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Pre-antiblurred image.

An image processing technique, which is inverse of blurring
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Lets say, this image is printed photograph of a coin. To the unaided eye it looks blurred image of a coin. But when you bring this image very close to an unaided eye at a distance of say, one inch, this image image becomes clear and appears apparantly to be perfectly in focus.

I am not sure if this is possible or not but I am wild guessing here.

This is not same as removing the blur after blurring has happened, which is an already available technique in image processing software. This is about doing inverse-blurring ( similar to inverse sine function, or inverse log function) preemptively , so that when burring happens, it will get neutralized and original clear image will be revealed.

To achieve this, I think we will have to find out what blurring does to an image (say, of a coin). Find inverse of those actions. Process these inverse actions on that image.

VJW, Feb 04 2011

Mirror Anamoprhis http://en.wikipedia.org/wiki/Anamorphosis
[MechE, Feb 04 2011]

Deconvolution http://en.wikipedia.../wiki/Deconvolution
It's possible in theory. [AntiQuark, Feb 05 2011]

That woman http://img43.images...0/blackthatcher.png
Greyscale image with red, green and blue colour information [nineteenthly, Feb 05 2011]

Arnold's cat map http://upload.wikim...a/a6/Arnold_cat.png
I also think this is sort of similar. [nineteenthly, Feb 05 2011]

Pre-altering image to cancel out eye distortions. http://dsplab.eng.f...lution_project.html
This paper proposes an image processing approach that will pre-compensate the images displayed on the computer screen, so as to counter the effect of the eye’s aberrations on the image. [AntiQuark, Feb 06 2011]

Anti-blurred image http://dsplab.eng.f..._files/image038.gif
From previous article [AntiQuark, Feb 06 2011]

[link]






       So take an out-of-focus picture and use a lens to put it in focus ? I always wondered that myself.   

       [edit]: nope, it's about using the eye at an out-of-focus distance of a cm or two as the unblurring lens.
FlyingToaster, Feb 04 2011
  

       No lens. Bring the picture very close to eye, thus intentionally blurring it. But since the picture already inverse-blurred, it will be very clearly visible.   

       Ex. log ( inverse_log( x)) = x
VJW, Feb 04 2011
  

       My immediate reaction to this is that for some reason it strikes me as breaking a law of thermodynamics but i can't put my finger on why. I think you would have to add information which has been lost, so it's like unfrying an egg. The image is the egg, blurring is frying through heating, and cooling the egg down doesn't turn it back into an unfried egg. I do know that eyes can't distinguish between the blurring that affects objects which are too close and objects which are too far away (for myopic vision, that is), and i think this makes this impossible. However, i also think it's possible to guess what a blurred object would look like if it hasn't been seen before due to previous experience, for instance a white circle with a red ring round it looks like a red circle with a pink ring round it. Can that be reduced to a function though?
nineteenthly, Feb 04 2011
  

       If an image appears blurred, it appears blurred at the focal plane that you’re sampling or experiencing the image at for some reason, and ordinarily, it will instead be focused at some point either before or after the focal plane. It’s just that that point isn’t where you’re experiencing the image. The ability to resolve detail, linked to the resolution of the image at the point of the focal plane, depends upon focusing the light rays on that plane. If the focus point is beyond or before the focal plane then quite a lot of detail can become ambiguous and unresolvable at the (out of focus) focal plane.   

       Imagine a fine grid, or perhaps a grating of parallel lines. Take it too far out of focus and you end up with a uniform grey patch. Continue to defocus that, and you end up with a grey blob with indistinct edges and hardly much of the original patches shape. Now how do you reverse engineer that back into the grid, or lattice, or grating (whichever it was)? What if the original was indeed a uniform grey patch? How could you tell? If you keep going further away from the focal plane, any interference patterns and harmonics will reduce to the point of irresolvability and at that juncture there could be any one of a number of possible routes to take to synthesise back to a plausible “in focus” image.
Ian Tindale, Feb 04 2011
  

       //I am not sure if this is possible or not// The short answer is, not, for the reasons [nine] and [Ian] give. The blurred image is not isomorphic with the focussed image, which is to say that there are many possible focussed images that give the exact same blurred image; therefore there is no unique transformation to convert from one to the other.   

       One way to reduce the problem is to decrease the size of the aperture, since it is the many possible paths between the object and the blurred image over the area of the pupil that create the non-isomorphic blurring. This could be done by wearing dark contact lenses with a tiny hole in the middle. The image would look darker, and less blurry (but still somewhat blurry). The result might be acceptable in bright natural light.   

       You could test this by making a pinhole in a piece of black paper or thin card. Hold this very close to your eye, and look through it at your image, held further away, say 1".   

       For the sake of completeness, when an image is in focus, there are still many paths from the object to the image, but for each point on the object, all paths lead to the same point on the image. The two are therefore isomorphic.   

       It just might be possible to produce a hologram which can allow a non-blurred image to be seen when it is held 1" from the eye, but I'm just guessing now, and the technology to generate holograms in real time is not mature.
spidermother, Feb 04 2011
  

       Especially without a reference beam.
Ian Tindale, Feb 04 2011
  

       entropy [-]
hippo, Feb 04 2011
  

       But, an intelligent observer accustomed to looking at a well-focussed image would extrapolate the clarity of other experiences and use information present in the photograph to conclude, possibly incorrectly, that the blurred parts of the image represent something specific. The parallel lines stretching off into the blurry distance will be assumed to be potentially sharply focussed. Therefore, whereas it may not be entirely accurate, i would think it was possible to mimic that through some kind of method which recognised that kind of thing. The question is, can that method be expressed as a mathematical function?
nineteenthly, Feb 04 2011
  

       My glasses remove the blur that my slightly-too-long eyeballs introduce. So these fit the requirement of deblurring before blurring.
Therefore, it seems like it should be possible to use a system of lenses to create a focussed image when a picture is viewed from closer than the eye's minimum focal length. However, that's a property of the viewing system rather than the photograph.
Loris, Feb 04 2011
  

       A system of lenses retains the phase information for the light that passes through it. This makes the 'blurring' invertible.
Wrongfellow, Feb 04 2011
  

       // it should be possible to use a system of lenses to create a focussed image when a picture is viewed from closer than the eye's minimum focal length //   

       AKA a microscope.
nineteenthly, Feb 04 2011
  

       Blurring is the measure of the distance between different photon paths carrying information about the same observed feature. The larger the distance, the greater the blur. If the paths are precisely co-linear, no blur.   

       An anti-blur would mean a negative distance between paths. Distance is the absolute value of the offset vector, thus is always positive.   

       <buzzer type="rude"><blink><b><font color="#FF0000"> X </font></b></blink></buzzer>
lurch, Feb 04 2011
  

       Would it sometimes be possible to separate photons on the basis of their characteristics? For instance, suppose you have a rectangle which emitting horizontally polarised light on the left hand side and vertically polarised on the right. Would it be possible to sort the photons according to their polarisation to resolve the situation? What about a rectangle which was red on one side and blue on the other? Sort colours to their probable positions? Then, suppose there's a green stripe in the middle which is obscured by the red and blue blurs, so it seems to be whitish in the middle. Sort out the blues and the reds and you find what seems to be a new visual feature.   

       If that works, how common would those situations be? Would it be possible to try different possibilities until the most realistic one was found?
nineteenthly, Feb 04 2011
  

       All of the above being said, it should be possible to create an apparently blurred image that focuses under a specific lens (most likely a distorted lens). This would be similar to the "magic eye" prints that take advantage of the ability to defocus binary vision.   

       Not the original idea by any means, and I doubt you could do it with just the eye-ball (our eyes are really good at filtering that distortion out) but something related.
MechE, Feb 04 2011
  

       Explain how.
Ian Tindale, Feb 04 2011
  

       The simplest version I can think of would be extreme stretching on a single axis, and shrinking on the other, combined with a lens that corrects these two factors. The printed image would appear extremely distorted, but correct through the lens. (Related to mirror anamorphis). This would be distortion, not blurring, but care in selecting colors and positions could probably start from something that appeared blurred.   

       Next version would be a multi-faceted lens that pulled specific pixels out of a blurred image in order to create a distinct image.   

       As I said, neither of these is true reversing of blurring, they're just using tricks to create an image from an apparently blurred one.
MechE, Feb 04 2011
  

       That’s highly unlikely to come anywhere near working the way you anticipate even for one specifically rigged fixed image and corresponding optics. The way most techniques work currently is to use “unsharp masking” (which I’ve done, using film overlays, back in the early 80s around the time it died out as a technique) which among other things isolates edges and enhances the contrast within a widened area around the edges (the unsharp mask) — start with an interneg, make   

       a pos of that, but out of focus, to ‘widen’ the exposed areas, then use that sandwich to make your mask, which now only lets ‘edges’ show through, which can have the contrast jacked up beyond belief leaving the relatively flat and featureless areas of image unaffected. It’s not actually sharpening anything back from blurred, but it is an interesting utilisation of a perceptually related cognitive effect of our cognitive perceptual er, stuff. A long time ago in one of my   

       first graphic designer jobs, I was frequently tasked with the task of making line reductions from screen bromides of black and white contones. I would use a rotring to run a black line along some of the edges of the object in the image, then a neighbouring white line alongside it (often achieved using a scalpel). This fools most of the people all of the time. These days, digital sharpening uses much a similar process in theory.
Ian Tindale, Feb 04 2011
  

       See the link for examples of the first. I repeat, I am not talking about recreating an image from a blurred version, I am talking about taking something that appears to be a blurred image and creating a sharp image from it.   

       The second one is essentially using the apparent blurred image as a color pallette, and selecting colors such that they create an image. The resulting image would, almost by definition, have to be smaller than the initial "blurred" image, in order to have the desired data buried in the main image. For a better mental picture, start with a fiber optic bundle, tight at one end with each fiber spread out and twisted around. Where each one comes out, put a pixel of the desired color for your final image. Fill the rest of this space with any given image, and blur the heck out of it, taking care not to affect your specific pixels. At the tight end of the bundle, you would see othe original image. If the initial "blurred" image is selected correctly the specific pixels will blend into the surroundings. This will also help relax the tolerance of the infidual lens facets (replacing the fibers) as a slight misalignment won't shift the color beyond recognition.
MechE, Feb 04 2011
  

       I don’t see what the first has to do with blurred imagery — the anamorphic original has perfect sharpness, as does the resulting mapped image. There’s no defocus involved anywhere.   

       The second, taking partial samples on a gradient outside of the CoC can’t re-resolve back to the focal plane. What it amounts to is simply reducing the size of the image, which has effects based on viewing distance, the resolution (lpmm) and a simulation of smaller aperture size (which as it is increased will in turn also lead to diffusion effects).
Ian Tindale, Feb 04 2011
  

       Let me repeat. I AM NOT TALKING ABOUT UNBLURRING AN IMAGE. I am talking about creating the appearance of doing so.
MechE, Feb 05 2011
  

       I think i get what you mean, [MechE]. You are referring to a clear image being altered in predictable and reversible ways to make it appear blurred. So, to use a digital example, you could take a pseudorandom number generator with a specific seed and use the sequence of numbers on an image to move pixels around and create another image which looks blurred. You could then use that sequence in reverse to put those pixels back where they came from. You seem to be thinking of optical examples rather than ones which can easily be carried out using mathematical methods. I think that that would involve "mixing" paths of light from the image in such a way that they would be hard to return to their original paths because they would interfere with each other. The equivalent in my example would be a method which placed pixels in places occupied by other pixels, leading to gaps in the image, so it couldn't be returned, but it would also be possible to skip pixels which had already been changed in this example. The question is, could you do that in reality?
nineteenthly, Feb 05 2011
  

       Some people were taking pictures through textured glass, resulting in highly distorted, unrecognisable images, then restoring the images to clarity by applying an algorithm that reverses the effect of the glass. This works because the way that the glass distorts the image is deterministic, and able to be reverse engineered, as it were. It's equivalent to having both an encrypted message and its key. I seem to remember finding that via some halfbakery links once.   

       It's maybe a matter of semantics whether you would call such images 'blurred'; I would prefer to call them 'transformed' or 'distorted', but they may well qualify as appearing blurred but not being blurred, if blurring implies a stochastic process. OK, that's pushing the definitions a bit, but I kind of see what [MechE] is getting at.
spidermother, Feb 05 2011
  

       What the conversation seems to be talking about is nothing to do with the original idea now, and has moved on to spatial distortions of various types. That has nothing to do with taking an image that simulates a different image not resolved at a focal plane but at a wrong distance, and somehow putting it back together as if it were an image that were resolved at the focal plane.
Ian Tindale, Feb 05 2011
  

       [Ian Tindale], perhaps the idea should be restated as follows   

       1) A speculation that there exists a deterministic image distortion which the naive human observer cannot distinguish from blurring.
2) A proposal to display images so processed, and view them with the inverse filter.
3) A justification. No, on second thought, no justification is needed. It's enough that it would be cool.
  

       Assumption #1 seems plausible for digitized images. Suppose a filter which does permutation of pixels in a local region. Now complicate that a bit as follows: suppose it swaps random pairs of pixels, and the probability of a swap taking place is governed by a bivariate Gaussian kernel convolved over the image. One would have to use "frozen" noise for the filter to be reversible. A few details still to be worked out, but you see what I'm getting at?
mouseposture, Feb 05 2011
  

       Not the mathematical bits of course, but generally yes — you’re playing with convolved noise instances.   

       If you want to take this in yet another direction somewhat associated with the original idea, look up ‘Cardinal Point’ (which is too complicated to understand – too many numbers and funny symbols) and ‘Circle of Confusion’ (which is something obsessed over by willy-measuring <del>photographers</del> <ins>camera equipment owners</ins> and again, mostly misunderstood by most).
Ian Tindale, Feb 05 2011
  

       //circle of confusion// I've heard of that -- no idea what it means, but I love the phrase. Like _Seven Kinds of Ambiguity_   

       [edit] I've just realized that the version of the idea I presented above has a serious, practical application. So much so, in fact, that I suspect it's baked.   

       Suppose you want to encrypt an image so that only people who know the key can see it. OK, nothing special about that. Now, suppose you want to encrypt it such that *anybody* can see the lo-res version, but you need the key to see the high-res version. This would work for that. Now, you could sell photographs the way some software companies sell their products: a freely downloadable, version, which is *complete* but functions only in "crippled" mode until you buy the key. The advantage here is that there's no second, longer download when you decide to buy the product. Software companies seem to like this arrangement, presumably because it lowers the barrier to purchasing, and encourages impulse-buying.   

       The frozen noise is the cryptographic key. In fact, you don't really need frozen noise, just a deterministic pseudorandom number generator, and the seed is the key.
mouseposture, Feb 05 2011
  

       A glib answer would be: That already exists — it’s called a “smaller” photograph, and what you might pay for is a “bigger” image, with more information, cunningly omitted in a mathematical way from the smaller picture.
Ian Tindale, Feb 05 2011
  

       ohhhh, I get it now... it's about using the eye's lens as an "unblurrer" at a focal distance of a cm or two...can you do that ?
FlyingToaster, Feb 05 2011
  

       No.   

       Look, to use a plumbing analogy: you can’t get stereo back from a mono signal. You can’t get colour back from a black and white photo.   

       If you make your information more generalised (an example being out of focus) then you lose specific information. You can’t accurately and predictably go back from general to specific. You can go back from a generalised state to a specific state, but maybe not the specific state. It’ll be a different specific state, according to your process (ie, hunting for digrams, trigrams, n-grams etc), but it won’t be the reverse of the route that was taken to get the specific information into a more generalised state. It’ll just play one on television.
Ian Tindale, Feb 05 2011
  

       [Ian Tindale] //That already exists// Agreed. It's actually like downloading, for free, two copies of the image, an unencrypted small one and an encrypted big one, together in one file. Then you buy the key to the big one. Except my implementation economizes bandwidth/filesize.   

       It only makes sense from a marketing perspective.
mouseposture, Feb 05 2011
  

       Possible in theory, see link. If you know the point response of a blurry pupil, then you can determine the inverse of that response using fourier transforms, and create an image that cancels out the blur.   

       However that makes assumptions on the "linearity" of your eye. Probably in practise, it wouldn't work.
AntiQuark, Feb 05 2011
  

       // you can’t get stereo back from a mono signal. You can’t get colour back from a black and white photo. //   

       On the one hand, you can have a mono signal and do something like separate vocal from instrumental, then allocate one to one channel and the other to a second channel, and in the case of black and white you can use false colour, though in both those cases you won't be producing the original signal or an image which is coloured in the same way (though it might be colourised). On the other, you can make stereo mono or make a colour photo greyscale but encode the "lost" information in a particular way which can later be recovered. With stereo, for example, you could make the left channel occupy only a lower part of the audio spectrum and the right channel only a higher one, and with a photograph you could separate red, green and blue and turn it into three monochrome pictures, one for each channel, in the same image.   

       The question is, is there a process you could apply to an image which some people would interpret as blurry, but which in fact removes no information and is reversible? Also, and this may be a side issue, could that process be applied via a lens?
nineteenthly, Feb 05 2011
  

       I'm not reading through all the comments, I am just saying that the idea as posted really isn't an idea, more of a wish, and not possible. In theory, a blurred image can be *slightly* unblurred by using the original device that performed the blurring, but even saying that is more than is in the original post. [-]
baconbrain, Feb 05 2011
  

       nineteenthly, - yes, your system for encoding the “lost” information in a way which can be recovered later, in this context, would be the reference beam (which was the original beam, through a beam splitter, reflected to the same length reflective path as the reflection off the object) which combines at the holographic plate but having no actual focal plane. The interference and diffraction effect gives us a hologram. In actual fact, holography isn’t confined to visual images — there is also acoustic holography.
Ian Tindale, Feb 05 2011
  

       Baked, in theory. (See link). They actually have a picture of an antiblurred image!
AntiQuark, Feb 06 2011
  

       Update: I testing the anti-blurred image by taking a photograph after de-focusing the lens until the letters appeared. It actually does work.   

       But, if I try to use my eyes, the effect isn`t visible. I figure that`s because a camera lens is a more precise instrument than the human eye, and the extra abberations of the eye interfere with the effect.
AntiQuark, Feb 06 2011
  

       Huh. I looked at the pre-altered images from the article, without my glasses on, and it worked a little. For the strongly horizontal parts, the diagonals were not so good. But it wasn't more than amusing or academic. It was easier to lean in and see the regular images clearly, and the pre-altereds weren't even poorly readable except at a certain distance.
baconbrain, Feb 06 2011
  

       I tried using my eyes without corrective lenses, too, and it didn't work, although there was definitely something interesting going on at a certain distance.   

       Looks like the particular image they printed works for a specific 6.0 diopter blurring lens, worn by subjects with normal vision. So it's not going to work just by looking at it without your glasses, unless your glasses happen to be exactly -6.0 diopters. Given your glasses prescription, they could generate a deblurred image tailored to your eyes.
mouseposture, Feb 06 2011
  

       I tried it and found it looked different than the usual blurring without my glasses. It sort of stood out as being a single sharper-looking image surrounded by the usual blurriness.
nineteenthly, Feb 06 2011
  

       Have not been able to respond due to frequent network outages which are usual in this part of the world.   

       I think fiu.edu's link is what I was talking about, but except the lense.   

       If this "unblurring" becomes achievable with the help of an unaided eye, then its applications would be numerous.   

       e.g. a Book, of the size of the a postage stamp. simply hold the page of book very close to the eye, things will be readable.
VJW, Feb 09 2011
  

       Lens. That other thing you said isn’t a word.
Ian Tindale, Feb 09 2011
  

       The image in the linked article also looks like something my eyes do spontaneously sometimes which i assume is part of my astigmatism. And, astigmatism is, come to think of it, very relevant here. I would say it's loosely speaking a form of blurring - the word "blur" would be used as a casual description of it - but it can be quite easily quantified in a way without the relatively severe loss of information other kinds of blur would involve. If it involves dots becoming horizontal lines and the same alteration applying to other shapes, there is presumably some crossing of paths of light which lead to the loss of information, but not to the same degree as conventional blurring would involve. This could be extended to something weird, like the transformation of all small filled circles into thirteen-pointed stars whose points were at pseudorandom angles to each other, and that could then be reversed. Information would be lost but "pixels" in the image where this occurred could be interpolated from neighbouring pixels. Ironically, this would make a previously sharp image look blurred.
nineteenthly, Feb 09 2011
  
      
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