25 October 1994 Wavelets, curvature, and chaining issues with applications to the computation of optical flow
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Abstract
Optical flow is an estimate of the velocity field based on the change of intensity patterns in successive images, and is an important quantity in computational vision for dense images. Because of the aperture problem optical flow computations can be ill-posed. This problem is compounded by derivative estimation errors. This paper presents an aggregate velocity scheme that uses iterative velocity refinement along object edge contours obtained via the Mallat- Zhong-Hwang wavelet and chaining algorithms. By working with edge information and aggregate velocities we avoid the aperture problem; iterative refinement compensates for errors in the derivative estimation. Our approach assigns a common velocity to the edge points of an image. When combined with a constant brightness assumption this yields an overdetermined set of linear equations. Since the data vector and matrix coefficients of this linear system consist of temporal and spatial derivative estimates, respectively, and both are subject to errors, the overdetermined system is solved using a total least squares approach. The resulting velocity estimate is then subtracted from the image sequence and the velocity estimation procedure is repeated for the new image sequence. This approach is very fast and accurate for images that have nearly the same edge velocity vectors as is usually the case for distant objects. A convergence analysis is given for the special case of 1D convected flow and it is shown that spatial and/or temporal smoothing enhances the convergence.
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Gary A. Hewer, Gary A. Hewer, Charles Kenney, Charles Kenney, Wei Kuo, Wei Kuo, } "Wavelets, curvature, and chaining issues with applications to the computation of optical flow", Proc. SPIE 2277, Automatic Systems for the Identification and Inspection of Humans, (25 October 1994); doi: 10.1117/12.191888; https://doi.org/10.1117/12.191888
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