Mathematical properties of the 2-D motion field: from singular points to motion parameters

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Abstract
The authors study the mathematical properties of the 2-D motion field which are useful for motion understanding. It has been shown that the location and the nature of singular points of the motion field carry most of the relevant information on 3-D motion. Moreover, since the singular points of the motion field are usually structurally stable, the extraction of 3-D motion information from them is robust against noise and small perturbations. The practical relevance of the proposed approach is justified by the observation that it is possible to obtain from a time-varying sequence of images a 2-D vector field which is very close to the true motion field. As a consequence the recovery of 3-D motion from structurally stable properties of the optical flow is feasible and provides good experimental results. Therefore, the whole framework seems very appropriate for computer vision.

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