Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 9-21 |
| Number of pages | 13 |
| Journal | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 4392 |
| DOIs | |
| State | Published - 2001 |
| Externally published | Yes |
| Event | Optical Processing and Computing: A Tribute to Adolf Lohmann - Orlando, FL, United States Duration: Apr 17 2001 → Apr 18 2001 |
Keywords
- Detectability
- Digital imaging
- Fourier analysis
- Image quality
- Wigner distribution function
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering