# A Review on Head-Related Transfer Function Generation for Spatial Audio
## 5 Anthropometric and Morphological Approaches for HRTF Personalisation
### Regression
#### 5.3.3 Three-Dimensional Meshes  
More recent methods approach the task from a 3D perspective. These approaches offer a higher degree of personalisation by capturing fine-grained spatial features, resulting in more accurate and individualised HRTFs. In 2021, [PERSON] et al. [166] proposed a regression method based on two steps: the extraction of anthropometric measures from a 3D mesh of the head followed by HRTF individualisation. The anthropometric parameters are automatically extracted from the mesh using the active shape model (ASM) algorithm trained on an available dataset. These parameters are employed as input for generalised regression neural networks (GRNNs) trained to predict the HRTF. The GRNNs, one for each value of the elevation angle of the source in the median plane, are trained using the spectral distortion (SD) to measure the distance between the current HRTF and the estimated one. Though it is widely used in HRTF personalisation studies, spectral distortion poorly correlates with subjective perception performance results. Thus, the authors train a second set of GRNNs using the sagittal-plane localisation model (see Section 2.2) as a metric.  
As another notable study, ref. [167] investigates the use of deep neural networks to predict individualised HRTFs from 3D ear shapes. Utilising data from 645 human subjects, 3D meshes of their heads and upper torsos are scanned and used to simulate ear HRTFs with the finite-difference time-domain (FDTD) method. The study evaluates two models: CNN-Reg, which employs a series of convolutional layers, and a 3D UNet model (UNet-Reg), which also predicts HRTFs from 3D inputs, both of which are trained separately for each frequency bin. Even though the two models achieve good results in minimising the spectral distance errors in the predicted HRTF magnitude spectra, the approach of training a separate model for each frequency bin presents limitations, making it less suitable for complex, real-time applications, where continuous frequency prediction is required. [PERSON] et al. [168] investigate the application of convolutional neural networks (CNNs) in predicting individualised HRTFs using detailed head scan data. In this approach, the input to the CNN consists of truncated spherical cap harmonic (SCH) coefficients, which efficiently represent the pinna geometry, an essential feature for accurate acoustic scattering, along with additional anthropometric measurements of the head and torso. The HRTFs are predicted as spherical harmonic (SH) coefficients, serving as the output of the model. Experimental results demonstrate that this method achieves a significantlylower log-spectral distortion (LSD) compared to the BEM when evaluated on the HUTUBS HRTF database [89].  
In 2023, [PERSON] et al. [169] introduced PRTFNet, a CNN model designed to reconstruct accurate spectral cues in HRTFs by reducing the influence of the head and torso. It uses a compact pinna-related transfer function and includes HRTF phase personalisation, adjusting phases based on the listener's head width. Validated with the HUTUBS HRTF dataset [89], the model transforms HRIRs into compact PRTFs to preserve spectral cues. In 2024, [PERSON] et al. [170] utilised 3D mesh features to predict HRTF spectra across vertical planes, ensuring spectral continuity and correlation across adjacent grids and frequencies. The evaluation results show that the model outperforms state-of-the-art methods in terms of LSD and enhances the prominence of peaks and notches in HRTF spectra.