Motion Parallax and Structure from Motion

Motion Parallax

Motion parallax is based on perspective: When a person moves relative to an object, or an object moves relative to a person, the closer parts of the object will move faster across the retina. If we hold up two pencils at different distances in front of one eye (keeping the other eye closed) and move our head back and forth horizontally, for example, we can easily observe that the closer pencil moves faster relative to the background. Another simple illustration is the motion across the eye of trees at different distances for a person looking out of the side window of an automobile. Because the trees are not actually moving, the variation in the speeds at which the images of the trees move across the retina must be a result of variations in their distances, with the images of the closer trees moving more rapidly across the retina. Hermann von Helmholtz illustrated the powerful effect of observer motion with the example of a person standing in a thick wood who is unable to distinguish from the mass of foliage which branch belongs to which tree or to perceive the separation of the trees. But when the person moves forward, the mass of foliage is disentangled and there is a clear perception of the separate branches and trees, just as in a stereoscopic view. This illustrates the “camouflage-breaking” quality of this depth cue. The use of this cue is as commonplace as moving one's head back and forth slightly while threading a needle. Motion parallax can also occur with a stationary observer and objects moving in the environment.

The information for motion parallax is relative speed in the image projected onto the retina. Objects, [Page 569]or features on objects, that move faster across the retina when the eye is moved are perceived as closer. Using motion parallax to determine the relative distances of objects in the environment is based on the constraint (assumption) that any variations in the projected motions of the objects are due to variations in their distances. Objects, or parts of objects, cannot be moving independently. This is referred to as the rigidity constraint, and is central to theoretical accounts of motion parallax. If motion parallax is based on head movements and the objects are stationary, this constraint is likely to be satisfied. But if the objects themselves are in motion, rigidity cannot necessarily be assumed. Two objects moving rigidly do not provide sufficient information for verifying this constraint because any difference in the projected speeds of two objects is consistent with rigid motion. If the number of moving objects is increased and their projected speeds continue to vary in a way that is consistent with rigid motion, it becomes increasingly likely that rigid motion will be perceived. Three objects moving together against a background are almost always perceived as moving rigidly. Motion parallax refers not only to the perception of the distances of separate objects, but to the perception of parts of a single object or features on an object's surface, such as the grain on a wood floor.

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