The motion field or the displacement field due to rigid motion on a system's retina possesses a global structure that is independent of the scene in view and depends only on the parameters of the underlying 3D motion. In this chapter, in order to make explicit aspects of this structure, we analyzed the locus of points on the image where motion vectors and directional motion vectors can take on certain values. We found constraints in the form of equalities and inequalities which showed that motion vectors of certain length lie on contours in the image and directional motion vectors of certain values or sign lie within bounded regions. In order to provide significance to the latter constraints we also presented an analysis proving theoretically that there is almost always enough information in the direction of motion fields to recover 3D motion uniquely.
The theory described here proves that there is valuable information encoded globally in motion fields, that has not yet been utilized in computational studies of visual navigation. The geometric analysis presented shows that global information can be made explicit through constraints, allowing us to formulate problems of visual navigation as simple pattern recognition problems that potentially can be solved in real time, thus leading to direct perception. The analysis also points to new ways of studying problems of visual motion. For example, to extend the framework one can study additional 2D image representations such as measurements obtained with differentiation and integration operators. Furthermore, we have only considered constraints manifested in one flow field, but there is information in the evolution of flow fields over time that arises from the constant scene structure which we need to unravel in order to account for the intrinsically dynamic nature of motion perception.
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Publication information: Book title: Visual Navigation:From Biological Systems to Unmanned Ground Vehicles. Contributors: Yiannis Aloimonos - Editor. Publisher: Lawrence Erlbaum Associates. Place of publication: Mahwah, NJ. Publication year: 1997. Page number: 175.