## 2 Motion Capture System
### Markerless Systems
#### 2.1.2 Model Definition, Generation, and Matching  
The points generated by the visual hull do not provide information about the specific body parts they represent; for example, it is impossible to determine whether they belong to the arm, leg, or torso. Moreover, these points are not linked to those in subsequent frames, which makes tracking movement over time unfeasible. To overcome this problem, an anatomical-kinematic model is used as a reference to interpret and organize the acquired data. This model is based on two main components:  
1. Anatomical model: The anatomical model describes the three-dimensional shape of the body as a triangular mesh--a structure composed of an ordered list of 3D points (called vertices) and triangles connecting these points to define surfaces. Each point is identified by three coordinates (\(x\), \(y\), \(z\)) in three-dimensional space, and each triangle is described by the three vertices that form it, listed in counterclockwise order. Figure 3: Example of silhouette extraction. 2. Kinematic model: The body is represented as an articulated system, composed of main segments (such as arms, legs, trunk, etc.) connected to each other by joints that allow complex movements, both rotational and translational. Each segment has a \"parent segment\" (for example, the arm is connected to the trunk) and may have one or more \"child segments\" (for example, the forearm is connected to the arm). It also has a local coordinate system that defines its position relative to the segment to which it is connected. Recently, an advanced algorithm was described in the literature by [PERSON] et al. [17] that allows the automatic generation of a specific model for each subject and includes kinematic information directly in the mesh of the various body segments, thus allowing for an integrated representation of shape and movement. The algorithm relies on a database of laser scans from various human subjects. To simplify processing, principal component analysis (PCA) is applied to reduce the complexity of body shapes. The human body is thus described as a combination of principal components, with approximately ten components being sufficient for most applications to achieve the required level of detail for movement analysis. The human body is described as a combination of some principal components, where, for most applications, about ten of these components are sufficient to obtain a level of detail sufficient to analyze movements. The mesh registration process is divided into four main phases:  
* A specific algorithm is applied to obtain the necessary transformations useful for aligning the segments of the reference mesh with the mesh of the subject to be analyzed. * The mesh of the subject is divided into body segments using a proximity criterion: each point of the mesh is associated with the closest body part of the reference mesh. * For each body segment, an inverse transformation is applied to the one adopted in the first step to realign the mesh of the subject to the reference pose. * Finally, the reference mesh is transformed to fit the shape of the subject, minimizing the difference between the vertices of the analyzed mesh and those of the reference mesh. The positions of joint centers (such as elbows, shoulders, and knees) are computed as linear combinations of seven vertices within the reference mesh. These joint locations are then linked to reliable mesh features, enabling a fully automated process. This approach allows the generation of an accurate anatomical and kinematic model, which is useful for biomechanical analysis and virtual movement representation. To analyze subject movement over time and reconstruct joint kinematics, it is necessary to determine the instantaneous pose of the subject in each frame. This is carried out using an algorithm that identifies the configuration of the three-dimensional model that best represents the collected data, namely the surface of the visual hull.