Singularities of the visual motion field: 3D rotation or 3D translation

This paper addresses the manner in which the structure and motion of the 3D world are manifest in the stable singularities of its imaged visual motion field. By focusing on stable structures the approach enjoys a degree of robustness and invariance to the particulars of recovering visual motion. The specific results to be described address situations where an optical sensor is undergoing pure rotational or pure translational motion through its environment. For the case of pure rotation it is shown that the singularities provide information about the axes, senses and relative magnitudes of rotation. For the case of pure translation it is shown that the singularities provide information about the shape of viewed surfaces as well as information about the translation itself. Finally, empirical results demonstrate the feasibility of applying the analysis to natural images.