Fermüller C, Pless R, Aloimonos Y
Center for Automation Research, University of Maryland, College Park, MD 20742-3275, USA.
Vision Res. 2000;40(1):77-96. doi: 10.1016/s0042-6989(99)00162-5.
A pattern by Ouchi has the surprising property that small motions can cause illusory relative motion between the inset and background regions. The effect can be attained with small retinal motions or a slight jiggling of the paper and is robust over large changes in the patterns, frequencies and boundary shapes. In this paper, we explain that the cause of the illusion lies in the statistical difficulty of integrating local one-dimensional motion signals into two-dimensional image velocity measurements. The estimation of image velocity generally is biased, and for the particular spatial gradient distributions of the Ouchi pattern the bias is highly pronounced, giving rise to a large difference in the velocity estimates in the two regions. The computational model introduced to describe the statistical estimation of image velocity also accounts for the findings of psychophysical studies with variations of the Ouchi pattern and for various findings on the perception of moving plaids. The insight gained from this computational study challenges the current models used to explain biological vision systems and to construct robotic vision systems. Considering the statistical difficulties in image velocity estimation in conjunction with the problem of discontinuity detection in motion fields suggests that theoretically the process of optical flow computations should not be carried out in isolation but in conjunction with the higher level processes of 3D motion estimation, segmentation and shape computation.
大内（Ouchi）图案具有一个惊人的特性，即微小的运动能够在嵌入区域和背景区域之间引发虚幻的相对运动。通过小幅度的视网膜运动或者纸张的轻微抖动就能产生这种效果，并且在图案、频率和边界形状发生较大变化时该效果依然稳定。在本文中，我们解释了这种错觉的成因在于将局部一维运动信号整合为二维图像速度测量值时存在统计困难。图像速度的估计通常存在偏差，对于大内图案特定的空间梯度分布，这种偏差尤为显著，导致两个区域的速度估计出现很大差异。为描述图像速度的统计估计而引入的计算模型，也解释了关于大内图案变化的心理物理学研究结果以及关于运动方格感知的各种发现。从这项计算研究中获得的见解对当前用于解释生物视觉系统和构建机器人视觉系统的模型提出了挑战。结合运动场中的不连续性检测问题来考虑图像速度估计中的统计困难，这表明从理论上讲，光流计算过程不应孤立进行，而应与三维运动估计、分割和形状计算等高阶过程协同进行。
