## 3 Evaluation
### Objective Metrics  
Figure 6 shows the HRTF magnitude spectrum of a typical subject (No. 1) at the 0\({}^{\circ}\) elevation in the median plane, in which the low frequencies (below 400 Hz) are eliminated due to measurement error. It can be seen that the predicted HRTFs and the original measured HRTFs are similar with a good consistency at the pinna-related spectral notches. Considering that the localization cues from pinnae are mainly concentrated in the frequency band from 5 kHz to 12 kHz, the predicted HRTFs using the proposed algorithm may not suffer from the deterioration of localization accuracy.  
Substituting the predicted and corresponding measured HRTFs into Equations (10) and (11), the SD as well as \(\overline{\text{SD}}\) of each subject in the validation group can be obtained. Figure 7 shows the variation of SD with elevations for each subject in the validation group. As shown, the predicted HRTFs of Subject No. 1, No. 2, and No. 5 have a smaller SD value than that of the KEMAR HRTF at most elevation directions, suggesting that the proposed algorithm is advantageous in the median plane. The predicted HRTFs of Subject No. 3 and Subject No. 4 have a larger SD value than that of the KEMAR HRTF at some elevation directions. This may be caused by the fact that Figure 7 only demonstrates the prediction performance of an illustrative example of the proposed algorithm (see Section 2.1); the limited number of subjects in the illustrative example (i.e., 30 subjects in the calculation group) may not be sufficient to achieve the best reconstruction performance. Moreover, the anthropometric parameters  
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \(A_{1}\) & \(A_{2}\) & \(A_{3}\) & \(A_{4}\) & \(A_{5}\) & \(A_{6}\) & \(A_{7}\) & \(A_{8}\) & \(A_{9}\) & \(A_{10}\) \\ \hline \(F\) value & 14.8 & 16.4 & 5.6 & 7.3 & 7.9 & 6.7 & 7.2 & 19.6 & 9.7 & 8 \\ \(p\) value & \textless{}0.0001 & \textless{}0.0001 & \textless{}0.05 & \textless{}0.0001 & \textless{}0.0001 & \textless{}0.0001 & \textless{}0.0001 & \textless{}0.0001 & \textless{}0.0001 & \textless{}0.0001 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Statistical test of the regression formulas.  
Figure 6: The HRTF magnitude of a typical subject in the validation group at elevation 0\({}^{\circ}\) in the median plane.  
of the CIPIC HRTF database used in the illustrative example are mainly measured via a photographic method; therefore, they are likely to contain measurement errors to certain extent.  
Furthermore, the \(\overline{\text{SD}}\) that is averaged across 25 elevations is calculated according to Equation (11). Similarly, the \(\overline{\text{SD}}\) values between KEMAR and the predicted HRTFs for the five subjects in the validation group are compared as shown in Figure 8. For most subjects, \(\overline{\text{SD}}\) of the predicted (customized) HRTFs is smaller than that of the KEMAR HRTF. In particular, the \(\overline{\text{SD}}\) values of Subject No. 1, No. 2, and No. 5 decrease by 1.2 dB, 1.1 dB, and 1.3 dB, respectively.  
Figure 7: Spectral distortion (SD) of the validation group at 25 elevations in the median plane. The values are averaged across left and right ears.  
In summary, for most subjects, the spectral characteristics of the predicted HRTFs are consistent with the original (i.e., measured) HRTFs; the \(\overline{\text{SD}}\) value of the predicted HRTFs is reduced as compared to the KEMAR HRTFs. Therefore, the proposed HRTF customization hybrid algorithm based on ICA decomposition and anthropometric parameter measurement is effective with the customized HRTFs prior to KEMAR HRTFs with respect to spectral characteristics.