A second order partial differential operator is applied to an image function. To this end we consider both the Laplacian and a more general elliptic operator. By using a multigrid operator known from the so-called approximation property, we derive a multiresolution decomposition of the image without blurring of edges at coarser levels. We investigate both a linear and a nonlinear variant and compare to some established methods.
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Keywords Elliptic multigrid image transform, Gradient pyramids, Laplace equation, Laplacian pyramids, Laplacian multigrid image transform, Lifting scheme, Multigrid methods, Multiresolution, Steerable pyramids, Wavelets
Publisher Springer Berlin Heidelberg
Editor X.-C. Tai (Xue-Cheng) , K.A. Lie , T.F. Chan , S. Osher
Series Mathematics and Visualization
de Zeeuw, P.M. (2007). The Multigrid Image Transform. In X.-C Tai, K.A Lie, T.F Chan, & S Osher (Eds.), Image Processing Based on Partial Differential Equations (pp. 309–324). Springer Berlin Heidelberg.