Noise robust spatial gradient estimation for use in displacement estimation

An important component of any spatial temporal gradient motion estimation algorithm is the accuracy by which spatial gradients are calculated. When an image sequence is corrupted by noise, the problem of determining these spatial gradients becomes extremely difficult. This is immediately apparent, since the magnitude response of the derivative operator is j!j. In other words, the components of an image are amplified upon differentiation in proportion to their frequency value. Thus, high-frequency noise terms will dominate any low-frequency features in the differentiated image. If this corrupted differentiated image is then used within a spatiotemporal gradient motion estimator, the noise will erroneously influence the estimated motion vector. In this paper, the problem of estimating the spatial gradient is treated as an inverse problem with noise. Formulating the problem in this manner results in a recursive gradient estimator that suppresses the effects of noise.