The objective of a high-fidelity 3D motion capture system is to accurately observe and track objects and structures in the real world. Our world is a three-dimensional space where all observable structures, objects and shapes have spatial geometries. To fully describe these geometries actually takes 6 dimensions, or 6 degrees of freedom (DoF). For example, a small projectile may be tracked at a position in space in three Cartesian coordinates (x, y, & z). To describe the projectile's orientation at that position requires three additional dimensions, often described in navigational terms as rotational dimensions, such as roll, pitch and yaw. (In unmanned aerial vehicles (UAVs) these rotations around the longitudinal, horizontal and vertical axis respectively are the key control and stability parameters determining the flight dynamics.)
Typically there is at least some motion between the observer (i.e. the viewer, the camera, or the sensor) and the observed objects or surfaces. From the observer's perspective an object's motion results in a trajectory (a path through space followed in time) with an instantaneous position, velocity, curvature and acceleration, where each of these quantities are functions which express the dimensions as a function of time.
Sometimes moving objects follow simple trajectories that can be fully modeled by elementary physics (for example, satellites, billiard balls, and ballistic projectiles). More often, things are not quite so simple. As an example, in robotics, when tracking grippers in robot arms, the observational system itself may be subject to noisy random or even chaotic multi-dimensional disturbances (rotations, translations, vibrations, or the like) resulting in compound measurement errors which can be considered a form of data flow entropy that furthermore complicates sensor data fusion at a system level.
Furthermore, objects and surfaces that are to be tracked may be non-rigid changing shapes such as, for example, a deformable elastic structure or an organic surface such as a human face. Tracking such a deformable surface or object with high accuracy favors methods with high relative local accuracy. This may, for example, take the form of a highly accurate measurement of the relative 3D displacements between points in a surface mesh. Once detected, such deformable objects and their changing 3D shapes and trajectories need to be positioned within some kind of global context (i.e., a stable reference system.) These local object measurements should be converted to a global spatial-temporal coordinates without a loss of accuracy.