# Pedestrian Localization in a Video Sequence Using Motion Detection and Active Shape Models
## 4 Experiments
### Quantitative Results  
A quantitative analysis of the results obtained by the combination of MDBS + ASM was performed to deepen the study of this proposal. Leave-one-out cross-validation [38] was selected to verify the accuracy of the fitness achieved by the model. The ASM model was trained with \(M-1\) frames, and the values obtained (or approximated) were evaluated with respect to the frame that was left out of the training. This process was repeated for \(M\) frames. The leave-one-out cross-validation is very useful to strengthen the validity of the experimental results when the available dataset is relatively small [39]--in this study, \(M=50\). The fit error for each frame \(m\) was obtained by Equation (21), which uses the Euclidean distances between the landmarks \((x_{l},y_{l})\) and the points approximated by ASM \((x^{\prime}_{l},y^{\prime}_{l})\) for the total of landmarks \(L\). \[e_{m}=\frac{1}{L}\sum_{l=1}^{L}\sqrt{(x_{l}-x^{\prime}_{l})^{2}+(y_{l}-y^{ \prime}_{l})^{2}} \tag{21}\]  
Despite its simplicity, the Euclidian distance was used in this work because it has proved its effectiveness as part of the ASM procedure. Even recent state-of-art research continues applying the Euclidian distance for this reason (references [16; 40]). Moreover, we consider using this parameter appropriate for the aim of this work because it calculates the distances between the landmarks and the approximate points obtained by the ASM during the contour detection. Then, the mean fit error of the ASM is given by Equation (22), where \(M=50\) and corresponds to the number of cross-validation iterations (number of frames) in the training set. \[\bar{\epsilon}=\frac{1}{M}\sum_{m=1}^{M}e_{m} \tag{22}\]  
Figure 11: Detection of a pedestrian walking at different orientations with respect to the camera in the CASIA Gait dataset. (**a**) Pedestrian walking at 0 degrees. (**b**) Pedestrian walking at 36 degrees. (**c**) Pedestrian walking at 54 degrees. (**d**) Pedestrian walking at 90 degrees. In this paper, we use the box-plot data analysis method to explain the behavior of experimental results obtained by the MDBS + ASM approach. This tool (also called the box and whisker plot method) easily allows the comparison of different datasets. It uses the median, the approximate quartiles (\(\mathbf{Q}_{f}\), where \(f=\{1,2,3\}\)), and the lowest (Min) and highest (Max) data points to convey the level, spread, and symmetry of a distribution of data values. It can also be easily refined to identify outlier values [41]. Figures 12 and 13, visually summarize and compare groups of data corresponding to the studied scenes. The data correspond to the accuracy of the fitness achieved by the model, and they are represented in terms of the mean fit error of pixels (Equation (22)). Details of data shown in Figures 12 and 13 are presented in Table 1, where important information for each scene, such as maximum and minimum values, ranges, IQR (interquartile range), and the average of pixels by quartiles is presented. The box plot in Figure 12 shows the mean fit error for the CDnet2014 dataset. Each frame in this dataset has a resolution of 360 \(\times\) 240 pixels for the office and sofa scenes and 720 \(\times\) 576 pixels for the PETS2006 scene. The number of evaluated frames was set to \(M=50\), the number of landmarks was \(L=50\), and the size of the landmarks in the gray-scale profiles was 40 pixels. The analysis was done twice. The office scene resulted in a mean fit error of 7.2 pixels, which is a satisfactory result considering the level of occlusion in the lower extremities of the pedestrian in the scene. In the PETS2006 scene, a mean fit error of 8.3 pixels was obtained, despite the challenges of floor reflections, shadows, and occlusion. Similarly, in the sofa scene, a mean fit error of 7.1 pixels was achieved.