# Mobile Augmented Reality Serious Game for Improving Old Adults' Working Memory
## 4 Proposed System
### Cognitive Training System
#### 4.3.1 Measurement of Range of Activities for the Elderly  
Markerless augmented reality follows an interaction method accompanied by a user's movements. However, it is important to reduce risks due to movements because the elderly have weakened physical functions and require particular attention to their daily living activities. Elderly persons, who are the main users of this system, have relatively large variations in body function. Rather than standardizing the user's range of activities by reflecting the elderly's physical functions, personalized interfaces set by the users themselves are more appropriate. The system was designed so that the screen for measuring the range of activities appears first when the user starts the game. The user only moves their upper body according to the instructions on the screen to find the area where they can act while drawing circles in a stationary state Figure 6. When measuring the angle of activity in this way, since there is no separate object in the AR space presented on the device screen, the user is very likely to concentrate on the act of moving their body rather than the AR space in the device screen. For the measurement of the range of activity, it is appropriate to support the universal posture taken by the user when they use the device. As shown in Figure 7a, when using the device, users typically tilt it while taking a posture in which the head is slightly bowed. If the range of activities is calculated in this state, the error between the actual range where the user can act, and the angle of activity measured by the system will be large. Therefore, a calculation process to compensate for the error that occurs just before calculating the final angle of activity as shown in Figure 7b should be undertaken. In order to derive the angle of activity, 3D space coordinates are calculated based on the user's location. In this process, the camera images of the device and the acceleration sensor can be used together to recognize user motions. A method to approximate a circle using the position values measured in units of one frame when the user moves according to the guide was used. The approximation derives the center of the measured position values and calculates the average distance between the values. The larger the average distance, the wider the user's range of activities. Figure 8a shows the positions of objects in an AR space projected onto an \(x-y\) plane. When it is assumed that a camera is placed at point A and objects are placed at points \(J\), \(F\), and \(I\), the direction vectors when the camera looks at each object are \(v\), \(u\), and \(u\). Here, the angle of activity becomes each CAB, and the maximum angle of activity varies according to the value that limits the range where an object can break away within the AR space. Both objects \(F\) and \(I\) on vector \(u\) have the same direction vector and angle of motion. For instance, although objects \(J\) and \(F\) are placed at the same distance along the \(Z\) axis, \(F\) has a larger angle of activities. Figure 8b shows the positions measured in the sections (number; \(n\)) where the range of the user's activities is measured expressed on the \(x-y\) plane. Figure 6: Activities required by the user to measure the activity angle. Figure 7: (**a**) Normally measured activity angle. (**b**) Activity angle before error correction. \(P_{i}\) in Equation (1) means a point on the \(z=1\) plane. Here, \(P_{c}\) is the center of each point, which is the average of the sum of the coordinates of \(p_{i}\). Each point \(P_{i}\) is measured at regular angular intervals, and all are placed at the position of \(z=1\). The vertical component, \(p_{iy}\) is weighted so that it can react relatively insensitively in the vicinity of the center and sensitively at large angles.