Abstract

Estimating the displacement, or velocity, vectors for points in an image plane is an important step in image-sequence analysis. An algorithm to determine the displacement vectors, based on the image-flow approach, is presented. The image-flow approach relates the intensity temporal gradient to the component of the displacement vector along the intensity spatial gradient. Pointwise results computed from this approach are known to be noisy. By formulating the estimation process as an ill-posed inverse problem, it is shown that the estimator cannot have arbitrarily high accuracy and the capability to resolve arbitrarily close displacement vectors simultaneously. Since not all the noise originates from the input data, satisfactory results cannot be obtained merely by smoothing the images or the estimated gradients. After a number of points in a neighborhood are observed and a set of overdetermined linear equations is formed, the total-least-squares method is used to estimate the displacement vector for that neighborhood. The rank-deficient case of this procedure corresponds to the ideal-edge-aperture problem. The performance of the algorithm is verified by experimental results obtained from both synthesized data and real image-sequence data.

© 1989 Optical Society of America

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