Estimate PSF from blurred and unblurred images.

I have a blurred image and I want to estimate the Point Spread Function (PSF) that blurred the image. I also have a sharp un-blurred image. I don't need to de-blur the blurred image, I just need the PSF.

Can anyone suggest a function or other method that makes use of the blurred and the sharp image to estimate the PSF?

I've experimented a lot with Matlab's blind deconvolution function as well as a few others like those by Fergus et al. and Prateek Garg, and these do estimate the PSF from the blurred image. But I keep thinking there must be a better way that makes use of the sharp image and perhaps improves performance?

Thank you

[Dan]

David you likely do not need the answer anymore but everyone else:

I decided to code this out : http://www.mathworks.com/matlabcentral/fileexchange/54944-calculate-blur-kernel-from-original-and-blurry-images

my old comment: This seems like a perfect task for SVDor QR factorization or least square means (an over-contrained system of equations).

esentially : blurredImg = sharpImg**Kernel Kernel is what you are trying to find.

Kernel = a matrix of mxn unknown doubles .

'**' = convolution = moving sum of dot product between Kernel and the pixels of the image in batches of size(mxn).

you can rewrite that entire mess into a series of many many equations which are along the lines of...

blurredImg(i,j) = Kernel.*sharpImg( i-m/2:i+m/2,j-n/2:j+n/2); % This will only work for odd size Kernel.

for each i,j you can write an equation like that. Let's call the sharpImg( i-m/2:i+m/2,j-n/2:j+n/2) the constants of the euqations such that

constants(:,i,j) =reshape(sharpImg( i-m/2:i+m/2,j-n/2:j+n/2),[1,1,m*n]));

least square mean solvers take in a set of equations writen in matrix form ( going back to the linear algebra basics of writing a system of equations as a matrix equation).

blurredImg(:,1) = (Kernel(:)'*constants(:,:,1))';

The simplest way to solve for kernels is QR factorization although there are other solvers available.

good luck

*The above was meant to be easy to understand , but at the cost of extremely inefficient and sub-optimal code.

[Dan]

this page may also help out : http://www.mathworks.com/help/matlab/math/systems-of-linear-equations.html#brzoiix scroll down to : Iterative Methods for Solving Systems of Linear Equations

[Jihang Wang]

Dan, what if I don't know the size of the psf but want to estimate both the size and kernel values?

Answer 1

[Image Analyst]

What do the theories tell you?

blurredImage = originalImage * * psf (Convolution)

In the Fourier domain:

blurredImageFT = originalImageFT * psfFT (Multiplication)

so

psfFT = blurredImageFT / originalImageFT

psf = inverseFT(blurredImageFT / originalImageFT)

It's essentially the inverse filter except that you're finding the psf instead of the original image. So code that up and see what happens.

[David]

Yes of course. I had tried similar earlier but hadn't used the frequency domain, so of course it hadn't worked.

Thank you Image Analyst

[David]

Hello again, I coded this up but I'm still puzzling over the output, I wonder if you could give me another point in the right direction please?

For the time being, I'm blurring an image with a synthesised PSF, below, and then doing psf = inverseFT(blurredImageFT / originalImageFT) to attempt to recreate it.

 <<http://dl.dropbox.com/u/2651967/synth_psf.png>>

But the image I get out looks like this:

Is there a filter I should use to achieve something more akin to the original psf? Or am I just asking for the impossible?

Thank you

[Jihang Wang]

David,

I got the same issue. Have you figured this out? Thanks!

[dong dong]

The noise in the image will make the methon impossible to work.

[Image Analyst]

Not impossible but with noise, the restored image might not be very good, depending on the magnitude of the noise. That's why the Wiener filter and Wiener Helstrom filter were invented - to handle noisy cases.

[pb]

Hi,

This is my very first day looking at image deblurring, so please excuse me if I am making an obvious mistake as I don't fully grasp the concepts yet.

Using the above theory, I coded up the following and am only getting a black screen in result.. Could you advise the mistake with my code, which I am sure is a conceptual mistake:

%read in crisp and blurred images
crisp = im2double(crisp);
blurred = im2double(blurred);

crispfft = fft(crisp);
blurredfft = fft(blurred);

PSFfft = blurredfft ./ crispfft;
PSF = ifft(PSFfft);

img = deconvwnr(crisp,PSF);
imshow(img)

[Image Analyst]

Try

imshow(img, [])

or

imshow(imadjust(img), []);

[pb]

Hi,

I tried, but

imshow(img,[])

didn't show anything.

imshow(imadjust(img), []) 

showed one barely visible white line through the middle;

The images were simply of my computer screen - I took a picture of it with my phone and then I took a picture with my phone moving it past the computer screen to get a motion blur. I am sure any PSF that would come out of that would not be good at all, as there are several factors in this scenario (hand movement, screen distance, etc) which I suppose would be described as "noise" - but at this stage I wasn't really looking at finding a good PSF first but rather just getting any result at all and then trying it later for a practical application (extracting a PSF for a moving object on a conveyor, and then using that PSF for deblurring further moving objects on that conveyor)

Now, I didn't know what a PSF was this time yesterday - so I may be taking for granted that I should still get a result in the above situation.

Also, in the deconvolution, just a side note I by mistake was trying to deconvolve the crisp image, not the blurred image (in the second last line of the code). I changed that but of course I don't think that's material to the no result coming at all

Let me know your thoughts - thanks!

[Image Analyst]

Start your own, new question after reading this link, and attach your images and script.

[pb]

created at: https://www.mathworks.com/matlabcentral/answers/585680-point-spread-function-calculation-from-known-images