Harris C M, Wolpert D M
Department of Ophthalmology, Great Ormond Street Hospital for Children NHS Trust, and Institute of Child Health, University College London, UK.
Nature. 1998 Aug 20;394(6695):780-4. doi: 10.1038/29528.
When we make saccadic eye movements or goal-directed arm movements, there is an infinite number of possible trajectories that the eye or arm could take to reach the target. However, humans show highly stereotyped trajectories in which velocity profiles of both the eye and hand are smooth and symmetric for brief movements. Here we present a unifying theory of eye and arm movements based on the single physiological assumption that the neural control signals are corrupted by noise whose variance increases with the size of the control signal. We propose that in the presence of such signal-dependent noise, the shape of a trajectory is selected to minimize the variance of the final eye or arm position. This minimum-variance theory accurately predicts the trajectories of both saccades and arm movements and the speed-accuracy trade-off described by Fitt's law. These profiles are robust to changes in the dynamics of the eye or arm, as found empirically. Moreover, the relation between path curvature and hand velocity during drawing movements reproduces the empirical 'two-thirds power law. This theory provides a simple and powerful unifying perspective for both eye and arm movement control.
当我们进行眼球的快速扫视运动或目标导向的手臂运动时，眼球或手臂到达目标可能采取的轨迹有无数种。然而，人类表现出高度刻板的轨迹，在短暂运动中，眼球和手部的速度曲线都是平滑且对称的。在此，我们基于单一的生理学假设提出一种关于眼球和手臂运动的统一理论，即神经控制信号被噪声干扰，且噪声的方差随控制信号大小的增加而增大。我们提出，在存在这种信号相关噪声的情况下，轨迹的形状会被选择以最小化最终眼球或手臂位置的方差。这种最小方差理论准确地预测了扫视运动和手臂运动的轨迹以及由菲茨定律描述的速度 - 准确性权衡。如实验所发现的，这些曲线对眼球或手臂动力学的变化具有鲁棒性。此外，在绘图运动中路径曲率与手部速度之间的关系再现了经验性的“三分之二幂定律”。该理论为眼球和手臂运动控制提供了一个简单而有力的统一视角。
