Unified computational theory for motion transparency and motion boundaries based on eigenenergy analysis

A unified theoretical framework for motion transparency and motion boundaries by devising fundamental constraint equations of multiple optical flow is proposed. This framework can handle flow discontinuities at motion boundaries as well as flow multiplicities due to transparency of objects in a unified manner. The constraint equations are formulated by a composition of homogeneously parametrized differential operators on the space-time image. Fitting algorithms for the constraints which result in eigensystem analyses are described. To determine the number of flows, the authors use the margin energy, a measure of goodness of fit which is the difference between the first and the second lower eigenenergy of the eigensystem. They also hypothesize a criterion for multiplicity. The measure and the criterion are derived from the analogy of quantum mechanics. It is demonstrated that the margin energy can determine the transparency and discontinuities of the flow field as regions of more than one flow