# Gait Energy Response Functions for Gait Recognition against Various Clothing and Carrying Status
Furthermore, we note that the importance (i.e., discrimination capability) of static and dynamic components, as well as the degree to which they are affected by the covariate conditions, differs among the body parts. For example, the head mainly contains static components and is seldom affected by carried objects, and hence the static components may be more important than the dynamic ones. In contrast, the leg contains more dynamic components and is often affected by clothing and carried objects; therefore, the dynamic components may be more important than the static ones. We therefore extend a spatially dependent version of GERF (called SD-GERF), and contrast it with the previous spatially independent version, which we denote as Global GERF, to consider the previously highlighted differences in the importance of static and dynamic components among the body parts. More specifically, instead of designing a single common GERF over the whole gait feature, we design multiple GERFs for individual vertical positions in the GEI (see the multiple profiles in the last column of Figure 1), and since responses for each GERF often localize to a certain body part, we further adopt a set of the spatially dependent GERFs (i.e., multiple SD-GERFs, corresponding to multiple images in the last column of Figure 1) to cover the whole body information and fuse the results of them for better accuracy. More explanations are given in Section 3.4. We summarize the contributions of this paper as follows:(1) Data-driven approach to intensity transformation. The proposed method learns the Global GERF in a data-driven way, unlike existing intensity transformation-based methods such as GEnl and masked GEI use handcrafted designs. Specifically, we use the training set including variation to train the Global GERF for the whole GEI to maximize the discrimination capability. This enables us to realize a good tradeoff between static and dynamic components, while existing methods only enhance the dynamic components. (2) Extension of the Global GERF into a spatially dependent function. We propose a spatially dependent framework for the Global GERF to consider the differences in the importance of static and dynamic components among different body parts. Specifically, we prepare individual GERFs for vertical positions of GEI as SD-GERF and train the SD-GERF simultaneously. Moreover, we exploit multiple SD-GERFs as shown in Figure 1, 4 th column, and integrate their scores in a score-level fusion framework to improve accuracy. (3) Closed-form solution for optimization. We train to maximize the ratios of dissimilarity between different-subject pairs and same-subject pairs, and consequently formulate this optimization process as a generalized eigenvalue problem both for Global GERF and SD-GREF. We therefore obtain an analytic solution in a closed form without any iteration, and hence avoid troublesome convergence problems, which are inseparable from a nonlinear optimization framework. (4) State-of-the-art accuracy for gait recognition under variations in clothing and carrying status. We achieve the state-of-the-art accuracies of gait recognition under variations in clothing and carrying status on three publicly available gait databases: the OU-ISIR Gait Database, the Treadmill Dataset B [21] (OU-TD-B), the OU-ISIR Gait Database, Large Population dataset with bag \(\beta\) version [22] (OU-LP-Bag \(\beta\)), and the CASIA Gait Database B [23] (CASIA-B). This paper is an extended version of a conference paper [20]. More specifically, the extensions include two main aspects: (1) we extend original Global GERF to SD-GERF considering the differences in the importance of static and dynamic components among different body parts; (2) we evaluate the proposed method on two other gait databases (OU-LP-Bag \(\beta\) and CASIA-B) containing another variation (i.e., carrying status). Experimental results show the SD-GERF achieves the state-of-the-art performance and outperforms Global GERF by a large margin in all databases.