The hybrid constraint equation for motion extraction

摘要

A new derivation of the constraint equation for motion extraction in the image flow is presented. The derivation was obtained by applying the constraint equation to the Fourier transform of the 2D images. It resulted in a hybrid equation joining time-space and frequency notations. The hybrid equation was numerically solved for the 1D case and tested with many image sequences representing coherent, rigid and incoherent motion patterns. Outlines of the 2D case are also presented with some solved examples. The algorithm seems superior to former derivations of the constraint equation for its ability to extract the movement parameters (magnitude and direction) in non-homogeneous movement fields for displacements greater than pixel size. The relevance of the present procedures to machine and organic motion detection is discussed.