Abstract

A technique is proposed for the measurement of two-dimensional (2-D) image motion. The basic component is a 2-D motion sensor that is made up of 12 circularly symmetric second-derivative operators arranged around a similar central operator. The Laplacian of a Gaussian is used to achieve the second-derivative operation. The sensor therefore consists of 12 pairs of overlapping operators, arranged in a radial pattern, and is capable of measuring speed in 12 separate directions at any point in the image. When an edge crosses the sensor, since the distance between operators is known, its speed along a given direction is determined by the relative times of occurrence of the two zero crossings in the temporal outputs of the operator pair oriented in that direction. The low-pass spatial filtering produced by the operators, along with their close proximity, helps to prevent more than one edge from fitting between the operator pairs at any one time, and the correspondence problem is thus minimized. The direction of the edge normal and the speed can be found from the distribution of time differences in each of the 12 sensor directions. These edge velocities are passed onto a second stage, which uses directionally tuned patternmotion detectors to solve the aperture problem. The entire system involves a simple network of weighted connections and is potentially a fast method of obtaining a 2-D optical flow field from a sequence of images.

© 1990 Optical Society of America

Differential techniques for optical flow

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