# Human Skeleton Data Augmentation for Person Identification over Deep Neural Network
## 4 3D Human Skeleton Model and Anthropometric Features  
Assume that a 3D human skeleton model consists of \(N\) joints with their set of indices \(J=\{1,\cdots,N\}\) and \(M\) limbs, which are represented by line segments between two joints. Let \(L=\{(i,j)|i\
eq j,i\in J,j\in J\}\) be the set of joint pairs for constructing the limbs [43]. The values of  
Figure 3: Schematic overview of proposed method for skeleton-based person identification. Figure 2: Feature vector extracted from original skeleton sequence is not different to that from synthetic skeleton sequence. Let \(\mathbf{P}_{j}=\left[x_{j},y_{j},z_{j}\right]\) be the position of the \(j\)th joint in the world coordinate system, where \(x_{j},y_{j}\), and \(z_{j}\) are the coordinates of the \(j\)th joint on the X-, Y-, and Z-axes, respectively. The Euclidean distance between the \(i\)th and \(j\)th joints \(d(\mathbf{P}_{i},\mathbf{P}_{j})\) is used as a distance feature. The anthropometric features can be categorized into seven types: (1) length of each limb, (2) height, (3) length of upper body, (4) length of lower body, (5) ratio of upper body length to lower body length, (6) chest size, and (7) hip size. After these values are calculated for each frame, their average values over all frames are used as the anthropometric features for person identification. For the frame index \(n\) and the frame length \(F\), the anthropometric feature is defined as follows. (1) \(f_{1}\): _Average length of each limb_. In most case, the length of each limb will differ from person to person. For this reason, in many studies, this anthropometric feature has been used for person identification [22; 23; 24; 25; 26; 27; 28]. The length of each limb is calculated for each frame and the average length of each limb over all frames is given by  
\[f_{1}=\frac{\sum_{n=1}^{F}d(\mathbf{P}_{i}[n],\mathbf{P}_{j}[n])}{F},\ \ (i,j)\in L, \tag{1}\]  
where \(\mathbf{P}_{i}[n]\) and \(\mathbf{P}_{j}[n]\) are the position of the \(i\)th and the \(j\)th joints at the \(n\)th frame, respectively. Since the 19 limbs shown in Figure 5a are used, the number of feature dimensions of \(f_{1}\) becomes 19. (2) \(f_{2}\): _Average height_. Human height is also one of the most important anthropometric features used for person identification and is measured as the vertical distance from the foot to the head [22; 23; 24; 25; 26; 28]. In general, the person is asked to stand up straight while their height is measured. However, for a walking person, it is difficult to measure the true height due to the posture difference. To alleviate this issue, as shown in Figure 5b, the person's height is calculated as the sum of the neck length, upper and lower spine lengths, and the average lengths of the right and left hips, thighs, and shanks. To clarify, let \(H[n]\) be the subject's height at the \(n\)th frame. Then, \(H[n]\) is defined by (2) as follows:  
\[H[n] =\underbrace{d(\mathbf{P}_{1}[n],\mathbf{P}_{2}[n])}_{=\text{ neck length}}+\underbrace{d(\mathbf{P}_{2}[n],\mathbf{P}_{11}[n])}_{=\text{ upper spine length}}+\underbrace{d(\mathbf{P}_{11}[n],\mathbf{P}_{12}[n])}_{=\text{ lower spine length}}\] \[+\underbrace{d(\mathbf{P}_{12}[n],\mathbf{P}_{13}[n])+d(\mathbf{ P}_{12}[n],\mathbf{P}_{14}[n])}_{=\text{average length of the right and left hips}}/2+\underbrace{\left\{d(\mathbf{P}_{13}[n],\mathbf{P}_{15}[n])+d( \mathbf{P}_{14}[n],\mathbf{P}_{16}[n])\right\}/2}_{=\text{average length of the right and left hips}}\] \[+\underbrace{\left\{d(\mathbf{P}_{15}[n],\mathbf{P}_{17}[n])+d( \mathbf{P}_{16}[n],\mathbf{P}_{18}[n])\right\}/2}_{=\text{average length of the right and left shanks}}. \tag{2}\]  
Figure 5: Anthropometric features by means of joints and limbs: (**a**) \(f_{1}\), (**b**) \(f_{2}\), (**c**) \(f_{3}\), (**d**) \(f_{4}\), (**e**) \(f_{6}\), and (**f**) \(f_{7}\). Using \(H[n]\) in (2), the average height over all frames is obtained by  
\[f_{2}=\frac{\sum_{n=1}^{F}H[n]}{F}. \tag{3}\]  
(3) \(f_{3}\): _Average length of upper body_. This feature was introduced by [PERSON] et al. [44; 45].