Massively parallel implementations of theories for apparent motion.

Two solutions for the correspondence problem for long-range motion are investigated. The first is a modification of the Minimal Mapping Theory (S. Ullman: The Interpretation of Visual Motion, MIT Press, Cambridge, 1979) that is implemented by a massively parallel network. In this network, every two units are interconnected, and thus, its convergence is fast and relatively independent of the number of image features. Computer simulations show that our method accounts as well as the Minimal Mapping Theory for apparent-motion phenomena, although some differences exist. Mathematical proofs provide conditions for the convergence of the network. The second 'solution' for the correspondence problem is called the Structural Theory. This theory assumes that the three-dimensional structure of viewed objects does not change fast in time. Then, the theory looks for the correspondence and three-dimensional structure that best fulfill this assumption. A massively parallel network implementation of this theory is also possible. However, its performance is poor due to the high complexity of its solution space. This supports Ullman's (1979) suggestion that the visual system separates the structure-from-motion process into two stages. First, a stage for motion measurement, and then a stage for structure recovery.