# Magnitude Modeling of Personalized HRTF Based on Ear Images and Anthropometric Measurements
## 1 Introduction  
In recent years, virtual reality (VR) and augmented reality (AR) have developed rapidly. Virtual stereo, as an important part of virtual reality, has been widely used in games, video conferencing, humanoid robot interaction, hearing aids, and other fields [1]. In short, the quality of spatial sound is particularly important for achieving high-fidelity immersive experiences in virtual environment. To generate virtual audio, it is necessary to study the spatial cues of the human auditory system. The positioning factors of spatial hearing are mainly based on binaural and monaural cues [2]. Binaural cues include the interaural time difference (ITD) and the interaural level difference (ILD). ITD describes the time difference between the same sound reaching the two ears, and ILD describes the difference in binaural intensity caused by the weakening of the sound caused by the diffraction effect of the pinna and head. These cues are closely related to the perceived horizontal direction of the sound source. The monaural cues include the scattering and diffraction effects of the pinna, torso, etc. on the sound [3, 4]. The listener can distinguish the spatial direction of the sound source to a certain extent based on these cues. At present, spatial audio technology has supported playback on various devices. The head-related transfer function is essential for the headset to reproduce virtual audio. The head-related transfer function (HRTF) or head-related impulse response (HRIR) in the time-domain describes the sound filtering effect of the head, torso, and pinna in the process from the sound source to the eardrum of the listener in a free-field environment. The HRTF depends on the morphological characteristics of the listener. Due to different anatomical parameters, the HRTFs of users are also different. When using non-personalized data, users are prone to \"head-center effect, front-to-back position confusion, and up-and-down confusion\" [5, 6]. To avoid the above problems and reduce sound source localization errors, the personalized HRTF that matches the morphological characteristics of each listener needs to be individually designed. To this end, researchers have proposed a variety of HRTF personalization methods, including acoustical measurement methods [7, 8, 9], database matching methods [10, 11], numerical modeling methods [12, 13, 14], and anthropometric parameter regression methods. Among them, the acoustical measurement method is the most accurate, [PERSON] et al. [9] provides an overview of some state-of-the-art measurement methods, but these methods require specialized equipment and environment. Therefore, the anthropometric parameter regression method is widely studied because the predictive model can be reused once it is determined. For instance, [PERSON] et al. [15] proposed to use principal component analysis (PCA) to obtain the weight matrix and feature matrix of HRTF, use canonical correlation analysis to remove redundant information of anthropometric features, and use generalized regression network (GRNN) to analyze the relationship between anthropometric features and HRTF weight matrix. [PERSON] et al. [16] proposed to use the isometric mapping (ISOMAP) method to extract the feature description of HRTF, use artificial neural network (ANN) to establish the relationship between physiological parameters and low-dimensional HRTF, and use the domain reconstruction method to reconstruct the HRTF in the complete space. With deep learning showing great ability in optimizing estimation [17], [PERSON] et al. [18] proposed a deep neural network (DNN) model. After inputting the head, torso, and pinna information, they let the DNN select the importance of training features and directly obtain the HRTF, thus simplifying the operation steps of the entire model. As measurements related to the pinna are still challenging to obtain in real life, [PERSON] et al. [19] further proposed to use a convolutional neural network (CNN) to extract features from ear images instead of directly measuring the human pinna.