A look at motion in the frequency domain

A moving image can be specified by a contrast distribution, c(x,y,t), over the dimensions of space x,y, and time t. Alternatively, it can be specified by the distribution C(u,v,w) over spatial frequency u,v and temporal frequency w. The frequency representation of a moving image is shown to have a characteristic form. This permits two useful observations. The first is that the apparent smoothness of time-sampled moving images (apparent motion) can be explained by the filtering action of the human visual system. This leads to the following formula for the required update rate for time-sampled displays. W(c)=W(l)+ru(l) where w(c) is the required update rate in Hz, W(l) is the limit of human temporal resolution in Hz, r is the velocity of the moving image in degrees/sec, and u(l) is the limit of human spatial resolution in cycles/deg. The second observation is that it is possible to construct a linear sensor that responds to images moving in a particular direction. The sensor is derived and its properties are discussed.