A second order partial differential operator is applied to an image function. By using a multigrid operator known from the so-called approximation property, we derive a new type of multiresolution decomposition of the image. As an example, the Poisson case is treated in-depth. Using the new transform we devise an algorithm for image fusion. The actual recombination is performed on the image functions on which the partial differential operator has been applied first. A fusion example is elaborated upon. Other applications can be envisaged as well.
Additional Metadata
Keywords Image fusion, Laplace equation, Laplacian pyramid, multigrid fusion algorithm, multigrid image decomposition, multigrid image transform, multigrid methods, multiresolution
Publisher Springer
Editor R. Kimmel , N. Sochen , J. Weickert
Series Lecture Notes in Computer Science
Citation
de Zeeuw, P.M. (2005). A multigrid approach to image processing. In R Kimmel, N Sochen, & J Weickert (Eds.), Scale Space and PDE Methods in Computer Vision (pp. 396–407). Springer.