## 4 Experimental Evaluation and Results
### Metrics  
Object keypoint similarity (_OKS_) [89] was used to calculate the average keypoint similarity between all keypoints of objects, depending on the size of the topic and the distance between the anticipated and ground-truth points. Each keypoint was assigned a similarity value ranging from 0 to 1, and _OKS_ was calculated as the average of all these values at all keypoints. \[OKS=\frac{\sum exp(-d_{i}^{2}/2s^{2}k_{i}^{2})\delta(v_{i}\geq 0)}{\sum_{i}\delta(v_{i} \geq 0)}\]  
where \(d_{i}\) is the Euclidean distance between a keypoint and its corresponding ground truth, \(s\) is the object scale (subject height), \(v_{i}\) is visibility of the ground truth, and \(k_{i}\) is a constant per keypoint; in our case \(k_{1}\) is always 1 because we assume that all keypoints are visible as they are inferred from other joint orientation. The mean average precision (_mAP_) [90] was used to show the accuracy of keypoint detection according to precision, was calculated as a ratio of true positive results to the total positive, and then obtained the mean of the average precision over multiple IoU thresholds throughout the model. The joints included in the evaluations are defined by the MPII dataset [54] which include: (1) right ankle, (2) right knee, (3) right hip, (4) left hip, (5) left knee, (6) left ankle, (7) pelvis, (8) thorax, (9) upper neck, (10) head top, (11) right wrist, (12) right elbow, (13) right shoulder, (14) left shoulder, (15) left elbow, (16) left wrist. \[mAP=\frac{1}{N}\sum_{i=1}^{N}AP_{i}\]  
where \(AP_{i}\) is the _AP_ value for the \(i\)-th joint and \(N\) is the total number of joints evaluated. The percentage of correct keypoints (PCK) [91] was used to measure the accuracy of the localization (a higher PCK value means better performance) of different keypoints within a threshold of 50 % of the pose head segment length of each test frame:  
\[PCK=\frac{\sum(Joint_{detected}\cap Joint_{groundtruth|vis>0})}{\sum(Joint_{ groundtruth|vis>0})}\]  
Figure 6: Subject image (**left**) and its pose reconstruction (**right**) (From top to bottom): subject leaning left, subject leaning forward, subject leaning backwards, subject leaning sideways, subject touching face. Figure 7: Example of joint overlay. where \(Joint_{detectal}\cap Joint_{groundtruth|vis>0}\) is the number of joints recognized successfully by the network, and \(Joint_{groundtruth|vis>0}\) is the number of visible joints tagged in the ground truth annotations. The \(PCK\) of the joints was determined in our implementation by taking visibility > 0 into account. Mean per joint position error (\(MPJPE\)) [92] was used as a metric for calculating 3D, by retrieving the Euclidean distance between the calculated 3D joints and the ground truth positions:  
\[MPJPE=\frac{1}{N}\sum_{i=1}^{N}||I_{i}-J_{i}^{*}||^{2}\]  
Here, N is the number of joints, \(J_{i}\) and \(J_{i}^{*}\) are the ground truth position and the calculated position of the \(i_{t}h\) joint. Range of motion error (\(ROME\)) [93] reflects the accuracy in the calculation of the largest amplitude of the motion  
\[ROME=[max()-min(x)]-[max(y)-min(y)]\]  
where \(x\) refers to the ground-truth human joint angles, and y are the joint angles obtained using the proposed method. The Sprague and Geers' metric [94] was used to measure the similarity of the amplitude and phase between the true and measured curves pointwise. Recently, it was used in a related context for assesing the parameters of children's gait [20]. Suppose that the two signals being compared are represented by \(p\) and \(m\). \(p\) is the projected data from the simulation model, while \(m\) is the observed data from the experiment. The S&G magnitude error is calculated by  
\[M_{SG}\ =\text{sig}(rme)\ \text{log}_{10}(1+|rme|)\]  
where the relative magnitude error \(rme\) is given by  
\[rme=\frac{\sum_{i=1}^{N}p_{i}^{2}-\sum_{i=1}^{N}m_{i}^{2}}{\sqrt{\sum_{i=1}^{N }p_{i}^{2}\sum_{i=1}^{N}m_{i}^{2}}}\]  
where \(N\) is the number of points.