# A Review on Head-Related Transfer Function Generation for Spatial Audio
## 6 Interpolation
### Neural Network-Based Interpolation  
In recent years, machine learning techniques and neural networks have also been applied to HRTF interpolation. [PERSON] et al. [214] provide a comprehensive overview of data-driven methods, highlighting the machine learning techniques used for HRTF interpolation and capturing and processing spatial audio in real-time environments. In 2021, [PERSON] and [PERSON] proposed pre-trained models for HRTF interpolation, focusing on real-time applications [181]. This approach exhibits minimal latency, making it suitable for VR/AR interactive applications. This study also explores the limitations of such models, particularly in terms of generalization to different head and ear shapes that were not included during training [181]. In 2022, [PERSON] et al. [188] explored the use of generative adversarial networks (GANs) for the spatial up-sampling of HRTF datasets. GANs are particularly suited to creating high-fidelity interpolations in sparse datasets, where traditional methods might struggle to maintain audio quality. This approach demonstrates significant improvements in the perceived spatial accuracy of audio, especially in complex 3D environments [188]. In the same year, [PERSON] et al. proposed an HRTF interpolation approach using an autoencoder for spatially sparse measurement datasets [182]. The network is designed so that only the encoder and decoder depend on the position. This characteristic also allows good performance for sparse measurements and subjects not included in the training [182]. In 2023, [PERSON] and [PERSON] proposed a 3D CNN based on a vector-quantised variational autoencoder (VQ-VAE) to spatially upsample sparse datasets [194].  
In the same year, [PERSON] et al. designed a neural network based on feature-wise linear modulation (FiLM) for incorporating HRTFs from datasets with different coordinate systems [37]. This approach is based on evaluating the neighbour HRTFs and anthropometric measurements, employing two conditioning methods. Results showed good generalisation with unknown datasets, outperforming the baseline [37]. In recent years, convolutional neural networks have often been used for HRTF interpolation [193; 195]. In [66], a CNN was employed to interpolate HRTF samples collected using a multi-sine signal while the listener moves freely (as introduced in Section 3). The process begins by scanning the listener's upper body and head using 3D sensors, creating a detailed mesh that serves as the basis for generating spatially dense and direction-dense HRTFs. The experimental results obtained with this approach are depicted in Figure 10. The methods based on CNN described above require a plane-sphere projection, which may exclude some HRTF features. In 2023, [PERSON] et al. investigated the problem of the coordinate system by proposing a spherical convolutional neural network to solve the plane-sphere projection with spherical harmonics representation [206]. Based on this, in 2024, also [PERSON] et al. also introduced a spherical convolutional conditional neural process (SConvCNP) that can manage spherical data typical of the HRTF geometry. This method has shown good results with the time-aligned HRTF spectrum; however, it introduces a high computational cost that makes the approach inapplicable to real-time solutions [207].