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On Poisson Solvers and Semi-Direct Methods for Computing Area Based Optical Flow
November 1994 (vol. 16 no. 11)
pp. 1133-1138

Simchony, Chellappa, and Shao (1990) proposed a semi-direct method for computing area based optical flow. Their method is based on the iterative application of a direct Poisson solver. This method is restricted to Dirichlet boundary conditions, i.e., it is applicable only when velocity vectors at the boundary of the domain are known a priori. The authors show, both experimentally and through analysis, that the semi-direct method converges only for very large smoothness. At such levels of smoothness, the solution is obtained merely by filling in the known boundary values; the data from the image is almost totally ignored. Next, the authors consider the Concus and Golub method (1973), another semi-direct method, for computing optical flow. This method always converges, but the convergence is too slow to be of any practical value. The authors conclude that semi-direct methods are not suited for the computation of area based optical flow.

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Index Terms:
image sequences; convergence of numerical methods; iterative methods; Poisson solvers; semi-direct methods; area based optical flow; iterative application; Dirichlet boundary conditions; velocity vectors; smoothness; convergence
A.K. Chhabra, T.A. Grogan, "On Poisson Solvers and Semi-Direct Methods for Computing Area Based Optical Flow," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 11, pp. 1133-1138, Nov. 1994, doi:10.1109/34.334395
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