時空間微分法によるオプティカルフローの検出可能性と3次元運動推定の一方法

抄録

Conventional methods of detecting the 3-D motion of an object from the sequence of brightness patterns in image frames used to be composed of two steps; first computing the optical flow from the brightness patterns, and then detecting the 3-D motion by interpreting the optical flow. The detectable magnitude of optical flow is dependent on pixel sizes, sampling periods, and spatial frequencies contained in the brightness patterns. However, any quantitative relations among them have yet been unknown.
This paper first shows an analytical result that the detectable magnitude of optical flow is inversely proportional to sampling periods and also to spatial frequencies in brightness patterns. The relation is used to examine the limit of detectable optical flow and to determine the design parameters of image processig systems using the temporal-spatial gradient method. The paper then presents a simplified model which describes the relation between the motion of a rigid body composed of planes and the derivatives of brightness patterns. It also presents a method of estimating the optical flow and the 3-D motion simultaneously, which is a combination of that model and the hierarchical estimation approach proposed by Sato, et al. The optical flow and the 3-D motion are estimated by eliminating the undetectable frequency components in image sequences and solving the model equation repeatedly. The paper last presents some simulation experiments about the method which show the successful 3-D motion estimation.