dan@rna.UUCP (Dan Ts'o) (05/18/89)
Can someone get me started on the topic of reconstructing blurred images ? Hopefully references and available programs. I understand that many schemes depend on knowing the characteristics of the blurring process, but not all. Although we can make a few guesses about our blurring process, just how bad are we off if we don't make any such assumptions ? Please email responses. Thanks. Cheers, Dan Ts'o 212-570-7671 Dept. Neurobiology dan@rna.rockefeller.edu Rockefeller Univ. ...cmcl2!rna!dan 1230 York Ave. rna!dan@nyu.edu NY, NY 10021 tso@rockefeller.arpa tso@rockvax.bitnet
jwl@ernie.Berkeley.EDU (James Wilbur Lewis) (05/18/89)
In article <579@rna.UUCP> dan@rna.UUCP (Dan Ts'o) writes: > > Can someone get me started on the topic of reconstructing blurred >images ? Hopefully references and available programs. Well, one approach you might want to look into is to deconvolve the image and blur function. Let's assume you know the point-spread function (i.e. what the blurred image of a single point would look like). It's not hard to show that the blurred image will be the convolution of the raw image and the point-spread function. Your job is now to invert the convolution to get the raw image from the blurred image and the point-spread function. You can do this with Fourier transforms -- a convolution in the spatial domain is identical to a point-by-point multiplication in the frequency domain. So the algorithm is to take the Fourier transform of the blurred image, divide out the Fourier transform of the PSF, and do the inverse FT on the result to obtain the raw image. There is one snag. If the transform of the PSF has zeroes in it, information is lost in the blurring process, and you can't perfectly recover the raw image. Too bad, eh? But you probably weren't expecting miracles anyway... :-) I guess when you do the division you could just skip over any (frequency domain) points where FT(PSF) == 0. Oh yeah...I guess the PSF would have to be constant over the image for this to work. > I understand that many schemes depend on knowing the characteristics >of the blurring process, but not all. Although we can make a few guesses >about our blurring process, just how bad are we off if we don't make any >such assumptions ? Hmmm. Can you fudge it by looking for isolated features in the blurred image which correspond to point sources in the raw image? That way you could read the PSF right off the image. You could probably also get some information out of edges....in fact, if the PSF is radially symmetric, as it ought to be for a process like defocusing, a single edge of arbitrary orientation is probably as good as an isolated point. (sheer conjecture on my part -- anyone know for sure?) references? hmmm...ok...(digdigdig)...how about Gonzalez & Wintz, _Digital Image Processing_? I've got some nifty 2-D FFT code (in C) if you need it. Good luck! -- Jim Lewis U.C. Berkeley
phil@ux1.cso.uiuc.edu (05/20/89)
Can this process of deblurring be applied where some points have a wider spead than others, such as is the case with limited depth of field photos? Also, what will aperturing effects do to the process? This is when you have a foreground subject exhibiting lots of apertures, and the background having some peculiar shape, such as photographing a cresent moon through a leafy tree, out of focus. The aperturing effect obvious distorts the PSF of the background subject, but perhaps the background subject can help define the aperturing pattern. --phil
jwl@ernie.Berkeley.EDU (James Wilbur Lewis) (05/20/89)
In article <5300011@ux1.cso.uiuc.edu> phil@ux1.cso.uiuc.edu writes: > >Can this process of deblurring be applied where some points have a wider >spead than others, such as is the case with limited depth of field photos? The deconvolution algorithm I described assumes that the blurring process is constant over the field of view. The power at each point in frequency space depends on the whole image, including the blurred and unblurred parts of the image; similarly, the intensity of each spatial point depends on the frequency spectrum as a whole. So if you alter the frequency spectrum in an attempt to correct the defocused background, I expect you'll end up blurring the in-focus portions of the image. I think you might have to eyeball the image to break it up into contiguous regions where the point-spread function is constant, and apply the technique to each region. It sounds like a real hassle -- there's probably a better way to do it, but I don't know how. >Also, what will aperturing effects do to the process? This is when you >have a foreground subject exhibiting lots of apertures, and the background >having some peculiar shape, such as photographing a cresent moon through >a leafy tree, out of focus. The aperturing effect obvious distorts the >PSF of the background subject, but perhaps the background subject can help >define the aperturing pattern. Now this one might be solvable, assuming the moon is perfectly focused and you just want to get rid of the aperturing effects. The moon, at the image scale I think you're talking about, is a pretty high-contrast object -- basically a uniformly bright(*), very sharply defined object, meaning (I think!) little low-frequency information content. I'm guessing that the "aperturing" effects you're talking about are some sort of mottling of the moon's image by out-of-focus leaves. Since the leaves are defocused, their image will be missing the higher spatial frequencies. So you ought to be able to use a high-pass filter to seperate the low-frequency noise due to the aperturing from the high-frequency signal from the moon. As above, this will wreak havoc with the rest of the image, but you could crop out the part of the image containing the moon and just operate on that. I'd use an exponential roll-off instead of a "brick wall" filter to avoid ringing in the filtered image, and play around with different filter radii to see which one gives the best results. Geez. Couldn't you have just moved the camera so you wouldn't have to shoot through the trees? :-) If any of that sounds bogus, let me know -- this is strictly handwaving, and for all I know I could be bullshitting you blind... I'll x-post to sci.astro in case any of those folks want to take a stab at it. -- Jim Lewis U.C. Berkeley (*) yeah, i know about limb darkening, maria, and so on -- but a low-pass filter should get rid of all those unsightly blotches on your nice clean lunar image!
lupton@uhccux.uhcc.hawaii.edu (Robert Lupton) (05/21/89)
The problem of de-blurring images is pretty standard, and pretty hard. The naive solution (for a constant PSF) of deconvolving by dividing in the Fourier domain usually fails horribly. The problem is that the FT of the image usually dissapears into noise, and the noise is amplified. If you want to do better you have to use some constraints (such as the object is positive everywhere, or bounded by a circle). Various techniques are around, such as Jansson's (sp?) and Maximum Entropy. The rule of thumb in astronomy is that you can gain about a factor of 2 in resolution. Robert
james@rover.bsd.uchicago.edu (05/22/89)
In article <3985@uhccux.uhcc.hawaii.edu>, lupton@uhccux.uhcc.hawaii.edu (Robert Lupton) writes... > >The problem of de-blurring images is pretty standard, and pretty hard. The >naive solution (for a constant PSF) of deconvolving by dividing in the >Fourier domain usually fails horribly. Agreed. One other trick is a method called "Iterative Deconvolution". If you have an object that you can get on your image with approximately a known shape for your projection, you can make ane "estimate" of the actual PSF (point spread function), convolve it with the shape, and compare the result to the image. It is best to vary as few parameters as possible, and to assume a general shape for the PSF (eg. a gaussian). There are various articles in MEDICAL PHYSICS and RADIOLOGY on this technique as applied to the blurring function of radiographic imaging systems. James Balter james@rover.uchicago.edu "If the hat fits, slice it!"
cme@cloud9.Stratus.COM (Carl Ellison) (05/23/89)
"Digital image deblurring by nonlinear homomorphic filtering" Thomas Michael Cannon August 1974 UTEC-CSc-74-091 Computer Science Dept. University of Utah Salt Lake City, Utah 84112 In his example photos, there's considerable ringing around restored features in the moderately blurred shots (although all the blur is gone) and the severely blurred shot (of road signs) remains unreadable. --Carl Ellison UUCP:: cme@cloud9.Stratus.COM SNail:: Stratus Computer; 55 Fairbanks Blvd.; Marlborough MA 01752 Disclaimer:: (of course)
rogerh@arizona.edu (Roger Hayes) (05/25/89)
Stuart Geman and Donald Geman, "Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images", IEEE Trans. on Pattern Analysis & Machine Intelligence, PAMI-6(6) (Nov 1984): 721-741. Consider the degraded image as the result of a stochastic process (blurring, noise). Use a local neighborhood process to find the most likely initial image, given the degraded image and some assumptions about the character of the initial image. With examples.