Image Velocity and Frequency Analysis

Abstract

This chapter describes the spatiotemporal input signal and models of image velocity using Fourier analysis. It is shown that velocity is a form of orientation in space-time, and has a very simple expression in the frequency domain. We begin with the 2-d translation of textured patterns and 1-d profiles, and then discuss the effects of spatiotemporal localization (windowing), the uncertainty relation, transparency, occlusion, temporal smoothing, sampling and motion blur. This perspective is also important for the design and understanding of linear filters which are characterized by the regions in the frequency domain to which they respond strongly or attenuate. Linear filters can be used as an initial stage of processing to separate image structure according to scale and velocity. The construction of a representation of the input based on a family of velocity-tuned filters is discussed in Chapter 4.