A signal analysis method similar to image pyramids is the discrete wavelet transform. The main difference is that while image pyramids lead to an overcomplete set of transform coefficients, the wavelet transform results in a nonredundant image representation.
The discrete 2-dim wavelet transform is computed by the recursive application of lowpass and highpass filters in each direction of the input image (i.e. rows and columns) followed by subsampling. Details on this scheme can be found in the reference section.
One major drawback of the wavelet transform when applied to image fusion is its well known shift dependency, i.e. a simple shift of the input signal may lead to complete different transform coefficients. This results in inconsistent fused images when invoked in image sequence fusion.
To overcome the shift dependency of the wavelet fusion scheme, the input images must be decomposed into a shift invariant representation. There are several ways to achieve this: The straightforward way is to compute the wavelet transform for all possible circular shifts of the input signal. In this case, not all shifts are necessary and it is possible to develop an efficient computation scheme for the resulting wavelet representation. Another simple approach is to drop the subsampling in the decomposition process and instead modify the filters at each decomposition level, resulting in a highly redundant signal representation. This approach is implemented in the image fusion toolbox.
The actual fusion process can be described by a generic multiresolution fusion scheme which is applicable both to image pyramids and the wavelet approach.