Quality time with the fractious Fourier family
Harrison H. Barrett · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
The Fourier family comprises a wide variety of mathematical transforms, some of them well established in the image-science community, some lesser known but deserving of more recognition. The goal of this paper is to survey the genealogy of this family and to show some possibly non-obvious applications of each member. Three central premises run through the discussion: (1) There can be no science of imaging without a scientific approach to the evaluation of image quality; (2) Image quality must be defined in terms of the information that is desired from the image and the method of extracting that information; (3) Digital images are discrete data obtained from a continuous object. These considerations will lead us to rely on rather different members of the Fourier family than the ones most often encountered in polite imaging society.