# Gait Energy Response Functions for Gait Recognition against Various Clothing and Carrying Status
Specifically, the intensity transformation-based approaches transform intensity values of an original gait feature (e.g., gait energies in the case of GEI) into more discriminative values to increase the robustness against change of the covariate conditions. A gait entropy image (GEnI) [12] is a typical intensity transformation-based gait feature whose intensities are transformed from the GEI. Because the gait energy of each pixel is regarded as a foreground probability in the GEI representation, Shannon entropy for the foreground probability at each pixel is computed as a transformed intensity at each pixel in the GEnI, to enhance the dynamic components while attenuating the static components. For example, the intensities of the pixels with small and large grayscale values (e.g., 0 and 255) in the GEI become small in the GEnI, while the intensities of the pixels with middle grayscale values (e.g., 127) in the GEI become large (see Figure 1,  
Figure 1: Concept of the proposed gait energy response functions (GERFs) as well as other existing intensity transformation-based approaches. In the fourth column, multiple profiles denote spatially dependent response functions for individual vertical positions ranging from upper position (red line) to lower position (blue line), and multiple images denote a set of spatially dependent response functions. first column). This means that the dynamic components are enhanced while the static components are attenuated, regardless of whether they come from a static foreground or background in the GEnI representation. Therefore, the GEnI is insensitive to the static component changes derived from clothing and carrying status variations to some extent. However, the static components discarded in the GEnI representation, still have some discrimination capability even under variations in clothing and carrying status. Moreover, another negative aspect of the GEnI is that a pair of different gait energies that are symmetrical with respect to the intermediate value (i.e., \(127.5-x\) and \(127.5+x\)), are transformed into the same intensity value in the GEnI (see Figure 1, first column); i.e., the dynamic component is also sacrificed. Masked GEI [13], as another intensity transformation-based gait feature, has been proposed to address the latter problem. It is generated by masking out (i.e., setting to zero) those gait energies with smaller gait entropy than a threshold, while the others are kept unchanged (see Figure 1, second column). Masked GEI therefore keeps the dynamic components as they are, while discarding useful static components. In addition, the threshold for masking out is a sensitive parameter and hence requires careful treatment. Based on the previously described observation that both GEnI and masked GEI are generated from GEI, we employ a mapping function named gait energy response function (GERF) to describe these gait energy transformation processes. Both use handcrafted GERFs, which more care about the dynamic components. However, such simply handcrafted GERFs cannot well handle various covariates, since different covariate conditions affect different components of the original gait features. For example, clothing and carrying status variations affect static components such as torso and limb shapes more than dynamic components such as leg and arm motion, while the speed variation exerts a greater effect on dynamic components. Therefore, a key to the success of the gait energy response function is their appropriate enhancement and/or attenuation of the static and dynamic components in the original gait features by taking the covariate conditions into account. We therefore proposed a more general and data-driven framework for designing the GERF to transform the GEI into more discriminative features (see Figure 1, third column) in our previous paper [20] and seek to show the effectiveness of the proposed method in gait recognition under variations in clothing and carrying status.