## Structure from Motion

Another compelling demonstration of how motion information gives strong 3D information is the rotating cylinder example. The observer sees a 2D projection of a pattern of dots that are painted on a rotating glass cylinder rotating about a vertical (or horizontal) axis (Fig. 8). When the cylinder is static the image on the screen looks like a random array of dots. When the cylinder rotates, the dots on the front and back surfaces move in opposite directions. Moreover, the dots in the center of the cylinder have a faster speed than the dots on the edge. Observers are able to integrate these different local motions into the percept of a transparent rotating cylinder.

How does the visual system extract depth from the 2D information generated by a moving 3D shape? Currently, there is not a clear physiological basis for this process. From geometrical constraints it has been shown that the 3D structure can be reconstructed from

Figure 8 Structure from motion. The observer is viewing the projection of a glass cylinder rotating clockwise with dots painted on its surface. The projection falls on a 2D screen. At each instant in time the projection is a 2D pattern of dots, but as the cylinder rotates the dot pattern changes in a way that conveys the 2D shape of the cylinder. The 2D projection of the dots near the center of the cylinder appears to move at a high velocity (either leftward or rightward depending on whether the dots are on the front or back surface of the cylinder), whereas the 2D projection of the dots near the edges of the cylinder has a low velocity (because actual 3D motion of the dots is primarily toward or away from the projection screen).

Figure 8 Structure from motion. The observer is viewing the projection of a glass cylinder rotating clockwise with dots painted on its surface. The projection falls on a 2D screen. At each instant in time the projection is a 2D pattern of dots, but as the cylinder rotates the dot pattern changes in a way that conveys the 2D shape of the cylinder. The 2D projection of the dots near the center of the cylinder appears to move at a high velocity (either leftward or rightward depending on whether the dots are on the front or back surface of the cylinder), whereas the 2D projection of the dots near the edges of the cylinder has a low velocity (because actual 3D motion of the dots is primarily toward or away from the projection screen).

just three different views of four points on a rigid object that are not in a single plane. Depth can also be mathematically reconstructed with fewer views of more points. Furthermore, the 2D pattern of moving dots on the screen is ambiguous; it is equally consistent with stationary dots affixed to a rotating cylinder and with a single plane of independent dots moving with different velocities. Humans appear to be biased to assume that the stimulus is an object that is moving rigidly. This is the rigidity constraint in the interpretation of optic flow. In fact, if we incorporate such a constraint it would have to be one of local rigidity since

Figure 9 Motion parallax. The woman on the bicycle is looking at the man as she pedals. Objects farther than the man appear to move with her, whereas objects closer than the man appear to move in the opposite direction. Specifically, the tree appears to move in the same direction as she does, and the flower beds appear to move backward.

Figure 9 Motion parallax. The woman on the bicycle is looking at the man as she pedals. Objects farther than the man appear to move with her, whereas objects closer than the man appear to move in the opposite direction. Specifically, the tree appears to move in the same direction as she does, and the flower beds appear to move backward.

the movement of most animate objects is not consistent with rigid body motion. Typically, head and limbs move with respect to the torso. It is perhaps this locally rigid motion that makes the phenomenon of biological motion so compelling. Biological motion depicts only the motion of the major joints of a human or animal. Gunnar Johansenn showed that a movie of a person walking in complete darkness, except for small lights attached to major joints, was instantly recognized as a human walking.