# Gait Energy Response Functions for Gait Recognition against Various Clothing and Carrying Status
## 4 Experiments
### Comparison with Intensity Transformation-Based Methods  
We conducted comparison experiments with a family of intensity transformation-based methods including GEnI [12], Masked GEI [13] and GEI [11] as a baseline to show the effectiveness of the proposed data-driven transformation methods Global GERF and SD-GERF.  
We first show some feature examples for the five gait features, that is, GEI, GEnI, Masked GEI, Global GERF and SD-GERF, along with profiles of three SD-GERFs corresponding to the three largest eigenvalues in Figure 5. Note that the proposed SD-GERF uses 10 eigenvectors as multi-response functions; here, we only list three of them as examples. As for the profile of Global GERF, it is drawn as a red curve in the third column of Figure 1.  
The profile reveals that on one hand the Global GERF compresses the intensity difference between typical dynamic components (intensity values around 127) and the complete foreground (intensity values around 255) to mitigate the effects of clothing variations, e.g., the leg is usually occupied by the typical dynamic components in the case of standard clothing, while sometimes occupied by the complete foreground in the case of long coats or skirts. On the other hand, it simultaneously emphasizes the difference between the complete background (intensity values around 0) and the typical dynamic components, because such differences are still useful under clothing variations. In addition, it also keeps the difference between complete background and foreground as this still contains meaningful information to discriminate subjects under conditions of clothing variations, unlike GEnI or Masked GEI, which make no such distinction.  
As for the SD-GERF, it exhibits similar trends in profile to those of the Global GERF, as shown in the second column (localized to the leg) and third column (localized to the torso) of Figure 5b. This implies that the SD-GERF highlights differences in dynamic components and retains static components such as the Global GERF. However, the first column (localized to the head) in Figure 5b shows monotonically increasing profiles unlike those for the leg and the torso (the second and third columns). This is because the head is not often affected by clothing variations and hence the original GEI is sufficient for discrimination. As such, the SD-GERF can consider the spatial dependency on the degree of effect of clothing variations and thus set appropriate response functions for each body part.  
Figure 5: Examples of features and profiles of the SD-GERF in OU-TD-B. (**a**) Features of five intensity transformation-based methods. Three features corresponding to the three largest eigenvalues are listed for the SD-GERF as examples. (**b**) Profiles of response functions of the SD-GERF corresponding to the three largest eigenvalues. R1, R2,..., R17 indicate row indices from the top to the bottom, where the control points are aligned. Note that some profiles of the SD-GERFs are not shown because they are overlapped with those of similar SD-GERFs.  
The DET curves with z-normalization and CMC curves of all the transformation-based methods are shown in Figure 6. In addition, the detailed EER with z-normalization and rank-1 identification rate are listed in Table 1. From the results, the proposed GERFs (Global GERF and SD-GERF) outperform the other three transformation-based methods, in the case of both verification and identification. Moreover, the SD-GERF achieves better accuracy than the Global GERF. For instance, the 4.27% lower z-EER and 10.9% higher rank-1 rate in OU-TD-B indicate that addition of spatial dependency in the GERF framework improves accuracy.