Path: utzoo!attcan!uunet!mcsun!unido!mpirbn!p560fgr From: p560fgr@mpirbn.mpifr-bonn.mpg.de (Frank Grieger) Newsgroups: comp.graphics Subject: Re: Cleaning up frame-grabbed images: "Fourier plane"? Message-ID: <1256@mpirbn.mpifr-bonn.mpg.de> Date: 1 Oct 90 12:32:52 GMT References: <1990Sep27.085647.13944@ste.dyn.bae.co.uk> Reply-To: p560fgr@mpirbn.UUCP (Frank Grieger) Organization: Max-Planck-Institut fuer Radioastronomie, Bonn Lines: 91 In article <1990Sep27.085647.13944@ste.dyn.bae.co.uk> adam@ste.dyn.bae.co.uk (Adam Curtin) writes: >Hi > >I'm considering buying a colour digitiser (video frame grabber) as a cheap >substitute for a colour scanner. > >However, all of the images I've seen have black lines across them, something >to do with the video signal and scanning and such, which spoil the image. > >My wife remembers from her physics undergraduate days that an image overlayed >with a grating could be optically processed to remove the grating - light from >the image was focused though a lens to come to a point at the fourier plane. >Then, somehow, the image the other side was a magically cleaned up version of >the original. (You can tell that I don't understand it very well :-). >She can't describe it well enough for me to code it (even if I could understand >it), but she tells me that the technique is often used for cleaning up images >from satellites. > >Can anyone illuminate me? > >Adam >-- >A. D. Curtin . Tel : +44 438 753430 >British Aerospace (Dynamics) Ltd. . Email: adam@ste.dyn.bae.co.uk >PB 230, PO Box 19, Six Hills Way, . >Stevenage, SG1 2DA, UK. . "My other car is an FJ1200" Hallo Adam, the physical explanation of spatial filtering is very simple: Please consider an optical setup were a lense forms am image in its focalplane, which will be projected on a detektor by a second lense. We call this a telescope looking at an image at infinity. If there is no dirt on the lense or any other negative influence on the image formation, a paralell light beam will be focused to a lgiht spot in the focal plane. This spot is a diffraction pattern called an airy disc. If there are some dirt particles on the first lense, light will be scattered out of the light spot in the focal plane and will have negative influence on the image formation on the detector. If you now center a pinhole in the focal plane of the first lense which will cover up the light which was scattered by the dirt particles, the information about the dirt ist lost and the result is a clean image on the detector. This technique is for example used to produce clean laser light beams for holography. For more complicated setups and more general images you need more complicated masks in the focal plane of the lense. If you now would like to clean images in the computer, you have to know something about the mathematics of this phisical efect: In the experement we discribed above, we had an image in the infinity, a lense which projected the image into its focal plane where the image quality was improved by the positioning of a mask, and we had a secound lense which showed us the result on a detector. In terms of mathematics the lenses perform a Fourier-Transform on the original image. The Fourier-Transform is discribed by: H(f) = int { h(t) exp [ -i 2 PI f t ] } dt H(f) is the image in the Fourier domain, f is its coordinate vector, int denotes an integration, h(t) is the original image and t is the vector in the image plane. To clean images in the computer, you take the image, perform a Fourier Transform and multiply a binary mask to the result or better fit "bad" regions whith values in the surrounding. Finaly you perform an inverse Fourier-Transform to obtain the clean image. For your specific problem: The stripes in your original image, will be represented by peaks in the Fourier domain which you will have to remove. On the computer you should use the fast fourier transform algorithm, which might be in your math library or is discribed in the litterature. Litterature: ALSOP, L. E., and A. A. NOWROOZI, "Fast Fourier analysis," J. Geophys. Res. Vol. 71, PP. 5482-5483, November 15, 1966 GOODMAN, J. W., "Introduction to Fourier Optics," McGRAW-HILL BOOK COMPANY BRACEWELL, R., "The Fourier Transform and ist Applications," McGRAW-HILL BOOK COMPANY result. I hope this is the information you wanted. Frank