# Anthropometric Ratios for Lower-Body Detection Based on Deep Learning and Traditional Methods
## 3 Materials and Methods
### Proposed Lower-Body Detection Framework Using Anthropometric Data
#### 3.3.2 Transformation of the Full-Body ROI into the Lower-Body ROI  
The HOG-SVM or CNNs algorithm can be used to directly detect the full-body ROI of a human in an image. This full-body ROI can then be cropped to obtain the lower-body ROI as shown in Equations (9)-(11). This process is also illustrated in Figure 14. In addition, the information of the anthropometric data of upper-body is shown in Table 1.  
\[R_{H\text{{U}}}=H_{\text{{U}}}/H_{F} \tag{9}\]  
where \(R_{H\text{{U}}}\) is the ratio height of upper-body per full-body, \(H_{\text{{U}}}\) is the height of upper-body, and \(H_{\text{{F}}}\) is the height of full-body. \[H_{Low\text{{r}}}=H_{\text{{F}}}*(1-R_{H\text{{U}}}) \tag{10}\]  
where \(H_{Low\text{{r}}}\) is the length of lower-body ROI, \(H_{\text{{F}}}\) is the length of full-body ROI, and \(R_{H\text{{U}}}\) is the ratio height of upper-body per full-body as shown in Table 1.  
\[W_{Lower}=W_{\text{{F}}} \tag{11}\]  
where \(W_{Lower}\) is the width of lower-body ROI and \(W_{\text{{F}}}\) is the width of full-body ROI. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Gender** & \(H_{\text{{U}}}\) & \(W_{\text{{U}}}\) & \(H_{\text{{F}}}\) & \(W_{\text{{F}}}\) & \(R_{H\text{{U}}}\) & \(R_{W\text{{U}}}\) \\ \hline Male & 71.6 & 55.1 & 179.9 & 55.1 & 0.398 & 1 \\ \hline Female & 60.3 & NA & 157.0 & NA & 0.384 & NA \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The anthropometric data of upper-body in cm (centimetres), NA = Not Available where \(H_{\text{{U}}}\) is the height of upper-body, \(W_{\text{{U}}}\) is the width of upper-body, \(H_{\text{{F}}}\) is the height of full-body, \(W_{\text{{F}}}\) is the width of full-body, \(W_{\text{{F}}}\) is the width of full-body, \(R_{H\text{{U}}}\) is the ratio of \(H_{\text{{U}}}\):\(H_{\text{{F}}}\), and \(R_{W\text{{U}}}\) is the ratio of \(W_{\text{{U}}}\3.3.3. Transformation of the Upper-Body ROI into the Lower-Body ROI  
As illustrated in Figure 15, \(V\)\(V\)\({}_{Upper}\) is used to detect the ROI of the upper-body; then, this ROI is converted into the full-body ROI by using \(R_{HUI}\) and \(R_{WUI}\) as shown in Equations (9), (12)-(14). \[H_{F}=H_{upper}/R_{HUI} \tag{12}\]  
where \(H_{F}\) is the height of full-body ROI and \(H_{upper}\) is the height of upper-body detection ROI by VJ algorithm and \(R_{HUI}\) is the ratio height of upper-body per full-body as shown in Table 1.  
\[R_{WUI}=W_{UJ}/W_{F} \tag{13}\]  
where \(R_{WUI}\) is the ratio width of upper-body per full-body, \(W_{U}\) is the width of upper-body, and \(W_{F}\) is the width of full-body. \[W_{F}=W_{upper}/R_{WUI} \tag{14}\]  
where \(W_{F}\) is the width of full-body ROI and \(W_{upper}\) is the width of upper-body detection ROI by VJ algorithm and \(R_{WUI}\) is the ratio width of upper-body per full-body as shown in Table 1.  
Subsequently, the estimated full-body ROI is cropped to obtain the lower-body ROI as shown in Equations (10) and (11). Figure 14: The framework of the HOG-SVM or CNNs for lower-body detection. 3.3.4. Transformation of the Face ROI into the Lower-Body ROI  
In case of using \(V|_{Face}\) to find the ROI of the human face, as demonstrated in Figure 15, the face ROI is converted into the full-body ROI by means of \(R_{HH}\) and \(R_{WH}\) as shown in Equations (15)-(18). Moreover, the information of the anthropometric data of head is shown in Table 2.  
\[R_{HH}=H_{H}/H_{F} \tag{15}\]  
where \(R_{HH}\) is the ratio height of head per full-body, \(H_{H}\) is the height of head, and \(H_{F}\) is the height of full-body. \[R_{WH}=W_{H}/W_{F} \tag{16}\]  
where \(R_{WH}\) is the ratio width of head per full-body, \(W_{H}\) is the width of head, and \(W_{F}\) is the width of full-body.