• Gabriel A.D. Lopes
  • José A.O. Costa
  • Jorge A.C. Ambrósio
  • Joao Abrantes
Keywords: Biomechanical models, computer graphics, kinematic constraints, multibody systems


It is widely accepted that the photograms of two or more cameras are required for the spatial reconstruction of the human motion. Each projection of the spatial coordinates of a given anatomical point of the human body is described by two equations. Consequently, two or more cameras are necessary for at least three independent linear equations required to obtain the original three coordinates of the point from its projected positions. If n cameras are used in the reconstruction process 2n equations are available for that purpose. In this case more equations than unknowns are available, and the solution for the reconstruction must minimize the error in those equations. Regardless of the number of cameras available, no information of the biomechanical model is generally used during the reconstruction process. In this work, a biomechanical model of 16 segments is used to support the motion reconstruction. The kinematic equations that characterize the dependency between the Cartesian coordinates of the points describing each component of the biomechanical model are used together with the two equations describing their projection in each frame. The single triangle describing the lower torso is defined by three points corresponding to nine spatial coordinates. For a given frame of a single camera six independent linear equations are defined. The remaining three equations needed to the spatial reconstruction of the triangle are the kinematic constraint equations ensuring that the distance between each two points remains constant throughout the motion. The system of nonlinear equations defined in this form has multiple solutions. For each subsequent camera frame the same process is followed to obtain the multiple solutions of the triangle reconstruction. The motion of the triangle representing the lower torso is selected as the combination of the solutions of the independent frames that minimizes a given function, defined as a measure of the smoothness of the triangle motion, variation of its angular orientation or increment of its distance between frames. Only the two solutions for the motion corresponding to the lower values of the functional, evaluated during four frames, are kept. Assuming that the motion for both solutions is feasible for the remaining frames, the method proceeds with the reconstruction of the segments adjacent to the lower torso, followed by the segments adjacent to the first set and so forth. A branch of solutions is eliminated if it cannot proceed from one frame to the next, either because no solution is possible or because the reconstructed motion develops behind the camera. Finally the reconstruction of the full motion is obtained in an automatic form. The methodology is applied to a case of complex human body motion demonstrating that it is feasible to reconstruct the three dimensional human motion using the photograms of a single stationary camera and a consistent biomechanical model.