The Differential Method for Image Motion Estimation

Abstract

Small variations of the apparent velocity of objects imaged by television cameras can be efficiently measured comparing the frame differences with the spatial variations of the luminance. The main lobe of the autocovariance of a block of picture elements of an image is first modeled as a paraboloid; afterwards, the comparison with the mutual covariance between two successive video frames, allows to determine their relative displacement. The curvatures of the autocovariance taken at the origin are proportional to the m.s. slopes of the image along the coordinate axes; it can be shown that the slopes should be calculated using a centered differentiation, rather than a non centered one, to avoid bias in the estimation of the displacement. To be able to precisely measure the displacement along a given direction, it is necessary that the m.s. slope in that direction be high enough; in fact, the measure of temporal and spatial image derivatives only constrains the projection of the actual displacement along the image gradient. More complex, but continuous, motion fields can be estimated with simple extensions of the original formulation of the differential method. A stochastic model for the motion field is therefore introduced, in order to derive a recursive estimation technique. The component of the motion paralel to the local image gradient is updated, on a pel by pel basis, while the other one is approximately kept constant. The practical results are sufficient for image coding, but not good enough to get a nicely smooth velocity field in real situations.