A method for efficiently calculating head-related transfer functions - - PowerPoint PPT Presentation

▶
a method for efficiently calculating head related
SMART_READER_LITE
LIVE PREVIEW

A method for efficiently calculating head-related transfer functions - - PowerPoint PPT Presentation

May 30, 2023 294 likes •608 views

Paper Number 9892 A method for efficiently calculating head-related transfer functions (HRTFs) directly from head scan point clouds Presented at the 143rd AES Convention October 21, 2017, New York, NY, USA Rahulram Sridhar (presenter) Edgar

slide-1
SLIDE 1

A method for efficiently calculating head-related transfer functions (HRTFs) directly from head scan point clouds

Presented at the 143rd AES Convention October 21, 2017, New York, NY, USA Rahulram Sridhar (presenter) Edgar Y. Choueiri

3D Audio and Applied Acoustics (3D3A) Laboratory Princeton University, Princeton, NJ, USA www.princeton.edu/3D3A

Paper Number 9892

1

slide-2
SLIDE 2

Outline

  • Introduction
  • Motivation
  • Method Formulation
  • Application
  • Validation
  • Conclusions
  • Future Work

2

Paper Number 9892

slide-3
SLIDE 3

Outline

  • Introduction
  • Motivation
  • Method Formulation
  • Application
  • Validation
  • Conclusions
  • Future Work

3

Paper Number 9892

slide-4
SLIDE 4

Introduction

  • Currently most accurate
  • Benchmarks for comparing computed HRTFs
  • Requires anechoic chamber
  • Cumbersome to set up
  • Can be tiresome for subject
  • Not ideal for commercial implementation

4

HRTFs from acoustical measurements

HRTF measurement setup at 3D3A lab

Paper Number 9892

slide-5
SLIDE 5

Outline

  • Introduction -
  • Motivation
  • Method Formulation
  • Application
  • Validation
  • Conclusions
  • Future Work

5

Paper Number 9892

Acoustically-measured HRTFs are accurate but not ideal for commercial use.

slide-6
SLIDE 6

Motivation

6

HRTFs from morphological data: Existing methods

Numerical technique Ex: BEM, FDTD, ARD, etc. Computed HRTFs 3D meshed scan of head/torso

I.

Refs: [3 - 6] All reference numbers correspond to those in the associated convention paper.

Paper Number 9892

  • Computationally expensive.
  • Inaccurate without an accurate 3D mesh.
slide-7
SLIDE 7

Motivation

7

HRTFs from morphological data: Existing methods

All reference numbers correspond to those in the associated convention paper.

Paper Number 9892

Anthropometric data

II.

Ref: [2]

Computed HRTFs Data-driven model Ex: PCA & regression-based

Requires explicit identification and measurement

  • f anthropometric features.
slide-8
SLIDE 8

Motivation

8

HRTFs from morphological data: Proposed method

Paper Number 9892

Point cloud

  • f head/torso

Spherical- harmonic decomposition Computed HRTF Data-driven model Regression-based

  • Requires only point cloud data.
  • Computationally inexpensive.
  • Does not require explicit identification and measurement
  • f anthropometric features.
slide-9
SLIDE 9

Outline

9

Paper Number 9892

  • Introduction -
  • Motivation -
  • Method Formulation
  • Application
  • Validation
  • Conclusions
  • Future Work

Acoustically-measured HRTFs are accurate but not ideal for commercial use. Meshed scans and anthropometric features for computing HRTFs using existing methods are difficult to obtain with required accuracy.

slide-10
SLIDE 10

Method Formulation

10

Basic idea

Point clouds of head/ torso of training subjects Measured HRTFs of training subjects Spherical-harmonic decomposition Spherical-harmonic decomposition Spherical-harmonic coefficients, cS Spherical-harmonic coefficients, cH Mapping from cS to cH Linear, least-squares regression Same type of basis functions

Paper Number 9892

cS for new subject cH for new subject Synthesize HRTFs

slide-11
SLIDE 11

Method Formulation

11

Spherical harmonic representation of point cloud data

θ φ r

Assumption: Scan is already aligned as shown above.

Paper Number 9892

Represent r(θ,φ) using spherical harmonics

slide-12
SLIDE 12

Method Formulation

12

Spherical harmonic representation of HRTF data

Paper Number 9892

Example features: (1) ITDs (2) HRTF frequency responses (3) HRTF magnitude responses

Represent H(θ,φ) using spherical harmonics Choose HRTF feature and represent as spatial function, H(θ,φ)

slide-13
SLIDE 13

Outline

13

Paper Number 9892

  • Introduction -
  • Motivation -
  • Method Formulation -
  • Application
  • Validation
  • Conclusions
  • Future Work

Acoustically-measured HRTFs are accurate but not ideal for commercial use. Meshed scans and anthropometric features for computing HRTFs using existing methods are difficult to obtain with required accuracy. Point clouds Spherical harmonics Matrix multiplications HRTFs

slide-14
SLIDE 14

Application

14

Data acquisition

Measured HRTF and head scan database RIEC* [12] Number of “training” subjects, U 23 HRTF features (1) HRTF magnitude spectra in dB (cf. [10]) (2) ITD computed by thresholding (cf. [13])

All reference numbers correspond to those in the associated convention paper. *http://www.riec.tohoku.ac.jp/pub/hrtf/index.html

Paper Number 9892

slide-15
SLIDE 15

Application

15

Data pre-processing

Paper Number 9892

  • Make measured HRIRs minimum-phase and truncate

to 5.8 ms [10].

  • Align head scan such that y-axis = interaural axis and

x-axis lies in both horizontal and median planes.

All reference numbers correspond to those in the associated convention paper.

slide-16
SLIDE 16

Application

16

Spherical harmonic representation of point cloud data Maximum possible degree = 3

“Degree” corresponds to degree of spherical harmonic expansion of point cloud data

Paper Number 9892

Mapping to Degree used HRTF magnitudes 2 ITDs 1

slide-17
SLIDE 17

Application

17

Spherical harmonic representation of HRTF feature data Maximum possible degree = 14

Paper Number 9892

HRTF feature Degree used HRTF magnitudes in dB 6 (cf. [10]) ITDs 3

slide-18
SLIDE 18

Outline

18

Paper Number 9892

  • Introduction -
  • Motivation -
  • Method Formulation -
  • Application -
  • Validation
  • Conclusions
  • Future Work

Acoustically-measured HRTFs are accurate but not ideal for commercial use. Meshed scans and anthropometric features for computing HRTFs using existing methods are difficult to obtain with required accuracy. Point clouds Spherical harmonics Matrix multiplications HRTFs Derive mappings from spherical harmonic representations of point clouds to those of (1) HRTF magnitudes in dB and (2) ITDs.

slide-19
SLIDE 19

Validation

19

Approach and Metrics

Paper Number 9892

  • Number of “test” subjects = 2
  • Metric to validate computed HRTF magnitudes: log-weighted

average spectral distortion in dB.

  • Metric to validate computed ITDs: absolute ITD error.
slide-20
SLIDE 20

Validation

20

Providing Perceptual Context

Paper Number 9892

  • Approx. perceptibility threshold for rms average spectral distortion

Frequency range (kHz) Perceptibility threshold (dB) 0 to 2 1 2 to 8 2 8 to 16 3

  • Approx. perceptibility threshold for absolute ITD error = 30µs
slide-21
SLIDE 21

Validation

21

Computed HRTF magnitudes

Paper Number 9892

Log-weighted average spectral distortion in dB dB

Elevation (deg.) Azimuth (deg.)

  • Approx. rms perceptibility threshold = 1 dB
slide-22
SLIDE 22

Validation

22

Computed HRTF magnitudes

Paper Number 9892

Log-weighted average spectral distortion in dB dB

Test Subject 1 Test Subject 2

Elevation (deg.) Azimuth (deg.)

  • Approx. rms perceptibility threshold = 2 dB
slide-23
SLIDE 23

Validation

23

Computed HRTF magnitudes

Paper Number 9892

Log-weighted average spectral distortion in dB dB

Elevation (deg.) Azimuth (deg.)

Test Subject 1 Test Subject 2

  • Approx. rms perceptibility threshold = 3 dB
slide-24
SLIDE 24

Validation

24

Paper Number 9892

Computed ITDs

Elevation (deg.) Azimuth (deg.)

µs

Absolute ITD error in µs

slide-25
SLIDE 25

Outline

25

Paper Number 9892

  • Introduction -
  • Motivation -
  • Method Formulation -
  • Application -
  • Validation -
  • Conclusions
  • Future Work

Acoustically-measured HRTFs are accurate but not ideal for commercial use. Meshed scans and anthropometric features for computing HRTFs using existing methods are difficult to obtain with required accuracy. Point clouds Spherical harmonics Matrix multiplications HRTFs Derived mappings from spherical harmonic representations of point clouds to those of (1) HRTF magnitudes in dB and (2) ITDs. Used two test subjects to objectively show (with perceptual context) that computed HRTFs are accurate up to approx. 6 kHz.

slide-26
SLIDE 26

Conclusions

  • Presented the following method to compute HRTFs from point cloud data of

an individual’s morphology:

  • HRTFs directly from point clouds and no need to identify anthropometric
  • features. This makes it suitable for commercial implementation.
  • The current implementation of our method may be used to compute HRTFs

that are likely indistinguishable from measured HRTFs for f < 6 kHz.

  • More data is required to determine how the method performs at higher
  • frequencies. So the 6 kHz limit above may not be a limitation of the

method.

26

Paper Number 9892

Point cloud

  • f head/torso

Spherical- harmonic decomposition Computed HRTF Data-driven model Regression-based

slide-27
SLIDE 27

Outline

27

Paper Number 9892

  • Introduction -
  • Motivation -
  • Method Formulation -
  • Application -
  • Validation -
  • Conclusions -
  • Future Work

Acoustically-measured HRTFs are accurate but not ideal for commercial use. Meshed scans and anthropometric features for computing HRTFs using existing methods are difficult to obtain with required accuracy. Point clouds Spherical harmonics Matrix multiplications HRTFs Derived mappings from spherical harmonic representations of point clouds to those of (1) HRTF magnitudes in dB and (2) ITDs. Used two test subjects to objectively show (with perceptual context) that computed HRTFs are accurate up to approx. 6 kHz. Our method is suitable to implement commercially, and shows promise for computing HRTFs accurately, but more data is needed.

slide-28
SLIDE 28

Future Work

28

  • Applying method to larger dataset.
  • Trying different types of HRTF features to represent using

spherical harmonics.

  • Trying different mapping techniques.
  • Trying to account for the fact that the head with pinnae is a non-

star-shaped object.

  • Validation using subjective listening tests.

Paper Number 9892

slide-29
SLIDE 29

A method for efficiently calculating head-related transfer functions (HRTFs) directly from head scan point clouds

Presented at the 143rd AES Convention October 21, 2017, New York, NY, USA Rahulram Sridhar (presenter) Edgar Y. Choueiri

3D Audio and Applied Acoustics (3D3A) Laboratory Princeton University, Princeton, NJ, USA www.princeton.edu/3D3A

Paper Number 9892

29