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The Laplacian Pyramid

The Laplacian Pyramid has been developed by Burt and Adelson in 1981 [4] in order to compress images. After the filtering, only one sample out of two is kept. The number of pixels decreases by a factor two at each scale.

The convolution is done with the filter h by keeping one sample out of two (see figure gif):

  
Figure: Passage from to , and from to .

To reconstruct from , we need to calculate the difference signal .

where is the signal reconstructed by the following operation (see figure gif):

  
Figure: Passage from to .

In two dimensions, the method is similar. The convolution is done by keeping one sample out of two in the two directions. We have:

and is:

The number of samples is divided by four. If the image size is , then the pyramid size is . We get a pyramidal structure (see figure gif).

  
Figure: Pyramidal Structure

The laplacian pyramid leads to an analysis with four wavelets [3] and there is no invariance to translation.



Pascal Ballester
Tue Mar 28 16:52:29 MET DST 1995