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.
Additional Metadata
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
Citation
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.