# A Review on Head-Related Transfer Function Generation for Spatial Audio
## 4 Physical Modelling
### Implementations of BEM
The approach is first validated on a rigid sphere and then applied to BHead210. Simulated HRTFs are compared with measured ones and with the known ones of the Kemar dummy head. The authors report significant differences between Kemar and BHead210. HRTFs produced by FMBEM are also compared with the measured ones in [118]. The purpose is a cross-validation aimed at overcoming possible sources of error in computer simulations (e.g., accuracy in the generation of the mesh and choice of the boundary conditions) and laboratory measurements (e.g., inaccuracy of transducers and experimental errors in subject and device positionings). In this paper, the authors present both spectral and temporal analyses of the data collected with measurements and simulations. The conclusion is that both methods have specific shortcomings, and that no single one is sufficient for providing a ground truth. The analysis identifies specific frequency bands where one method is more reliable than the other, making it possible to correct one with the other (cross-validation). An optimisation in the implementation of a conventional BEM using a graphic processing unit (GPU) is presented in [119]. This study shows that the use of GPUs makes the fast generation of HRTFs by means of conventional BEM possible on a personal computer, without using the reciprocity principle. Though more efficient, the reciprocity principle, as pointed out by the authors, may lead to inaccuracies in the final result. In addition, they investigate the perceptual effectiveness of the generated HRTFs. In [120], the authors propose a simulation framework for calculating room acoustic transfer functions in a low-frequency range, where traditional methods based on geometric acoustics do not prove to be effective. The task is required for the auralisation of virtual spaces. The framework includes the directionality of both the sound source and receiver. The sound field in the vicinity of the receiver and source is expanded into spherical harmonics (see Equations (26) and (27). The BEM is used to calculate the coefficients of the expansion of the fields in the vicinity of the receiver. In order to exploit the best of both methods, a system that combines BEM with deep neural networks (DNNs) is proposed in [121]. Instead of training the network to directly predict HRTFs from data, they condition the network to predict differences between measures and simulations. The method has been proven to outperform BEM and SPCA-DNN approaches in all the audible range, as measured with spectral distortion. SPCA-DNN is a special framework introduced by the authors that uses neural networks in an approach based on a spatial principal component analysis (SPCA) factorisation of the HRTF. In [122], [PERSON] and [PERSON] construct a database of HRTFs of children aged 5-10 years using BEM as a supporting tool. This knowledge is important in the auralisation of virtual environments appropriate for children, but data are scarce and, as shown in this paper, the available dataset and Kemar models for adults are significantly inadequate. BEM simulations are performed with the Mesh2 HRTF [109] simulation tool and partially validated with COMSOL Multiphysics(r)[106]. The simulations are used to evaluate the quality of the dataset and the effect of head movement on measurements. In fact, it is more difficult to carry out controlled measures with children than with adults. In [123], the authors propose a method for HRTF personalisation based on the reconstruction of ear meshes from high-quality images. The reconstructed meshes are integrated with a model of the human body to generate the personalised HRTF via BEM simulations run with COMSOL Multiphysics(r).