# Surround by Sound: A Review of Spatial Audio Recording and Reproduction
## 2 Binaural Recording and Rendering
### Binaural Rendering
#### 2.2.1 Individualized HRTF  
The direct acoustic measurement on a listening subject is the most accurate and important way of obtaining the individualized HRTFs, which include all of the relevant static cues, such as ITD, ILD, and spectral cues, for sound localization in 3D, especially in terms of azimuth and elevation. However, these measurements are discrete over space and frequency, and thus should be used with interpolation for binaural rendering [43; 44]. The methods can be classified as _local interpolation_, where HRTFs are computed from the measurements at its adjacent directions, i.e., bilinear interpolation [45] and inter-positional transfer function based interpolation [46], or _global interpolation_, where HRTFs are computed from all measurements based on a model using appropriate basis functions, i.e., the Spherical Harmonic based interpolation [26] and principle component analysis based interpolation [47]. Especially, the Spherical Harmonics, which are spatially continuous and orthogonal over sphere, are  
Figure 2: The signal flow of a binaural rendering system.  
now widely used for HRTF representation [33; 48]; based on this continuous representation, a novel spatial audio rendering technique for area and volumetric sources in VR was developed [18].  
Due to the fact that HRTF individualization is strongly related to the anthropometry of a person, methods have been proposed for HRTF personalization by choosing a small set of anthropometry features with a pre-trained model [49; 50; 51; 52; 53; 54]. The training was established based on a direct linear or nonlinear relationship between the anthropometric data and the HRTFs, where the first step is to reduce the HRTF data dimensionality. The effectiveness of this kind of model is heavily dependent on the selection of the anthropometry features [55]. For example, the study in [53] investigated the contribution of the external ear to the HRTF and proposed a relation between the spectra notches and pinna contours.  
Recently, researchers from Microsoft proposed an indirect method for HRTF synthesis using sparse representation [56; 57]. The main idea is firstly to learn a sparse representation of a person's anthropometric features from the training set and then apply this sparse representation directly for HRTF synthesis. Further work shows that, in this method, the pre-processing and post-processing are crucial for the performance of HRTF individualization [58].  
Some other techniques used for HRTF individualization include perceptual feedback (tunneling-based HRTF manipulation) [59], binaural synthesis using frontal projection headphones [60], and by finite element modelling of the human head and torso to simulate the source-ear acoustic path [61]. Especially, a significant amount of work has been done in HRTF numerical simulations, such as using boundary element method [62; 63] and finite difference time domain simulation [64], or estimating key localization cues of the HRTF data from anthropometric parameters [65]. Recently, a collection of 61-subject HRTFs and the high-resolution surface meshes of these subjects obtained from magnetic resonance imaging (MRI) data are released in the SYMARE database [66]. The predictions using the fast-multiple boundary element method show a high correlation with the measurement ones, especially at frequencies below 10 kHz.  
Notice that, due to the logistical challenges of obtaining the individualized HRTF, the database of non-individualized HRTFs are often used in the acoustic research [67; 68]. In addition, the perception using non-individualized HRTFs can be strengthened if dynamic cues are appropriately included as shown in the following section.