 kHz notches occur in the HRTF magnitude response,
that are caused by pinnae (anti) resonances [17] and are
highly sensitive to small changes of sound incidence, or
microphone position [6]. Hence, the median difference
between measured and modeled HRTFs increases to ap-
prox. ±3 dB. For 90% of the source positions the error
remains well below ±10 dB, whereas the maximum error
occasionally exceeds this range. Results for the right ear
were of comparable magnitude.
High frequency differences in the HRTFs could be ei-
ther induced by mechanical inaccuracies of the measure-
ment setup, or by simplifying assumptions underlying
the BEM simulation, making them difficult to correct.
Observed low frequency differences, however, are clearly
caused by non-ideal loudspeaker characteristics and could
therefore be corrected by extrapolation: Xie [18] pro-
posed a linear interpolation of magnitude and phase re-
sponses, Bernsch¨utz [19] coupled a time and level aligned
low pass filter to the measured HRIRs, Algazi et al. [20]
fitted analytically modelled transfer functions derived
from fitted spherical/elliptical head and torso models,
and Gumerov et al. [21] suggested using data obtained
from BEM simulations. The latter was applied in our
case, too, assuming the modeled data to be valid for
low frequencies. To avoid discontinuities, measured and
modeled HRTF magnitude and unwrapped phase spec-
tra were combined separately using a linear fade between
200 and 500 Hz.
Discussion and outlook
In the current study, we presented high-resolution HRTF
datasets for various head-above-torso orientations which
we measured acoustically, and simulated numerically us-
ing the BEM. We presented results from temporal and
spectral analyses of both types of data. Thereby, we came
to the conclusion that both, measured and modeled data
suffered from specific shortcomings in so far that none of
them alone could provide us with a general ground truth.
However, from our analyses we could identify frequency
ranges in which each of the data sets appeared to be more
reliable than the other one, in turn using the more reli-
able data for a correction (cross-validation) of the other.
Thus, small TOA deviations which we observed in mea-
sured data and which could be ascribed to asymmetries
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.1 110 20
−12
−8
−4
0
4
8
12
f in Hz
Deviation in dB
Figure 5: Deviations between measured and modeled
HRTFs for 40 auditory filter band averaged across source po-
sitions before (colored) and after low frequency extrapolation
(gray scale; Median errors given by black and orange solid
lines; 10%-90% percentile range by solid gray/red lines; 0%-
100% percentile range by dashed gray/red lines).
of the mechanical measurement setup were corrected by
aligning them to the modeled data by means of fractional
delay correction. Additionally, we investigated the dif-
ferences between measured and modeled HRTF magni-
tude spectra in 40 auditory filter bands. Below 200 Hz,
measured HRTFs were found to be invalid due to the
non-ideal loudspeaker frequency response, hence, missing
low-frequency information was recreated using the mod-
eled data. Above 200 Hz, magnitude spectra were found
to be reasonably comparable and differences were of an
order as reported, e.g., by Gumerov et al. [21]. Above
6 kHz, however, spectral differences increased presum-
ably caused by slightly mismatched pinna notches. As in
this case, causes for discrepancies could not be satisfac-
torily identified, we refrained from correcting either data.
For the future we plan to extrapolate the missing mea-
sured HRTFs at low elevations using an approach as
suggested by Ahrens et al. [22]. Furthermore, we aim
at psycho-acoustically validating the localization perfor-
mance obtainable with our HRTF sets using a model sug-
gested by Baumgartner et al. [23].
Acknolwdgement
The work is part of the Simulation and Evaluation of
Acoustical Environments (SEACEN) project funded by
the German Research Foundation (DFG WE 4057/3-2).
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