The how and why of what went where in apparent motion: Modeling solutions to the motion correspondence problem

A model that is capable of maintaining the identities of individuated elements as they move is described. It solves a particular problem of underdetermination, the motion correspondence prob-lem, by simultaneously applying 3 constraints: the nearest neighbor principle, the relative velocity principle, and the element integrity principle. The model generates the same correspondence solu-tions as does the human visual system for a variety of displays, and many of its properties are consistent with what is known about the physiological mechanisms underlying human motion perception. The model can also be viewed as a proposal of how the identities of attentional tags are maintained by visual cognition, and thus it can be differentiated from a system that serves merely to detect movement. Many researchers have described the goal of visual percep-tion as the construction of useful representations about the world (e.g., Horn, 1986; Marr, 1976,1982; Ullman, 1979). These representations are derived from the information projected from a three-dimensional visual world (the distal stimulus) onto an essentially two-dimensional surface of light receptors in the eyes. The interpretation of the distal stimulus must be determined from the resulting pattern of retinal stimulation (the proximal stimulus). However, the information represented in the proximal stimu-lus cannot, by itself, completely determine the nature of the distal stimulus. This is because the proximal stimulus does not preserve the full dimensionality of the physical world. The mapping from three-dimensional patterns to two-dimensional patterns is a many-to-one mapping and is not uniquely inverti