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Fast Surface Interpolation Using Hierarchical Basis Functions
June 1990 (vol. 12 no. 6)
pp. 513-528

An alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented. Conjugate gradient descent is used in conjunction with a hierarchical (multiresolution) set of basis functions. The resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed. Simulation results showing the speed of convergence and its dependence on the choice of interpolator, the number of smoothing levels, and other factors are presented. The relationship of this approach to other multiresolution relaxation and representation schemes is also discussed.

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Index Terms:
conjugate gradient; picture processing; surface interpolation; hierarchical basis functions; multigrid relaxation; convergence; smoothing levels; convergence of numerical methods; interpolation; picture processing; relaxation theory
R. Szeliski, "Fast Surface Interpolation Using Hierarchical Basis Functions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 6, pp. 513-528, June 1990, doi:10.1109/34.56188
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