Hansard Miles, Horaud Radu
Institut National de Recherche en Informatique et en Automatique (INRIA) Rhône-Alpes, 38330 Montbonnot, France.
IEEE Trans Syst Man Cybern B Cybern. 2010 Feb;40(1):151-61. doi: 10.1109/TSMCB.2009.2024211. Epub 2009 Jun 23.
The human visual system obeys Listing's law, which means that the cyclorotation of the eye (around the line of sight) can be predicted from the direction of the fixation point. It is shown here that Listing's law can conveniently be formulated in terms of rotation matrices. The function that defines the observed cyclorotation is derived in this representation. Two polynomial approximations of the function are developed, and the accuracy of each model is evaluated by numerical integration over a range of gaze directions. The error of the simplest approximation for typical eye movements is less than half a degree. It is shown that, given a set of calibrated images, the effect of Listing's law can be simulated in a way that is physically consistent with the original camera. This condition is important for robotic models of human vision, which typically do not reproduce the mechanics of the oculomotor system.
人类视觉系统遵循利斯廷定律，这意味着眼睛的旋转（绕视线）可以根据注视点的方向来预测。本文表明，利斯廷定律可以方便地用旋转矩阵来表述。在此表示形式中推导出定义观察到的旋转的函数。开发了该函数的两个多项式近似，并通过在一系列注视方向上进行数值积分来评估每个模型的准确性。对于典型的眼球运动，最简单近似的误差小于半度。结果表明，给定一组校准图像，可以以与原始相机物理上一致的方式模拟利斯廷定律的效果。这一条件对于人类视觉的机器人模型很重要，因为这些模型通常不重现眼动系统的力学原理。
