Constraints for the computation of optical flow

A number of constraints are proposed for which both the components of optical flow can be obtained by local differential techniques and the aperture problem can usually be solved. The constraints are suggested by the observation that it is possible to describe spatial and temporal changes of the image brightness in terms of infinitesimal deformations. An arbitrary choice of two of the four equations which correspond to the elementary deformations of a 2-D pattern implies that the spatial gradient of the image brightness is stationary and leads to a linear system of equations for optical flow which seems best suited for numerical implementation on real data in the absence of a priori information. In that case, the error term between the computed optical flow and the motion field-that is, the 2-D vector field associated with the true displacement of points on the image plane-is derived and the conditions under which it can safely be neglected are discussed. Experiments on real images are reported which show that the obtained optical flows allow the estimate of 3-D motion parameters, the detection of discontinuities in the flow field, and the segmentation of the image in different moving objects.<>