People are able to recognize an indefinite variety of events visually. Motions in events have been shown to provide the information. The question is what optical information do people use to recognize events, that is, how do motions get into optics? The difficulty is that events are inherently time extended so that the structure used to identify events must also be time extended.
Historically, the trend in analysis of optical structure has been from structure that is strongly local in space and time towards more global structures. This trend has been largely motivated by the intractability of the problems formulated on the basis of very local structure. The optic array was introduced by Gibson (1961) to emphasize spatially extended structure surrounding an observer and to provide a means of capturing optical flow. Wlth the introduction of optic flow, the relevant structure became extended in time beyond instantaneous snapshots. However, the extension in time has only progressed in the majority of extant analyses to a sequence of two or three images obtained over a few milliseconds and yielding a mere snapshot of optical flow over distances within an infinitesimal neighborhood of a point in the flow field. Because of the strongly local character of these measurements, the results of the analyses have not been stable in the face of noise engendered by the sensory apparatus. An assumption that the event consists of strictly rigid motions has been used in an attempt to make analysis less local. Rigidity of motion means that distances between points in 3-space are preserved so that the motions of a given point constrain those of neighboring points. However, recent investigations have shown that only truly global analysis will resolve these difficulties (Bertero, Poggio & Torre, 1988; Eagleson, 1987; Hildreth & Grzywacz, 1985; Hildreth & Koch, 1987; Jacobson & Wechsler, 1987; Nagel, 1988; Ullman, 1984; Verri & Poggio, 1987; 1989).
A global analysis is advocated in this paper for a different but related reason.