# Vision-Based Hand Rotation Recognition Technique with Ground-Truth Dataset
## 4 Experiment  
We conducted an experiment to evaluate the performance of our suggested method to capture hand rotation. To obtain performance evaluation and refraction correction  
Figure 4: Process of pattern analysis for behavior recognition. Figure 5: Data-sliced shape used for pattern analysis. values while taking into consideration camera refraction, the experiment imposed different distances between the camera and the experimental robot. The selection criteria for the distances was: 57 cm based on the minimum distance at which both hands can stably enter the camera angle, 77 cm with the left and right hands of the experimental robot on the same line on the three-division baseline, and 97 cm with both hands of the experimental robot at the center when we divided the input image into nine division grid cells. Because the purpose of the experiment was to measure the accuracy of the behavioral data measurement index, we established the following hypotheses for variables that may occur during hand rotation. The situations in which the hypotheses occur comprised 30 tasks, as shown in Table 1.  
Human-to-human hand rotation angle difference. Changes over time between rotations while performing rotational actions. Change in rotational speed while performing rotational action. Rotation angle change while performing rotational action. Synchronization changes between both hands during rotation, e.g., increasingly, synchronization between both hands is wrong. In order to carry out the five hypotheses listed above, we constructed the variables shown in Table 1 as the following: angle of rotation, number of rotations, time between rotations (TBR), time of keeping state (TOK), time of rotation change amount (TCA), and angle of rotation change amount (ACA). To describe each variable in detail, the angle of rotation and number of rotations represent the angle or number of rotations performed by the robot arm, as indicated by the variable name. TBR and TOK are variables representing the retention time of the rotation between each rotation time in milliseconds. For example, if there is a three-rotation 50 TBR, the time between the first and second rotations is 50 ms, the time between the second and third rotations is 100 ms, and the time between the rotations is equal to TBR. TOK is applied to the keeping state described in Section 3.1 with the same principle. Finally, TCA and ACA also form an equal sequence in units of TCA and ACA. TCA represents the amount of change in the total time it takes to perform one rotation. Simply put, if TCA is negative, the rotational speed increases as the number of rotations increases, and in the case of a positive number, rotational speed decreases. ACA represents a unit of rotation angle change, and in the case of negative numbers, as the number of rotations increases, the rotation angle performed by the robot arm becomes smaller, and in the case of positive numbers, the rotation angle becomes wider and wider. We derived the average by performing 30 tasks three times each. We measured the right hand and left hand for the designated task execution rotation time, average rotation angle, and total hand rotation speed. We used the mean absolute percentage error (MAPE) to verify the accuracy of the measurement index, as depicted by Equation (7  
constant 0.018319779725, which is added as the distance between the robot arm and the camera, increases by 1 cm at 57 cm using the difference between the value extracted using the 180\({}^{\circ}\) hand rotation image. We extracted the basic constant using the distance between the robot arm and the camera, and the angle of rotation measurement index was refracted according to distance, as shown as follows in Equation (8). \[Angle\ of\ rotation=(Distance-57)\times 0.018319779725+0.28953692 \tag{8}\]  
We use SPSS for statistical analysis on a computer with an Intel(R) Core(TM) i7-11700 KF processor, 128 GB RAM, an ABKO QHD 1944P webcam as the video input device, and Windows 10 Education 64-bit.