Differential and Numerically Invariant Signature Curves Applied to Object Recognition
International Journal of Computer Vision
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The seemingly simple everyday actions of moving limb and body to accomplish a motor task or interact with the environment are incredibly complex. To reach for a target we first need to sense the target's position with respect to an external coordinate system; we then need to plan a limb trajectory which is executed by issuing an appropriate series of neural commands to the muscles. These, in turn, exert appropriate forces and torques on the joints leading to the desired movement of the arm. Here we review some of the earlier work as well as more recent studies on the control of human movement, focusing on behavioral and modeling studies dealing with task space and joint-space movement planning. At the task level, we describe studies investigating trajectory planning and inverse kinematics problems during point-to-point reaching movements as well as two-dimensional (2D) and three-dimensional (3D) drawing movements. We discuss models dealing with the two-thirds power law, particularly differential geometrical approaches dealing with the relation between path geometry and movement velocity. We also discuss optimization principles such as the minimum-jerk model and the isochrony principle for point-to-point and curved movements. We next deal with joint-space movement planning and generation, discussing the inverse kinematics problem and common solutions to the problems of kinematic redundancy. We address the question of which reference frames are used by the nervous system and review studies examining the employment of kinematic constraints such as Donders' and Listing's laws. We also discuss optimization approaches based on Riemannian geometry. One principle of motor coordination during human locomotion emerging from this body of work is the intersegmental law of coordination. However, the nature of the coordinate systems underlying motion planning remains of interest as they are related to the principles governing the control of human arm movements.