This paper takes a Fourier perspective on the various multiresolution approaches to digital image processing such as Laplacian Pyramids, Gaussian Scale Space, and wavelet transform (both discrete and continuous). From this perspective, it is possible to highlight the strong similarity between those different approaches. Dangers or possible dangers of some approaches will be highlighted, while at least one case of porting a successful algorithms from one formalism to another one will be presented, opening the perspective of more transparence between the different approaches. The successful porting of efficient feature detection and tracking algorithms from one formalism to another opens the perspective of benefiting from the advantages of each, ad putting these strong points to the service of image-based modeling and rendering.