On the Qualitative Structure of Temporally Evolving Visual Motion Fields

This paper presents a qualitative analysis that relates stable structures in visual motion fields to properties of corresponding three-dimensional environments. Such an analysis is fundamental in the development of methods for recovering useful information from dynamic visual data without the need for highly accurate and precise sensing. Methodologically, the techniques of singularity theory are used to describe the mapping from image space to velocity space and to relate this mapping to the three-dimensional environment. The specific results of this paper address situations where an optical sensor is undergoing pure rotational or pure translational motion through its environment. For the case of pure rotational motion it is shown that the qualitative structure of visual motion provides information about the axes and relative magnitudes of rotation. For the case of pure translational motion it is shown that the qualitative structure of visual motion provides information about the shape and orientation of viewed surfaces as well as information about the translation itself. Further, the temporal evolution of the visual motion field is described. These results suggest that valuable information regarding three-dimensional environmental structure and motion can be recovered from qualitative consideration of visual motion fields.