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From: jwl@ernie.Berkeley.EDU (James Wilbur Lewis)
Newsgroups: comp.graphics,sci.astro
Subject: Re: Reconstruction of blurred images...
Message-ID: <29246@ucbvax.BERKELEY.EDU>
Date: 20 May 89 01:50:41 GMT
References: <579@rna.UUCP> <5300011@ux1.cso.uiuc.edu>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: jwl@ernie.Berkeley.EDU.UUCP (James Wilbur Lewis)
Organization: University of California, Berkeley
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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!