Optic flow.

Abstract

This paper offers a quick review of the subject of "optic flow" in its conceptual and computational aspects. The theory is evaluated in terms of possible applications in the neurophysiology and experimental psychology of spatial sensorymotor behaviour and perception. The problem of which kind of detector is suited to extract various aspects of optic flow is given special attention. It is shown that the possibilities are actually much more various than is reflected in the current (even the frankly speculative) literature. It is argued that a system that is sensitive to the relative time changes of the orientation differences of image details is especially suited for an analysis of the optic flow with regard to the information concerning the three dimensional shape of objects such as is contained in the flow. Thus the orientation sensitive elements that are known to be abundantly present in the primary visual cortex of many vertebrates are hereby implicated as a quite likely substrate for the extraction of the solid shape of environmental objects. In our opinion this possibility should be investigated with the same ardour as the usual interpretation, which holds this system responsible for the initial extraction of the contours of flat (i.e. defined in the image) shapes. A new, partial solution to the "structure from motion problem" is offered, that not only covers the usual case of shape extraction in the presence of rigid motions of the object, but also the much wider class of (non-rigid) bending deformations (such as occur in the non-rigid deformations of inextensible shells). These solutions violate all conditions required by the well known "structure from motion theorem": the solutions are possible for point configurations in which no fourtuple of points moves as a rigid structure and for input data from merely two views. A numerical example illustrates how this algorithm can be used to predict side views of an object from very limited input data.