boundary element method modelling of kemar for binaural rendering: mesh production … ·...

Boundary element method modelling of KEMAR for binauralrendering: Mesh production and validation

KAT YOUNG1, TONY TEW2 AND GAVIN KEARNEY3

1-3AudioLab, Department of Electronics, University of York, Heslington, UK1e-mail: [email protected]: [email protected]

3e-mail: [email protected]

September 23rd 2016.

Abstract

Head and torso simulators are used extensively within acoustic research, often in place of human subjectsin time-consuming or repetitive experiments. Particularly common is the Knowles Electronics Manikinfor Acoustic Research (KEMAR), which has the acoustic auditory properties of an average human head.As an alternative to physical acoustic measurements, the boundary element method (BEM) is widelyused to calculate the propagation of sound using computational models of a scenario. Combining thistechnique with a compatible 3D surface mesh of KEMAR would allow for detailed binaural analysis ofspeaker distributions and decoder design - without the disadvantages associated with making physicalmeasurements.

This paper details the development and validation of a BEM-compatible mesh model of KEMAR,based on the original computer-aided design (CAD) file and valid up to 20 kHz. Use of the CADfile potentially allows a very close match to be achieved between the mesh and the physical manikin.The mesh is consistent with the original CAD description, both in terms of overall volume and oflocal topology, and the numerical requirements for BEM compatibility have been met. Computationallimitations restrict usage of the mesh in its current state, so simulation accuracy cannot as yet becompared with acoustically measured HRTFs. Future work will address the production of meshes suitablefor use in BEM with lower computational requirements, using the process validated in this work.

1 Introduction

The perception of spatial sound is known to be a com-plex phenomenon. In order to determine the locationof a sound source, the human auditory system com-bines information from a number of cues; the differ-ences between the signals at the ears (interaural leveland time difference, ITD and ILD respectively) andthe filtering applied by the outer ear, as well as anyavailable visual cues. The ITD, ILD and the pinnaecues are all contained in a head-related transfer func-tion (HRTF) pair. The contribution of interaural dif-ferences to localisation is well understood and easilyimplemented within spatial audio reproduction sys-tems, however including accurate information fromthe whole HRTF, including pinnae cues, is more dif-ficult. HRTFs are unique to each individual as thefiltering is due to the shape of the listener’s head and

ears, whilst also varying as a function of sound sourcedirection. However, when HTRFs are used correctlyand effectively the sound field they generate at theentrance to the listener’s ears is ideally identical tothat produced by a physical sound source.

Much of binaural research centres around the ac-curate capture, analysis and synthesis of HRTFs. Un-fortunately, the experimental procedure for the cap-ture of HRTFs is time-consuming, complex and repet-itive, requiring subjects to remain as still as possi-ble for long periods of time. If HRTFs are requiredwithin an audio reproduction system, one solution isto use generic HRTFs captured from a head and torsosimulator (HATS) in place of the human subject. Aparticularly common HATS is the Knowles Electron-ics Manikin for Acoustic Research (KEMAR) seen inFig. 1, which has acoustical properties derived fromstatistical research of the average human body, mean-

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BEM modelling of KEMAR for binaural rendering Young, Tew, Kearney

ing that KEMAR has the same acoustic properties asan average human [5].

Whilst physical acoustic measurement is perhapsthe most accurate approach to capturing HRTF data,computational modelling techniques provide an ap-pealing alternative by solving the wave equation sub-ject to certain boundary conditions. The bound-ary element method (BEM) is the most common ofthese numerical techniques used in the calculationof HRTFs. BEM uses a surface mesh model of ascenario and defined sources and receivers to calcu-late the propagation of sound through the scenario.Therefore, a change in workflow to use a BEM com-patible 3D surface mesh of a HATS such as KEMARwould allow for binaural analysis of speaker distri-butions and spatial decoder designs in a very similarway to current techniques, but without the disadvan-tages associated with physical measurements of hu-man subjects. This could then be expanded to BEMcalculations using mesh models of the human subjectsif such meshes were available.

Figure 1: KEMAR model 45BC

This paper describes the development and valida-tion of a mesh model of KEMAR based on the orig-inal KEMAR computer-aided-design (CAD) file. Tofacilitate the production of a variety of mesh modelssuitable for BEM calculation in the future, a workflowis needed to ensure the resulting mesh is consistentwith the original whilst also meeting the requirementsfor BEM calculation. This process has been validatedusing a number of analysis techniques, and opens thedoor for the creation of a family of meshes optimisedfor different computational situations.

1.1 Boundary Element Method

To avoid measuring HRTFs, analytical and numeri-cal methods can be used. The simplest solution forHRTF calculation is the analytical solution for scat-tering on a sphere, where the head is approximated asa rigid sphere without the pinnae and torso [2]. With-out the pinnae the produced results are only valid forlow frequencies, as the pinnae begin to have an in-fluence above approximately 5 kHz [7]. This solutioncan be extended to include the torso in what is knownas the ‘snowman model’ [1] but this is still missing thedetails in the pinnae.

To account for this complex geometry, researchersdeveloped various numerical methods, the most com-mon of which is the boundary element method, orBEM. In BEM the boundary problem of the waveequation is converted into a surface integral, which isthen discretised into a number of elements. This setof simultaneous equations can then be solved to findthe pressure at a point on the surface.

There are two BEM techniques used in acous-tic computation: direct and indirect BEM (DBEMand IBEM respectively). DBEM is based on theHelmholtz formula, which relates the pressure inthe fluid domain (in this case air) to the pressureand its normal on the boundary, and creates a non-symmetric matrix of equations. IBEM assumes thatthe pressure field is caused by a monopole distribu-tion on the boundary surface, and creates a symmet-ric set of equations. These equations contain a com-ponent for every element in the mesh, and there is anequation for each element. Hence, with dense meshesthis equation matrix can get very large. Determiningwhich method to use depends on the problem size.For problems over a few hundred elements the directmethod is better, as it is optimised for speed. How-ever, as it solves a full set of simultaneous equationsthe storage required is large. The indirect method isslower, but requires less storage [11].

In order to be used within a BEM calculation, thesurface must both be closed and discretised into amesh. This discretisation converts a smooth surfaceinto a number of smaller planar elements, the sizeof which determines the maximum valid frequencyof the resulting calculation. It is generally acknowl-edged that a limit of 6 elements per wavelength is ac-ceptable, although this can be pushed to 4 per wave-length. The maximum frequency is then determinedby:

fmax =c

edgemax × 6(1)

where c is the speed of sound in ms-1 and edgemax

is the length of the longest edge in m. This means

Interactive Audio Systems Symposium, September 23rd 2016, University of York, United Kingdom. 2


that for a mesh to be valid at 10 kHz, the maxi-mum edge length anywhere in the mesh must be lessthan 5.67 mm. For 20 kHz validity, this maximum is2.83 mm.

BEM has been historically restricted to fairly lowfrequency calculations because of the storage require-ments, but advances in computational resources arecontinually raising the upper frequency limit.

2 Historic Work

Weinrich was the first to attempt modelling the soundfield around the head in 1984 using a number of nu-merical techniques [16]. The ear canal was modelledas a series of cylinders of varying radius, and thesound field calculated using transmission line theory.The sound field of a simple two-dimensional geomet-ric model of the pinna was calculated using a finitedifference time domain approach, and showed roughlythe dependence of the first HRTF notch on soundsource elevation. A coarse surface mesh for the headwas also created, minus the pinnae, with the responsecalculated using BEM. The maximum validity of themesh was only 1.7 kHz, but the results in this rangecompared favourably with measurements made on aphysical replica of the BEM model.

In the early 2000s Katz used BEM to calculate in-dividualised HRTFs, focussing on the contribution ofhead and pinnae shape to the HRTF [12]. Modellingthe head in a BEM environment allows for modifica-tions such as the removal of the pinnae - crucial to in-vestigating the contribution made to the HRTF, butnot something possible with a real human subject.The work was limited by available computational re-sources, with 5.4 kHz being the maximum valid fre-quency: even after simplifying the requirements thefull calculation took 50 days of CPU time.

As the optical scanner used by Katz was restrictedto line-of-sight only, behind the ears, the cavities ofthe ear, and the ear canal were all viewed as filled.This is not a problem in the case of the ear canal, asmost HRTF measurements are done using a blockedear canal. It has been shown that the ear canaldoes not provide any directionally dependent infor-mation [6], and ear canal-related resonance wouldonly need to be included if the sound reproductionsite were to be at the eardrum itself. The filled-innature of the ear cavities will probably have causederrors in the final solution results, but these wouldlikely have been above the valid frequency of the cal-culation. Modifications of the mesh outputted by theoptical scanner were also required. The top and bot-tom of the mesh were closed, as the scanner could not

handle perpendicular surfaces or those which extendbeyond the machine, and holes in the mesh were filledin. The mesh was then coarsened to make the compu-tation more manageable and refined in regions wherelarge elements existed. Katz could not locate any ex-isting software to do this coarsening and refining, soa brute force approach was taken.

Jin et al. used Fast Multipole BEM (FM-BEM)to calculate the HRTFs of a large database ofsubjects scanned using magnetic resonance imaging(MRI), culminating in the Sydney York Morpholog-ical and Acoustic Recordings of Ears (SYMARE)database [8]. The database contains both the meshessuitable for use within BEM at a range of frequen-cies and the HRTFs calculated from them. Vari-ous software applications were used in the process-ing workflow to perform steps similar to those de-scribed by Katz [12]. The SYMARE database isavailable at a number of frequency resolutions: 6 kHz,8 kHz, 10 kHz, 12 kHz, and 16 kHz, whilst thehead-only mesh is available at 15 kHz, 16 kHz and20 kHz. An average mesh has approximately 130,000elements. The Amira software [3] was used to ex-tract the surface meshes from the scan data. Ge-omagic Studio (now discontinued, replaced by Geo-magic Wrap [4]) was then used to clean the meshand fill in holes (ear canal, nose etc). Geomagic Stu-dio and the open source software MeshLab [13] wereused to complete the various alignments and mergesrequired across mesh resolutions. The open sourcesoftware ACVD [15] was then used to improve uni-formity of the surface elements across the mesh, andGeomagic Studio used again to reduce the number ofelements by applying a small amount of smoothing.

In a large body of work culminating in [10],Kahana and Nelson used a laser-scanned model ofKEMAR in BEM calculations to look at contribu-tions made by the pinnae to the HRTF (known aspinna-related transfer functions: PRTFs) by usingboth KEMAR and a baffled pinnae, in similar workto Katz. Their results were also limited in frequencydue to the available computational resources, withthe calculations valid below 10 kHz.

The scanned surface was decimated using an al-gorithm by Johnson and Hebert [9] to create a morehomogenous distribution of nodes and elements, cre-ating a mesh with 23,000 elements valid up to 10 kHz(using the rule-of-thumb of 6 elements per wave-length). Their work showed the feasibility of BEMusage up to higher frequencies, but full mesh calcu-lation was still limited by computation requirements.The baffled pinnae mesh was valid up to 20 kHz dueto the physically smaller size of the mesh.

Previous work using KEMAR within BEM has



relied on a scanned version of some form. This hasbeen shown to have certain limitations. Often scan-ners are restricted to line-of-sight, meaning occludedareas cannot be captured. This leads to regions suchas behind the ear and resonant cavities within the earbeing seen as filled [12], an obvious difference whencompared to an actual pinna. Important morpholog-ical details can also be lost if the scan is not of ahigh enough resolution [10], as well as requiring postprocessing to combine scans from multiple directions.In the present work, however, the original CAD fileof KEMAR used to produce the physical dummy isused rather than a scan, meaning complete accuracycan in principle be obtained.

3 Methodology

Following the work of Jin et al. [8], a number of soft-ware applications were used to create a mesh suit-able for BEM usage from the initial CAD file. TheCAD information describes the entirety of KEMAR,including torso and base. Perfect consistency withthe physical KEMAR was therefore theoretically pos-sible, and the model should not suffer from the disad-vantages associated with some scanning techniques.Once created by the designer, the 3D shape in theCAD file is described using a series of large faces,defined by cartesian coordinate points and curvedsplines known as boundaries. These large curvedfaces can be seen in Fig. 2. This type of definition isunsuitable for BEM calculation, so conversion was re-quired to create a discretised planar polygonal mesh.

Figure 2: Head portion of the KEMAR CAD file

Geomagic Wrap [4] was used to convert the CADfile to a polygonal mesh, defined by information con-tained within the STEP CAD file format. The re-sulting mesh had 200,014 vertices and 400,001 faces,but with an irregular and undesirable distribution ofshape and size. The maximum edge length in thismesh was 28.3 mm (as can be seen in Figures 3a

and 3b), most likely due to larger flatter areas ofthe torso defined using fewer mesh elements. As themaximum valid frequency is dependent on the largestedge length present in the mesh, a remeshing proce-dure was required to create a mesh that is valid upto 20 kHz by breaking up these large flat regions andreducing the edge lengths.

Edge Length (mm)0 5 10 15 20 25 30

Fre

quen

cy

×105

0

0.5

1

1.5

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(a) Prior to remeshing: full histogram

Edge Length (mm)5 10 15 20 25

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0

100

200

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(b) Prior to remeshing: tail of histogram

Edge Length (mm)0 1 2 3 4 5

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(c) After remeshing: full histogram

Figure 3: Distribution of edge lengths in mesh before andafter remeshing

The ‘remesh’ feature of Geomagic Wrap was usedto redefine the surface mesh with a target edge lengthof 2 mm. This process resulted in a mesh with amuch improved distribution of edge lengths (as seenin Fig. 3c); whilst not all are under the target lengthof 2 mm, the largest is only 4.04 mm, giving a max-imum valid frequency of 14 kHz when assuming 6edges per wavelength. This is better than the origi-nal mesh, but still not ideal. The shape of some faces



was also undesirable, in that they were too long andthin. Equilateral triangles are much preferred overlong thin triangles.

To create more nearly equilateral triangles acrossthe mesh, the open source software ACVD [15] wasused. This improved the distribution of edge lengths,as seen in Fig. 4. The maximum edge length was re-duced to 2.49 mm (valid to 22.7 kHz when assuming6 edges per wavelength) but at the expense of manymore vertices and faces.

Edge Length (mm)0 0.5 1 1.5 2 2.5

Fre

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cy

×104

0

2

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Figure 4: Distribution of edge lengths in final mesh

The remeshing process introduced a large numberof unreferenced vertices: more specifically, the proce-dure did not remove the vertices associated with theprevious arrangement of triangles, resulting in morevertices than were used. This did not affect the struc-ture of the mesh, but would require a BEM solver todo more calculations than was strictly needed. Theopen source software MeshLab [13] was used betweenGeomagic Wrap and ACVD to remove these unrefer-enced vertices.

The final mesh had 360,017 vertices and 720,015faces, a portion of which including the pinnae appearsin Fig. 5. It can been seen that the mesh containsconsistently small equilateral triangles.

The volume of the mesh at each stage of process-ing was also calculated to ensure no large discrep-ancies were introduced, as a change in volume fromthe original mesh invalidates any BEM calculations.These volume calculations, and their difference fromthe original CAD file, can be seen in Table 1. There isa very small loss of volume at each stage that can beattributed to the slight rounding of sharp corners dur-ing the remeshing and redistribution processes, how-ever no particular stage introduced a large variationin volume, suggesting that all software applicationsand processes used were valid. This is investigatedfurther in the next section.

Figure 5: Pinna portion of the final mesh

4 Validation

A number of validation steps were required duringthe process of mesh production to inform decisions.As detailed in the previous section, maximum edgelength and volume were the primary criteria for va-lidity at each stage of the process.

In addition to the maximum edge length crite-rion, BEM solvers often have a minimum and max-imum internal angle requirement to help avoid theinclusion of long thin triangles. In this and relatedfuture work, the PACSYS PAFEC-FE software [14]is the intended BEM solver, which enforces angles tobe between 15°and 150°. All angles in the final meshwere between these limits (as seen in Fig. 6), with theminimum at 16.0°and maximum at 146.7°.

Angle (degrees)0 20 40 60 80 100 120 140 160

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Figure 6: Distribution of angles in the final mesh

The local topology of the mesh was also of im-portance to ensure no regions were distorted by theprocess, so the distances between the faces in the orig-inal CAD data and the processed mesh were calcu-lated. These values show that the local topology isconsistent with the original, with all values less than0.64 mm and the majority less than 0.1 mm; somefaces had zero distance between them. This distribu-tion can be seen in Fig. 7. The larger distances liein regions such as the edge of the base and withinthe eyes, where the radius of curvature can be rela-tively small and the shape has been rounded during



Mesh Volume (mm3) Difference from originalOriginal CAD file 28492978 0%

Initial mesh 28489372 -0.0127%Remeshed at target edge length 28488486 -0.0158%

Redistributed mesh 28486546 -0.0226%

Table 1: Volume calculations for each stage of processing - mm3 is required for the differences to be visible.

the remeshing or redistribution process. These re-gions are not of critical importance to the BEM cal-culation however; the values in the region around thepinnae are of higher importance. Whilst not zero, thevalues here are small enough to be considered valid,although further testing is required to confirm thisfor different applications. Fig. 8 shows the distancesbetween the faces as a function of colour, with blackat zero and white at the maximum value of 0.63mm.Whilst the pinna lights up a small amount, there isnot as much white as in other regions of the mesh.

Unfortunately, whilst the mesh is numericallyvalid for BEM and consistent with the original CADfile, the size of the mesh renders it unusable by cur-rent solvers. A mesh consisting of 720,015 faceswould require 7725GB of RAM to store the neces-sary equations to then solve using the PAFEC-FEsoftware. This means that HRTFs of KEMAR can-not be calculated using this version of the mesh: aphysically smaller mesh or one with a lower frequencylimit would be required. Additionally, even if themesh could be used for BEM calculation of HRTFs,this mesh includes the ear canals, and there are nodatabases of acoustically measured KEMAR HRTFswhich include the ear canal to compare against.

Distance between meshes (mm)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

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(a) Full histogram

Distance between meshes (mm)0.1 0.2 0.3 0.4 0.5 0.6 0.7

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(b) Tail of histogram

Figure 7: Distribution of distances between the twomeshes



Figure 8: Distances in mm between the two meshes, plotted on the final mesh as a colourmap

5 Conclusion

The original KEMAR CAD file was converted usinga number of processing stages to a mesh which meetsthe topological constraints for BEM compatibility.The original 3D surface data has been discretised,remeshed and redistributed to meet the edge lengthrequirement for a 20 kHz maximum valid frequencyand the angle limitations imposed by the BEM solver.The volume and topology of the meshes prior to andafter processing have been compared to ensure con-sistency between the original and the final mesh, andwhilst there are small differences these are likely tobe within the margin of error introduced when com-paring a calculated result with a physically measuredresult. The workflow created in this paper is applica-ble more generally to the processing of meshes editedfrom an original, with consistency and validity as-sumed.

5.1 Further Work

Due to computational limitations the final mesh isnot usable in BEM calculations in its current state.The primary aim of this work was to determine theworkflow required to accurately convert the CAD in-formation into a BEM-friendly mesh; further work isneeded to address the problem of computation andusage. This could include a reduction in maximumvalid frequency, by permitting longer edges and there-fore larger faces, or by using different meshes for dif-

ferent frequency ranges. Physical mesh size couldalso be adjusted: a mesh consisting of only headand shoulders would be sufficient for the majorityof HRTF calculations, whereas the entire torso ofKEMAR is present here. A mesh without ear canalswould also be of more use than the current mesh, al-lowing comparison between typical acoustically mea-sured HRTFs and those calculated using BEM.

6 Acknowledgements

This work is supported by Meridian Audio Ltd andMQA Ltd. Thanks also to Mr Laurence Hobden, MrPatrick Macey and Mr John King from PACSYS, andto G.R.A.S for supplying the CAD file of KEMAR.

References

[1] V Ralph Algazi, Richard O Duda, Ramani Du-raiswami, Nail A Gumerov, and Zhihui Tang.Approximating the head-related transfer func-tion using simple geometric models of the headand torso. The Journal of the Acoustical Societyof America, 112(5):2053–2064, 2002.

[2] Richard O. Duda and William L Martens. Rangedependence of the response of a spherical headmodel. The Journal of the Acoustical Society ofAmerica, 104(5):3048, nov 1998.



[3] FEI. Amira 3D Software for Life Sciences, 2016.

[4] Geomagic. Geomagic Wrap 3D Imaging soft-ware, 2016.

[5] G.R.A.S. Head & Torso simulators, 2016.

[6] D Hammershøi and H Møller. Sound transmis-sion to and within the human ear canal. TheJournal of the Acoustical Society of America,100(1):408–27, 1996.

[7] David Howard and Jamie Angus. Pinnae andhead movement effects. In Acoustics and Psy-chacoustics, chapter 2.6.3, page 103. Focal Press,2 edition, 2001.

[8] Craig Jin, Pierre Guillon, Nicolas Epain, RezaZolfaghari, Andre Van Schaik, Anthony I Tew,Carl T Hetherington, and Jonathan B Thorpe.Creating the Sydney York Morphological andAcoustic Recordings of Ears Database. IEEETransactions on Multimedia, 16(1):37–46, 2014.

[9] Andrew E Johnson and Martial Hebert. Controlof polygonal mesh resolution for 3-d computervision. Graphical Models and Image Processing,60(4):261–285, 1998.

[10] Yuvi Kahana and Philip A Nelson. Boundaryelement simulations of the transfer function of

human heads and baffled pinnae using accurategeometric models. Journal of Sound and Vibra-tion, 300:552–579, 2007.

[11] Brian F. G. Katz. Boundary element method cal-culation of individual head-related transfer func-tion. I. Rigid model calculation. The Journal ofthe Acoustical Society of America, 110(5):2440,2001.

[12] Brian F. G. Katz. Boundary element method cal-culation of individual head-related transfer func-tion. II. Impedance effects and comparisons toreal measurements. The Journal of the Acousti-cal Society of America, 110(5 Pt 1):2449–55, nov2001.

[13] MeshLab. MeshLab, 2016.

[14] PACSYS Ltd. PAFEC-FE, 2016.

[15] S. Valette, J.-M. Chassery, and R. Prost.Generic Remeshing of 3D Triangular Mesheswith Metric-Dependent Discrete Voronoi Dia-grams. IEEE Transactions on Visualization andComputer Graphics, 14(2):369–381, 2008.

[16] Søren Gert Weinrich. Sound field calculationsaround the human head. Acoustics Laboratory,Technical University of Denmark, 1984.


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