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ANIMATION OF FIGURE 5.1

Illustration of 3-D space-time frequency effects of 2-D motion -- no camera motion

Example involving camera tracking a moving person.

The sensing of 2-D retinal image motion is often best understood as a 3-D space-time filtering operation, where two of the dimensions are spatial and the third is time. To see this, consider the individual frames of a video sequence stacked up one of top of the next to form a 3-D volume, with two dimensions corresponding to the spatial dimensions of the images and the third dimension corresponding to time. Moving entities in the sequence show up as tilted streaks in the space-time volume, with the tilt of the streak away from the orientation of the time axis dependent on the speed of image motion (Bolles, Baker, & Marimont, 1987).

Original video sequence

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Stack of images

stack of images

Dynamic cut through the cube

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Contrast boundaries produce streaks in the space-time volume. These streaks are oriented parallel to the time axis if there is no image motion. Image motion produces diagonal streaks, which are particularly apparent if the volume is cut so you can see the top have of the video over time. As this occurs, the evolution of the middle line of this video over time will appear. Here, the diagonal streak correspond to the moving person, while the stationary background generates streaks oriented with the time axis.