# Magnitude Modeling of Personalized HRTF Based on Ear Images and Anthropometric Measurements
## 4 Performance and Evaluation
### HRTF Personalization Results  
To choose an appropriate truncation order \(L\), this paper compares the \"Full-measurements\" HRTF\" personalization results when \(L\) = 4 and \(L\) = 7. Figure 10 shows the results of \((L+1)^{2}\) = 25 and \((L+1)^{2}\) = 64 SH coefficients. When \(L\) = 4 is used, the global SD is 5.22 dB, and the global SD is 5.78 dB when \(L\) = 7.  
Figure 10: Coefficients of the SH basis: (a) \(L\) = 4 and (b) \(L\) = 7.  
Figure 9: Magnitude comparison: (a) Original HRTF and reconstructed HRTF of subject003 at 5 kHz, (b) Original HRTF of subject003 and subject010 at 5 kHz, (c) RMSE of the original HRTF and reconstructed HRTF at different frequencies, and (d) Original HRTF and reconstructed HRTF at \(L\) = 7.  
When \(L=4\) is used, the reconstructed HRTF is better. It is possible that the reason is that the CIPIC dataset is small, and the network structure should not be too deep. Thus, the larger the \(L\) value, the more accurate the SH coefficient needs to be predicted by the model, and the small model is difficult to learn. Therefore, this paper chooses \(L=4\) as the order.  
Section 4.3 shows the effectiveness of spherical harmonic decomposition in fitting the global personalized HRTF at a single frequency. In order to prove the effectiveness of the method for modeling in the frequency range of the human ear audible range, Figure 11 shows a magnitude comparison of the measured, smoothed and predicted HRTF when \((\theta,\phi)=(0,0)\). Among them, \"Measured HRTF\" is the result of the measured HRIR after 256 Fourier transform, \"Smoothed HRTF\" is the HRTF after the inverse transformation of the true spherical harmonic coefficients, and \"Predicted HRTF\" is the HRTF after inverse transformation of the predicted spherical harmonic coefficients by the model. Due to the difference in the number of sampling points, it can be seen that \"Measured HRTF\" is more refined, and the HRTF generated by the model is similar to \"Smoothed HRTF\", but both lost some details.  
The global performance comparison of this method with other methods is given in Table 2. The HRTF obtained by the proposed method has an SD of 5.31 dB compared to the original HRTF, and an SD of 4.47 dB compared to the smoothed HRTF. In particular, SD only drops by 1.7% compared to the Full-measurements HRTF. Note that the Full-measurements HRTF is obtained using precise pinna measurements, which are practically difficult to obtain from the human ear. Compared with using the average HRTF, the SD of the HRTF estimated by both methods based on our model is greatly reduced. Compared to TFACE HRTF, which also uses pinna images, our model provides SD values with the same error level for each subject and provides a global personalized HRTF.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **Global SD** \\ \hline Average HRTF & 7.61 dB \\ Full-measurements HRTF & 5.22 dB \\ TFACE HRTF & 5.31 \(\pm\) 3.154 dB \\ Proposed HRTF & 5.31 dB \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparing Global SD of Different Methods.  
Figure 11: Magnitude comparison of measured, smoothed, and predicted at the frontal direction, where \((\theta,\phi)=(0,0)\).  
Figure 12 presents the global SD values of the proposed method on 32 subjects. It can be seen that the global SD value of the proposed method is 5.31 dB, the highest is 6.95 dB, and the lowest is 4.39 dB.