HRTF modeling for efficient auralization

이 연구는 중앙면 상에서 주성분 분석법을 이용하여 시간 및 주파수 영역에서 머리전달함수의 모형화 기법들을 다룬다. 시간영역의 머리전달함수, 복소수 값의 머리전달함수, 확장된 머리전달함수, 로그 크기의 머리전달함수에 기반하여 각각 주성분 분석법을 수행하여 얻은 네 가지 머리전달함수 모형들에 대해서 최소자승오차 관점에서 모형화 성능을 비교하고, 모형들간의 이론적인 관계를 살펴보는 것이 이 연구의 목적이다. 모형화에 사용되는 기저함수의 수가 동일하다면, 시간영역에서의 머리전달함수 혹은 확장된 머리전달함수에 기반한 모형이 복소수 값의 머리전달함수에 기반한 모형보다 최소자승오차 관점에서 더 효율적인 모형화 성능을 지닌다. 시간영역에서의 머리전달함수에 기반한 모형과 확장된 머리전달함수에 기반한 모형은 이론적으로 동일한 모형이며 서로 푸리에 변환 관계가 있다. 로그 크기의 머리전달함수에 기반한 모형은 다른 모형들과 모형화 성능 및 이론적인 관계를 비교할 수가 없는데, 이는 로그 크기의 머리전달함수에 기반한 모형은 머리전달함수의 크기 정보만을 로그 크기로 다루는 반면에 다른 모형들은 선형 크기로 머리전달함수의 크기와 위상정보를 모두 다루기 때문이다. This study deals with modeling of head-related transfer functions(HRTFs) using principal components analysis(PCA) in the time and frequency domains. Four PCA models based on head-related impulse responses(HRIRs), complex-valued HRTFs, augmented HRTFs, and log-magnitudes of HRTFs are investigated. The objective of this study is to compare modeling performances of the PCA models in the least-squares sense and to show the theoretical relationship between the PCA models. In terms of the number of principal components needed for modeling, the PCA model based on HRIR or augmented HRTFs showed more efficient modeling performance than the PCA model based on complex-valued HRTFs. The PCA model based on HRIRs in the time domain and that based on augmented HRTFs in the frequency domain are shown to be theoretically equivalent. Modeling performance of the PCA model based on log-magnitudes of HRTFs cannot be compared with that of other PCA models because the PCA model deals with log-scaled magnitude components only, whereas the other PCA models consider both magnitude and phase components in linear scale.

This paper introduces a continuous functional model for head-related transfer functions (HRTFs) in the horizontal auditory scene. The approach uses a separable representation consisting of a Fourier-Bessel series expansion for the spectral components and a conventional Fourier series expansion for the spatial components. Being independent of the data, these two sets of basis functions remain unchanged for all subjects and measurement setups. Hence, the model can transform an individualized HRTF to a subject specific set of coefficients. A continuous functional model is also developed in the time domain. We show the efficient model performance in approximating experimental measurements by using the HRTF measurements from a KEMAR manikin and the synthetic data from the spherical head model. The statistical results are determined from a 50-subject HRTF data set. We also corroborate the predictive capability of the proposed model. The model has near optimal performance, which can be ascertained by comparison with the standard principle component analysis (PCA) and discrete Karhunen-Loeve expansion (KLE) methods at the measurement points and for a given number of parameters.

Toward orthogonal non-individualised head-related transfer functions for forward and backward directional sound: cluster analysis and an experimental study

Head related transfer function (HRTF) is a continuous function of spatial direction. In practice, only HRTFs at discrete directions can be measured. In order to obtain HRTFs at unmeasured directions, a continuous reconstruction (or interpolation) procedure is needed. In this paper, a method for continuous reconstruction of HRTF based on optimal-degree spherical harmonics expansion is developed. Expansion coefficients were derived by using the pseudo-inverse method. To address the ill-posed problem in inverse calculation, the expansion degree for each frequency bin was optimized by a heuristic method. This method searches the minimum-norm errors of the reconstructed HRTFs with respect to measured ones which were not used to derive the coefficients. The KEMAR HRTF at 710 directions and a human HRTF at 493 directions were employed in reconstruction. Measured HRTFs from KEMAR or human subject were dived into three groups according to directions, in which the first group of 2/5, the second group of 2/5, and the third group of 1/5 data were used to calculate the expansion coefficients, determine the optimal expansion degree, and evaluate the reconstruction performance, respectively. Compared with the expansion methods using a constant degree for all frequency, the reconstruction performance of the current method is prior.

In this paper we analyze several auditory localization neural models that are based on head related transfer functions (HRTFs). HRTFs represent the combined directional-spectral response of the pinnae head and torso. The role of HRTFs in such modeling has hitherto been underestimated despite substantial experimental evidence to its relevance in spatial hearing, especially in determining direction of highfrequency sound sources. In the first section we suggest a neural model that links the physiology of binaural processing to a neural network that extracts spectral ratios. These ratios correspond to HRTFs ratios and can provide auditory directional cues. Next, we compare several methods of matching HRTFs ratios using discriminative matching measure (DMM). We consider several solutions to the matching problem from a neural signal processing viewpoint. We compare correlation based approaches with DMM optimization approach and with a non-linear approach based on neural back-propagation algorithm. All three models can be implemented by neural networks. Finally, we include experimental results of simulations that are conducted using these methods. Experiments show that the back-propagation based neural network yields the best results in terms of DMM both for narrow-band and broad band excitation. The back-propagation neural network is also superior in matching noisy HRTF ratio vectors. [Neurol Res 2001; 23: 489-500]

Applications in the creation of virtual auditory spaces (VAS) and sonification require individualized head related transfer functions (HRTFs) for perceptual fidelity. HRTFs exhibit significant variation from person to person due to differences between their pinnae, and their body sizes. We propose and preliminarily implement a simple HRTF customization based on the use of a published database of HRTFs (Algazi et al., 2001) that also contains geometrical measurements of subject pinnae. We measure some of these features via simple image processing, and select the HRTF that has features most closely corresponding to the individual's features. This selection procedure is implemented along with the virtual auditory system described in (Zotkin et al., 2002), and listener tests conducted comparing the customized HRTF and a fixed HRTF. Despite the simplicity of the method, tests reveal average improvement in localization accuracy of about 25 percent, though performance improvement varies with source location and individuals.

Human beings have a remarkable ability to determine the direction of arrival of a sound and to separate sounds of interest. Replicating this ability is a challenging problem in audio signal processing. In this paper we present a model for the head related transfer function (HRTF) developed with the localisation objective in mind. This is achieved by splitting the 3D localisation cues in terms of two functions which can be independently evaluated. We illustrate the theory for calculating these functions and validate the results against actual HRTF data. We find the model to be a close match for a significant number of potential source locations.

This paper presents a deep-learning technique for modeling Head-related Transfer Function (HRTF) using a large data-set from IRCAM [7] of 49 subjects with 115 directions/subject. We use a log-spectral distortion metric that we have used to optimize the performance of the deep-learning model. The presented model first uses a sparse autoencoder (AE) for capturing the salient representation (peaks, and notches for elevation) from the user-captured HRTFs, in its latent representation, and then uses a generalized regression neural network (GRNN) to approximate the latent representation of the corresponding HRTFs at arbitrary angles. The sparse AE then decodes the GRNN output to reconstruct the HRTF. The proposed approach is shown to outperform, objectively using the log-spectral distortion, the state-of-the-art linear-least-squares optimum solution (viz., derived from Principal Component Analysis) to perform better generalization over the HRTFs in the IRCAM dataset. Towards this, Bayesian optimization has been performed to tune the hyper-parameters of the sparse AE and the GRNN.

Purpose – The purpose of this paper is to present a system for customized binaural audio delivery based on the extraction of relevant features from a 2-D representation of the listener’s pinna. Design/methodology/approach – The most significant pinna contours are extracted by means of multi-flash imaging, and they provide values for the parameters of a structural head-related transfer function (HRTF) model. The HRTF model spatializes a given sound file according to the listener’s head orientation, tracked by sensor-equipped headphones, with respect to the virtual sound source. Findings – A preliminary localization test shows that the model is able to statically render the elevation of a virtual sound source better than non-individual HRTFs. Research limitations/implications – Results encourage a deeper analysis of the psychoacoustic impact that the individualized HRTF model has on perceived elevation of virtual sound sources. Practical implications – The model has low complexity and is suitable for implementation on mobile devices. The resulting hardware/software package will hopefully allow an easy and low-tech fruition of custom spatial audio to any user. Originality/value – The authors show that custom binaural audio can be successfully deployed without the need of cumbersome subjective measurements.

Head-related transfer function (HRTF) plays an important role in the construction of 3D auditory display. This paper presents an individual HRTF modeling method using deep neural networks based on spatial principal component analysis. The HRTFs are represented by a small set of spatial principal components combined with frequency and individual-dependent weights. By estimating the spatial principal components using deep neural networks and mapping the corresponding weights to a quantity of anthropometric parameters, we predict individual HRTFs in arbitrary spatial directions. The objective and subjective experiments evaluate the HRTFs generated by the proposed method, the principal component analysis (PCA) method, and the generic method. The results show that the HRTFs generated by the proposed method and PCA method perform better than the generic method. For most frequencies the spectral distortion of the proposed method is significantly smaller than the PCA method in the high frequencies but significantly larger in the low frequencies. The evaluation of the localization model shows the PCA method is better than the proposed method. The subjective localization experiments show that the PCA and the proposed methods have similar performances in most conditions. Both the objective and subjective experiments show that the proposed method can predict HRTFs in arbitrary spatial directions.

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This paper provides a small set of essential parameters for a personalized and effective real-time auralization with headphones. An image-guided procedure with two 2D images of the user’s head guides the mixed structural modeling of head-related transfer function (HRTF), combining a spherical head model with ear displacement with the HRTF high-frequency magnitude selected from a database according to ear anthropometry. Room acoustics phenomena are simplified following the scattering delay network (SDN) approach which allows an accurate spatialization of first order reflections. Finally, statically significant improvements in localization performances within a virtual reality (VR) test allow to identify some benefits of the proposed customized auralization model compared to the widely used higher-order ambisonics (HOA) rendering with generic HRTFs.

The understanding and simplified modeling of the Head Related Transfer Function (HRTF) is very important for applications in virtual audio reality. However HRTF depends on many factors such as the shape of head and pinnae, torso, refraction by the body, and others. In this work we investigated the influences of a thin-elastic layered structure of a head on the HRTF. The analytical solution is applied to a six-layer model of the head. The elastic properties of layers are taken into account in the modeling. The results are compared with the results of spherical rigid model and experiments. The numerical results showed the new peaks of HRTF caused by elastic scattering and re-reflecting from layers. However this effect is very small and can be neglected at high frequency.

The use of Head Related Transfer Functions (HRTFs) in audio processing is a popular method of obtaining spatialized sound. HRTFs describe disturbances caused in the sound wave by the human body, especially by head and the ear pinnae. Since these shapes are unique, HRTFs differ greatly from person to person. For this reason measurement of personalized HRTFs is justified. Measured HRTFs also need further processing to be utilized in a system producing spatialized sound. This paper describes a system designed for efficient collecting of Head Related Transfer Functions as well as the measurement, interpolation and verification procedures.

Head related transfer functions (HRTFs) are needed to present virtual spatial sound sources via headphones. Since individually measured HRTFs are very costly and time consuming, in this paper the individualization of the dummyhead's HRTFs will be discussed. Here, the individualization is based on a scalable ellipsoidal head model. From this model the individualization is splitted into the individualization of the interaural time difference (ITD) and the spectral domain. The ellipsoidal modeling of the ITD gives quantitatively good results, considering the individual measurements. The second approach in spectral domain scales the transfer function in frequency. An angle dependent factor is calculated by the head dimensions of the subject. Afterwards, the scaling results are compared and discussed with individual measurements.