Direct Estimation of First Order Optic Flow

Time to contact can be approximated from the divergence of the ow eld. Direct diierentiation of a measured ow eld is not feasible in practice because of the ill-posedness of diierentiation. We propose a group theoretical framework for direct determination of higher order ow elds. The basis is the invariance of the power spectrum of the Fourier transform to translations. By change of coordinate-system, invariance to other groups of actions can be constructed. Using this phase-based estimation the group element acting on the image can be recovered simply by taking inner products in the normal retinal coordinate system. The theory is applied to estimation of rst order optic ow.