Image flow, the apparent motion of brightness patterns on the image plane, can provide important visual information such as distance, shape, surface orientation, and boundaries. It can be determined by either feature tracking or spatio-temporal analysis. We consider spatio-temporal methods, and show how differential range can be estimated from time-space imagery.
We generate a time-space image by considering only one scan line of the image obtained from a camera moving in the horizontal direction at each time interval. At the next instant of time, we shift the previous line up by one pixel, and obtain another line from the image. We continue the procedure to obtain a time-space image, where each horizontal line represents the spatial relationship of the pixels, and each vertical line the temporal relationship.
Each feature along the horizontal scan line generates an edge in the time-space image, the slope of which depends upon the distance of the feature from the camera. We apply two mutually perpendicular edge operators to the time-space image, and determine the slope of each edge. We show that this corresponds to optical flow. We use the result to obtain the differential range, and show how this can be implemented on the Pipelined Image Processing Engine (PIPE). We discuss several kinds of edge operators, show how using the zero crossings reduces the noise, and demonstrate how better discrimination can be achieved by knowledge of range.