2007-01-01
The Multigrid Image Transform
Publication
Publication
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 |
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.
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techReport
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techReport
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techReport
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