Hi there, Suppose an image is out-of-focus blurred. We have the original image and its blurred version. What is the best approach to estimate the blur function? That is, given y(m), x(m), how to we estimate the point spread function (or impulse response function) h(m): y(m) = h(m)*x(m) + n(m) where n(m) is some kind of background noise. We are expecting to use some kind of minimized mean square error to get a parametric and non-parametric estimation of the h(m). Please note, unlike general setup of image deblurring, where the original image is not available. Our case is that both the original image and its blurred version is available. We feel this problem is somehow like a system identification problem, e.g., given the input and output and unknown noise, identify the impulse response. Any advises, suggestions, pointers to right references would be highly appreciated. Thanks.
image out-of-focus blur identification
Started by ●November 30, 2011
Reply by ●November 30, 20112011-11-30
On 30 Nov, 14:35, Ling Chen <erie.stev...@gmail.com> wrote:> Hi there, > > Suppose an image is out-of-focus blurred. We have the original image > and its blurred version. What is the best approach to estimate the > blur function? �That is, given y(m), x(m), how to we estimate the > point spread function (or impulse response function) h(m): > y(m) = h(m)*x(m) + n(m) > > where n(m) is some kind of background noise. > > We are expecting to use some kind of �minimized mean square error to > get a parametric and non-parametric estimation of the h(m). > > Please note, unlike general setup of image deblurring, where the > original image is not available. Our case is that both the original > image and its blurred version is available. We feel this problem is > somehow like a system identification problem, e.g., given the input > and output and unknown noise, identify the impulse response. > > Any advises, suggestions, pointers to right references would be highly > appreciated.This could also be viewed as 'deconvolution'. Given the two images x and y, the blurring operation is expressed as y = h (*) x where h is the system response to be found, and (*) denotes convolution. Extracting this system function h is 'system identification' while extracting an unknown x from is 'deconvolution'. The naive way of solving for this, given x and y, is to compute the 2D DFT: DFT{y} = DFT{ h (*) x } DFT{y} = DFT{h}DFT{x} Y = HX H = X/Y However, *don't* use this naive approach, as it is very sensitive to numerical and other noise. You might try and ask this question on comp.soft-sys.matlab, where some of the regulars are experienced in iage processing. Rune
Reply by ●November 30, 20112011-11-30
Rune Allnor wrote:> On 30 Nov, 14:35, Ling Chen <erie.stev...@gmail.com> wrote: > >>Hi there, >> >>Suppose an image is out-of-focus blurred. We have the original image >>and its blurred version. What is the best approach to estimate the >>blur function?> This could also be viewed as 'deconvolution'. > > Given the two images x and y, the blurring operation is expressed > as y = h (*) x where h is the system response to be found, and (*) > denotes convolution. > > Extracting this system function h is 'system identification' > while extracting an unknown x from is 'deconvolution'.No. An image is an intensity picture. That is, abs(x) not x. It makes for a nasty problem.> The naive way of solving for this, given x and y, is to compute > the 2D DFT:The naive way for solving of this. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●November 30, 20112011-11-30
On 30 Nov, 16:13, Vladimir Vassilevsky <nos...@nowhere.com> wrote:> Rune Allnor wrote: > > On 30 Nov, 14:35, Ling Chen <erie.stev...@gmail.com> wrote: > > >>Hi there, > > >>Suppose an image is out-of-focus blurred. We have the original image > >>and its blurred version. What is the best approach to estimate the > >>blur function? > > This could also be viewed as 'deconvolution'. > > > Given the two images x and y, the blurring operation is expressed > > as y = h (*) x where h is the system response to be found, and (*) > > denotes convolution. > > > Extracting this system function h is 'system identification' > > while extracting an unknown x from is 'deconvolution'. > > No. > > An image is an intensity picture. That is, abs(x) not x.Wrong. abs(x) would indicate that there is a -x. How do you define negative intensity?> It makes for a > nasty problem.Deconvolution is nasty no matter the properties of the data themselves. Rune
Reply by ●November 30, 20112011-11-30
Rune Allnor wrote:> On 30 Nov, 16:13, Vladimir Vassilevsky <nos...@nowhere.com> wrote: > >>Rune Allnor wrote: >> >>>On 30 Nov, 14:35, Ling Chen <erie.stev...@gmail.com> wrote: >> >>>>Hi there, >> >>>>Suppose an image is out-of-focus blurred. We have the original image >>>>and its blurred version. What is the best approach to estimate the >>>>blur function? >>> >>>This could also be viewed as 'deconvolution'. >> >>>Given the two images x and y, the blurring operation is expressed >>>as y = h (*) x where h is the system response to be found, and (*) >>>denotes convolution. >> >>>Extracting this system function h is 'system identification' >>>while extracting an unknown x from is 'deconvolution'. >> >>No. >> >>An image is an intensity picture. That is, abs(x) not x. > > Wrong. abs(x) would indicate that there is a -x.???? Let the input be X and the output be F(X). How would you approach a system identification if only |X| and |F(X)| are available?> How do you define negative intensity?That's the problem. If it could be an original hologram and a blurred hologram, then it would be possible to solve for the scattering function. But as all we have are the intensity pictures, it makes the problem intractable. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●November 30, 20112011-11-30
On 30 Nov, 17:31, Vladimir Vassilevsky <nos...@nowhere.com> wrote:> Rune Allnor wrote: > > On 30 Nov, 16:13, Vladimir Vassilevsky <nos...@nowhere.com> wrote: > > >>Rune Allnor wrote: > > >>>On 30 Nov, 14:35, Ling Chen <erie.stev...@gmail.com> wrote: > > >>>>Hi there, > > >>>>Suppose an image is out-of-focus blurred. We have the original image > >>>>and its blurred version. What is the best approach to estimate the > >>>>blur function? > > >>>This could also be viewed as 'deconvolution'. > > >>>Given the two images x and y, the blurring operation is expressed > >>>as y = h (*) x where h is the system response to be found, and (*) > >>>denotes convolution. > > >>>Extracting this system function h is 'system identification' > >>>while extracting an unknown x from is 'deconvolution'. > > >>No. > > >>An image is an intensity picture. That is, abs(x) not x. > > > Wrong. abs(x) would indicate that there is a -x. > > ???? > > Let the input be X and the output be F(X). How would you approach a > system identification if only |X| and |F(X)| are available?You seem to be stuck in the realm of DSP, where a 'signal' is isomorph to a 'wave' which has both positive and negative devations from equilibrium. That's not the case in image processing, where one deals with non-negative intensities. Since intensity can not be negative, what is measured is x, not |-x|. Rune
Reply by ●November 30, 20112011-11-30
Rune Allnor wrote:> On 30 Nov, 17:31, Vladimir Vassilevsky <nos...@nowhere.com> wrote: > >>Rune Allnor wrote: >> >>>On 30 Nov, 16:13, Vladimir Vassilevsky <nos...@nowhere.com> wrote: >> >>>>Rune Allnor wrote: >> >>>>>On 30 Nov, 14:35, Ling Chen <erie.stev...@gmail.com> wrote: >> >>>>>>Hi there, >> >>>>>>Suppose an image is out-of-focus blurred. We have the original image >>>>>>and its blurred version. What is the best approach to estimate the >>>>>>blur function? >> >>>>>This could also be viewed as 'deconvolution'. >> >>>>>Given the two images x and y, the blurring operation is expressed >>>>>as y = h (*) x where h is the system response to be found, and (*) >>>>>denotes convolution. >> >>>>>Extracting this system function h is 'system identification' >>>>>while extracting an unknown x from is 'deconvolution'. >> >>>>No. >> >>>>An image is an intensity picture. That is, abs(x) not x. >> >>>Wrong. abs(x) would indicate that there is a -x. >> >>???? >> >>Let the input be X and the output be F(X). How would you approach a >>system identification if only |X| and |F(X)| are available? > > > You seem to be stuck in the realm of DSP, where a 'signal' > is isomorph to a 'wave' which has both positive and negative > devations from equilibrium. That's not the case in image > processing, where one deals with non-negative intensities. > Since intensity can not be negative, what is measured is > x, not |-x|.Doctor Rune = idiot. The blurring happens in the wave domain. If the intensity images are all that available, then the problem is intractable. VLV
Reply by ●November 30, 20112011-11-30
On 30 Nov, 18:01, Vladimir Vassilevsky <nos...@nowhere.com> wrote:> Rune Allnor wrote: > > On 30 Nov, 17:31, Vladimir Vassilevsky <nos...@nowhere.com> wrote: > > >>Rune Allnor wrote: > > >>>On 30 Nov, 16:13, Vladimir Vassilevsky <nos...@nowhere.com> wrote: > > >>>>Rune Allnor wrote: > > >>>>>On 30 Nov, 14:35, Ling Chen <erie.stev...@gmail.com> wrote: > > >>>>>>Hi there, > > >>>>>>Suppose an image is out-of-focus blurred. We have the original image > >>>>>>and its blurred version. What is the best approach to estimate the > >>>>>>blur function? > > >>>>>This could also be viewed as 'deconvolution'. > > >>>>>Given the two images x and y, the blurring operation is expressed > >>>>>as y = h (*) x where h is the system response to be found, and (*) > >>>>>denotes convolution. > > >>>>>Extracting this system function h is 'system identification' > >>>>>while extracting an unknown x from is 'deconvolution'. > > >>>>No. > > >>>>An image is an intensity picture. That is, abs(x) not x. > > >>>Wrong. abs(x) would indicate that there is a -x. > > >>???? > > >>Let the input be X and the output be F(X). How would you approach a > >>system identification if only |X| and |F(X)| are available? > > > You seem to be stuck in the realm of DSP, where a 'signal' > > is isomorph to a 'wave' which has both positive and negative > > devations from equilibrium. That's not the case in image > > processing, where one deals with non-negative intensities. > > Since intensity can not be negative, what is measured is > > x, not |-x|. > > Doctor Rune = idiot.Maybe.> The blurring happens in the wave domain.No, it doesn't. You need to distinguish between the EM wave that propagates through space and the optical system, and the properties of the image itself. There are several FTs involved in optics, and one needs to keep them apart: - The EM spectrum of the impigning light wave. - The 2D spatical spectrum of the intensity image. The PSD is defined in 2D spatial domain. I know, it takes a little bit of contemplation to see the difference.> If the intensity images are all that available, then the problem is > intractable.Again, you are stuck with DSP. Different data domain -> different signal properties -> different challenges -> different methods. Rune
Reply by ●November 30, 20112011-11-30
Rune Allnor wrote:>>Doctor Rune = idiot. > > Maybe.Indeed he is.>>The blurring happens in the wave domain. > > No, it doesn't.OK. How about this: Here is a sharp image A. Here is the image A', which is the same image as A, but blurred. Here is the other image B', blurred by the same function. Now derive the blur function from A and A', and apply the inverse of this function to B' to get a clean image B.> Again, you are stuck with DSP. Different data domain -> > different signal properties -> different challenges -> > different methods.I do the image processing, too. It is mainly about very simple and primitive methods optimized for the bulk processing. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●November 30, 20112011-11-30
On 11/30/11 11:52 AM, Rune Allnor wrote:> On 30 Nov, 17:31, Vladimir Vassilevsky<nos...@nowhere.com> wrote: >> Rune Allnor wrote: >>> On 30 Nov, 16:13, Vladimir Vassilevsky<nos...@nowhere.com> wrote: >> >>>> Rune Allnor wrote: >> >>>>> On 30 Nov, 14:35, Ling Chen<erie.stev...@gmail.com> wrote: >> >>>>>> Hi there, >> >>>>>> Suppose an image is out-of-focus blurred. We have the original image >>>>>> and its blurred version. What is the best approach to estimate the >>>>>> blur function? >> >>>>> This could also be viewed as 'deconvolution'. >> >>>>> Given the two images x and y, the blurring operation is expressed >>>>> as y = h (*) x where h is the system response to be found, and (*) >>>>> denotes convolution. >> >>>>> Extracting this system function h is 'system identification' >>>>> while extracting an unknown x from is 'deconvolution'. >> >>>> No. >> >>>> An image is an intensity picture. That is, abs(x) not x. >> >>> Wrong. abs(x) would indicate that there is a -x. >> >> ???? >> >> Let the input be X and the output be F(X). How would you approach a >> system identification if only |X| and |F(X)| are available? > > You seem to be stuck in the realm of DSP, where a 'signal' > is isomorph to a 'wave' which has both positive and negative > devations from equilibrium. That's not the case in image > processing, where one deals with non-negative intensities. > Since intensity can not be negative, what is measured is > x, not |-x|. >maybe x is complex and there's phase. :-\ -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
