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Recovering three-dimensional structure and motion of jointed objects from orthographically projected optical flow

When humans observe two-dimensional projected images of a moving object, they can recognize its three-dimensional structure and its motion. This paper presents a method which can recover the three-dimensional structure from the orthogonally projected image of a jointed object. First, a method is presented for a rigid rod, when the direction of the angular velocity is spatially fixed. Then, the three-dimensional structure and motion can be recovered by observing the positions and velocities of both ends on the image. The method is extended to the case of two moving jointed rigid rods, where the direction of the angular velocity vector of the rotational motion of one rod is spatially fixed, and that of the other rod is fixed relative to the former. The method can recover the three-dimensional structure and motion by observing the positions and velocities of the ends and the joint. By a computer simulation, a satisfactory result was obtained.