# Gait Energy Response Functions for Gait Recognition against Various Clothing and Carrying Status
## 5 Conclusions  
In this paper, we described a data-driven framework to learn GERFs (i.e., Global GEI and SD-GERF) for gait recognition against clothing and carrying status. Specifically, we first proposed the Global GERF to transform an original gait energy into another value to make it more discriminative under variations. In addition, since the discrimination capability of gait energies, as well as the degree to which they are affected by the covariate conditions, differs among body parts, we then extended the Global GERF to SD-GERF which accounts for spatial dependence. Moreover, the proposed GERFs were represented as a lookup table vector and optimized through an efficient generalized eigenvalue problem, which enables us to obtain an analytical solution in a closed form without any iterations. To further improve accuracy, two post-processing techniques (i.e., Gabor filtering and 2 DPCA+2 DLDA) were employed. Experimental results using three publicly available datasets showed the state-of-the-art performance of the proposed GERF compared with other state-of-the-art methods.  
Because the proposed framework can be regarded as a kind of feature learning method, we will apply the method to other problems such as gait-based gender and age estimation or even more dissimilar fields where intensity plays an important role in comparison, such as face recognition. Moreover, considering the good performance of deep learning-based methods, integrating the GERF model into a deep network architecture will remain as another future work.  
[PERSON] developed the program for the proposed algorithm, performed most of the experiments and drafted the initial manuscript. [PERSON] guided the paper's content, including the idea, experimental design, data analysis, as well as initial manuscript revision. [PERSON] participated in the implementation of post-processing techniques and provided part of the experimental results. [PERSON] and [PERSON] developed the main idea and equations of the proposed method. [PERSON] and [PERSON] supervised the work providing technique support and general guidance of the whole work. All authors participated in review of the final manuscript.  
This work was supported by JSPS Grants-in-Aid for Scientific Research (A) 18H04115, the National R&D Program for Major Research Instruments (Grant No. 61727802), the National Natural Science Foundation of China (Grants No. 61703209).  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **Running Stage** & **Machine Specification** & **Training Time** & \begin{tabular}{c} **Query Time of Each Sequence** \\ (\#Gallery Sequences) \\ \end{tabular} \\ \hline Gabor+RSM-HDF [27] & \
\begin{tabular}{c} Intel Core i5 3.10 GHz \\ processor \\ \end{tabular} & 320.090 & 0.600 (122) \\ \hline Proposed method &
\begin{tabular}{c} Intel Core i7 4.00 GHz \\ processor \\ \end{tabular} & 13.330 & 0.016 (48) \\ \hline Proposed method (estimated) & 75\% computing power & 17.773 & 0.054 (122) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Running time (Seconds) comparison.