Custom Made Pyramids

Cover Custom Made Pyramids
Custom Made Pyramids
Shmuel Peleg
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For example, uniform resampling of an A^-vector to an M-vector corresponds to weighted sampling where the weights are all equal to p = M/N. The backward weights are then also all equal, and have value p"^ = N/M. Thus uniform resam- pling for contraction is paired with uniform resampling for expansion.
As another example, we showed in Figure 2 the weighted sampling of a 4- vector to a 3-vector with weights (1, 1, 1/2, 1/2). The resulting backward weights are (1, 1, 2), so that the weighted backw
...ard resampling becomes Page 8 Peleg, Federbusch, and Hammel Figare 5a Page 9 Custom-Made Pyramids Figure 5b Figure 5. A custom-built two-dimensional Laplacian pyramid with level sizes as marked. Levels are enlarged to full size for visibility. Figure 5a show the Gaussian pyramid, while the Figure 5b contains the levels of the Laplacian pyramid. The ab- solute value of the data is displayed, with larger values shown more darkly.
vi' = V2' = V3' = wo Wl H'2 W2 vo VI V2 + Vi 2 V2 + V3 Page 10 Peleg, Federbusch, and Hummel as depicted by Figures 6a and 6b.


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