Assessing Spherical Harmonics Interpolation of Time-Aligned Head-Related Transfer Functions

Arend, Johannes M.; Brinkmann, Fabian; Pörschmann, Christoph

doi:10.17743/jaes.2020.0070

Cited by 18 publications

(45 citation statements)

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“…This approach has been shown to be more robust against measurement noise than methods based on onset detection [24] and obtained promising results in recent perceptual studies [22,23]. However, it is expected that methods based on onset detection would perform similarly [40]. [16], and (c) after setting its phase to zero.…”

Section: Time-alignment (Ta)mentioning

confidence: 99%

Assessing HRTF preprocessing methods for Ambisonics rendering through perceptual models

2022

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Binaural rendering of Ambisonics signals is a common way to reproduce spatial audio content. Processing Ambisonics signals at low spatial orders is desirable in order to reduce complexity, although it may degrade the perceived quality, in part due to the mismatch that occurs when a low-order Ambisonics signal is paired with a spatially dense head-related transfer function (HRTF). In order to alleviate this issue, the HRTF may be preprocessed so its spatial order is reduced. Several preprocessing methods have been proposed, but they have not been thoroughly compared yet. In this study, nine HRTF preprocessing methods were used to render anechoic binaural signals from Ambisonics representations of orders 1 to 44, and these were compared through perceptual hearing models in terms of localisation performance, externalisation and speech reception. This assessment was supported by numerical analyses of HRTF interpolation errors, interaural differences, perceptually-relevant spectral differences, and loudness stability. Models predicted that the binaural renderings’ accuracy increased with spatial order, as expected. A notable effect of the preprocessing method was observed: whereas all methods performed similarly at the highest spatial orders, some were considerably better at lower orders. A newly proposed method, BiMagLS, displayed the best performance overall and is recommended for the rendering of bilateral Ambisonics signals. The results, which were in line with previous literature, indirectly validate the perceptual models’ ability to predict listeners’ responses in a consistent and explicable manner.

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Section: Time-alignment (Ta)mentioning

confidence: 99%

Assessing HRTF preprocessing methods for Ambisonics rendering through perceptual models

2022

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“…The current GAN-based approach cannot yet be directly compared to other state-of-the-art HRTF interpolation methods, such as the ones described by Arend et al (2021), since it up-samples over 1 dimension only. Introducing up-sampling over an additional dimension (e.g., azimuth, in addition to elevation) would allow a direct comparison, but would require a compression or mapping of the 3D surface to 2D, possibly using graph networks and 2D convolutional layers for both the discriminator and the generator.…”

Section: Discussionmentioning

confidence: 99%

“…This is done by representing the HRTF set as a weighted sum of surface SH, and then sampling the resulting spherical function at the desired directions. This interpolation method has been shown to be most effective if the HRTF set is initially preprocessed to reduce its direction-dependency, such as removing the ITDs prior to calculating the SH representation (Arend et al, 2021;Engel et al, 2022). This method works well when the HRTF set is sampled evenly around the sphere.…”

Section: Hrtf Spatial Up-samplingmentioning

confidence: 99%

Spatial up-sampling of HRTF sets using generative adversarial networks: A pilot study

Siripornpitak

Engel

Squires

et al. 2022

Front. Signal Process.

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Headphones-based spatial audio simulations rely on Head-related Transfer Functions (HRTFs) in order to reconstruct the sound field at the entrance of the listener’s ears. A HRTF is strongly dependent on the listener’s specific anatomical structures, and it has been shown that virtual sounds recreated with someone else’s HRTF result in worse localisation accuracy, as well as altering other subjective measures such as externalisation and realism. Acoustic measurements of the filtering effects generated by ears, head and torso has proven to be one of the most reliable ways to obtain a personalised HRTF. However this requires a dedicated and expensive setup, and is time-intensive. In order to simplify the measurement setup, thereby improving the scalability of the process, we are exploring strategies to reduce the number of acoustic measurements without degrading the spatial resolution of the HRTF. Traditionally, spatial up-sampling of HRTF sets is achieved through barycentric interpolation or by employing the spherical harmonics framework. However, such methods often perform poorly when the provided HRTF data is spatially very sparse. This work investigates the use of generative adversarial networks (GANs) to tackle the up-sampling problem, offering an initial insight about the suitability of this technique. Numerical evaluations based on spectral magnitude error and perceptual model outputs are presented on single spatial dimensions, therefore considering sources positioned only in one of the three main planes: Horizontal, median, and frontal. Results suggest that traditional HRTF interpolation methods perform better than the proposed GAN-based one when the distance between measurements is smaller than 90°, but for the sparsest conditions (i.e., one measurement every 120°–180°), the proposed approach outperforms the others.

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“…Describing and interpolating HRTFs in the spherical harmonics (SH) domain is an efficient and recently quite popular approach. (Evans et al, 1998;Richter, 2019;Arend et al, 2021). However, the highest representable frequency is limited by the SH order N, following the relation N ~kr (Rafaely and Avni, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…Sparsely measured HRTF sets with N sparse < N max cannot meet this requirement and their SH representation suffers from so-called sparsity errors (see Section 2.2). Various recent publications investigated SH interpolation of sparse HRTF sets and the associated sparsity errors (Ben-Hur et al, 2019;Arend et al, 2021). These studies only considered sparse HRTF sets sampled on regular (explicitly defined) grids, for which the SH order is usually known (Zotter, 2009b) (Rafaely, 2015, Chap.…”

Section: Introductionmentioning

confidence: 99%

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

Bau

Arend²,

Pörschmann³

2022

Front. Signal Process.

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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.

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Assessing Spherical Harmonics Interpolation of Time-Aligned Head-Related Transfer Functions

Cited by 18 publications

References 0 publications

Assessing HRTF preprocessing methods for Ambisonics rendering through perceptual models

Assessing HRTF preprocessing methods for Ambisonics rendering through perceptual models

Spatial up-sampling of HRTF sets using generative adversarial networks: A pilot study

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

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