Spatial reconstruction of human motion by means of a single camera and a biomechanical model

The value of the results of the inverse dynamic analysis procedures used in the study of human tasks is dependent on the quality of the kinematic and kinetic data supplied to the biomechanical model that supports it. The kinematic data, containing the position, velocity and acceleration of all anatomical segments of the biomechanical model, result from the reconstruction of human spatial motion by means of the evaluation of the anatomic points positions that enable to uniquely define the position of all anatomical segments. Furthermore, the motion data must be kinematically consistent with the structure of the biomechanical model used in the analysis. The traditional photogrammetric methodologies used for the spatial reconstruction of the human motion require images of two or more calibrated and synchronized cameras. This is due to the fact that the projection of each anatomical point is described by two linear equations relating its three spatial coordinates with the two coordinates of the projected point. The need for the image of another camera arises from the fact that a third equation is necessary to find the original spatial position of the anatomical point. The methodology proposed here substitutes the projection equations of the second camera with the kinematic constraint equations associated with a biomechanical model in the motion reconstruction process. In the formulation the system of equations arising from the point projections and biomechanical model kinematic constraints, representing the constant length of the anatomical segments, are solved simultaneously. Because the system of equations has multiple solutions for each image, a strategy based on the minimization of a cost function associated to the smoothness of the reconstructed motion is devised. It is shown how the process is implemented computationally avoiding any operator intervention during the motion reconstruction for a given time period. This leads to an automated computer procedure that ensures the uniqueness of the reconstructed motion. The result of the reconstruction process is a set of data that is kinematically consistent with the biomechanical model used. Through applications of the proposed methodology to several sports exercises its benefits and shortcomings are discussed.