# Motion-Sphere: Visual Representation of the Subtle Motion of Human Joints
## 1 Introduction  
The main aim of this study is to analyze and visually represent subtle variations of similar human motion in a structured manner. Human joint-bone motions can have numerous subtle orientation variations. Although these subtle variations are visually similar, the underlying orientations can differ markedly. Visualizing human motion with 244 kinematic degrees of freedom (DoF) is a challenging study area. Generally, existing research represents user poses and positions over time in order to visualize human body motion in 3D [1]. Together with spatial and temporal data, object orientation in 3D produces extensive data sets that require processing, organizing, and storing for 3D reconstruction. This paper proposes Motion-sphere for visualizing human motion using data from multiple inertial measurement units (IMUs). Most contemporary motion capture studies record human joint orientations using sensors and/or camera and then apply them directly to a 3D avatar for reconstruction [2; 3]. However, there is a considerable requirement for the accurate and correct visualization of human motion at the minute scale, offering insights into and visual differentiation of subtle changes in intended human motions. It has become common practice to use IMUs for motion capture and analysis, providing more precise orientation estimates for any rigid body (in this case, human bones) as compared to camera-based or any other form of motion capture system [4]. Consequently, commercial vendors commonly offer hardware support for filtering noisy data, software compensation for heading drift, multiple IMU time synchronization, etc. [5]. Rigid body orientations that are calculated by sensors are presented as quaternions (four-dimensional (4D) numbers) that are widely used to realize three-dimensional (3D) rotation in animation and inertial navigation systems. Quaternions can communicate multiple orientation changes as a single change without causing gimbal lock situations. Hence, we adopted quaternions as the basic mathematical unit to represent human body orientation in 3D, consistent with most human motion analysis research [6; 7; 8]. Any human motion is a sequence of quaternion rotations, visually represented as a trajectory on a 3D unit sphere. Figure 1 shows an overview of the proposed Motion-sphere. A 3D LiDAR sensor is used to track the position of a moving human body. The 3D position of the pelvis is computed while using the segmentation of raw point cloud data based on the user's height and IMU sensors are used to estimate the orientation of each bone joints during human body motion in a real environment. When a user performs a motion, orientation data from the IMU sensors are transformed into a 3D avatar's coordinate frame for reconstruction. The quaternion frames are decomposed into swing and twist [9] rotations and visualized as trajectories on a unit sphere. Mapping a grid on the unit sphere helps us to quantify specific human motion and individual bone movements and their respective rotations can be visually analyzed. The Motion-sphere enables comparisons between two sets with visually similar motion patterns. Therefore, the technique opens up itself to a wide range of applications, including athletic performance analysis, surveillance, man-machine interfaces, human motion tracking, kinesiology, physical fitness training, and therapy. Each subtle movement is mapped on the unit sphere as a series of 3D points rotating about given \(X\), \(Y\), and \(Z\) axes. For example, lower limb movement in a sit-up action would be represented as a trajectory on a unit sphere. Although the left and right legs have similar movements, the subtle variation in orientation could not be identified in a video. Likewise, a sit-up performed a second time may have a different trajectory to the first. The human motion details are contained within the axis and orientation changes reflected by the quaternion trajectory.