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