| correlation between images [message #65922] |
Thu, 02 April 2009 05:33  |
Wout De Nolf
Messages: 194
Registered: October 2008
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Senior Member |
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Hi all,
I have two images and I want to check (statistically) whether they are
"the same" and show it to others so they will believe me :-).
The first thing I thought of was using the Pearson correlation
coefficient:
R=correlate(img1,img2)
However, R close to 1 doesn't necessarily means they are "the same" or
in other words, img1 vs. img2 is linear.
( Some examples of R=0.8:
http://upload.wikimedia.org/wikipedia/commons/b/b6/Anscombe. svg)
I can off course show the scatter plot
plot,img1,img2
with LADFIT(img1,img2) to draw a line through it and
correlate(img1,img2) to add a correlation coefficient.
I'm still not satisfied though. Does anyone use another statistical
method to compare images? (I tried IDL's c_correlate but I can't
figure out what the result means...)
Thanks
Wox
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| Re: correlation between images [message #66004 is a reply to message #65922] |
Wed, 08 April 2009 07:20  |
Mike[2]
Messages: 99
Registered: December 2005
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Member |
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On Apr 8, 4:04 am, Wox <s...@nomail.com> wrote:
> On Mon, 6 Apr 2009 10:12:07 -0700 (PDT), Mike
>
> <Michael.Mill...@gmail.com> wrote:
>> That reminded me that the open source program gqview includes a tool
>> for finding duplicate images based on a similarity measure. Maybe the
>> code would shed some light...
>
> The code can be found in "similar.c"
>
> It seems that both images are subdivided in 32x32 subimages. For each
> subimage the average value is calculated. Then the (normalized) sum of
> differences between the two resulting 32x32 arrays is taken as
> similarity measure.
>
> So this is similar to the RMS approach.
>
> As for the SPMs: it seems I'll have to invest a lot of time to
> understand and implement this. You seem to have doubts about its use
> in my case. Do you think it's worth the effort?
That depends on the details of how what you'd be using it for. The
section on experimental design in www.fil.ion.ucl.ac.uk/spm/doc/intro/
might help you answer that question.
As for implementing it for a single experiment, it's not that hard.
Making a general system would be complicated, but you could use the
(matlab-based (please forgive my heresy)) SPM software.
Mike
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| Re: correlation between images [message #66011 is a reply to message #65922] |
Wed, 08 April 2009 01:04 |
Wout De Nolf
Messages: 194
Registered: October 2008
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Senior Member |
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On Mon, 6 Apr 2009 10:12:07 -0700 (PDT), Mike
<Michael.Miller5@gmail.com> wrote:
> That reminded me that the open source program gqview includes a tool
> for finding duplicate images based on a similarity measure. Maybe the
> code would shed some light...
The code can be found in "similar.c"
It seems that both images are subdivided in 32x32 subimages. For each
subimage the average value is calculated. Then the (normalized) sum of
differences between the two resulting 32x32 arrays is taken as
similarity measure.
So this is similar to the RMS approach.
As for the SPMs: it seems I'll have to invest a lot of time to
understand and implement this. You seem to have doubts about its use
in my case. Do you think it's worth the effort?
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| Re: correlation between images [message #66073 is a reply to message #65922] |
Mon, 06 April 2009 10:12 |
Mike[2]
Messages: 99
Registered: December 2005
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Member |
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On Apr 6, 11:46 am, David Fanning <n...@dfanning.com> wrote:
> My son is an intellectual property specialist for
> a company that represents photographers and sells
> images. They hire an Israeli company to search the
> web for images that have not been paid for.
>
> Whatever software they are using (and they don't say,
> naturally) is VERY good. They can find images that
> have been flipped, re-colored, resized, clipped,
> and manipulated in other various ways. I'm pretty
> sure they are not relying totally on RMS difference. ;-)
That reminded me that the open source program gqview includes a tool
for finding duplicate images based on a similarity measure. Maybe the
code would shed some light...
Mike
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| Re: correlation between images [message #66076 is a reply to message #65922] |
Mon, 06 April 2009 09:59 |
Mike[2]
Messages: 99
Registered: December 2005
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Member |
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On Apr 6, 11:13 am, Wox <s...@nomail.com> wrote:
> But what is "close enough"? I guess nobody knows.
There are robust methods for evaluating statistical parametric maps
(SPMs). Very generally, all of these methods involve using a set of
images to calculate, at each point in the images, the statistical
parameter appropriate for the null hypothesis under question.
Applying a Bonferroni correction is required to keep the error rate at
an acceptable level. The result is a map of the statistical parameter
(or p-value) that is thresholded at a significance level. In order to
account for correlations within each image, the data are often
smoothed.
There is a nice online bibliography at http://www.fil.ion.ucl.ac.uk/spm/doc/biblio/.
A good starting point might be J Comp Assisted Tomography 19 (1995)
788, "Estimating Smoothness in Statistical Parametric Maps:
Variability of p Values." Or just google for SPM.
If you have only two images, you will always have trouble calculating
an SPM. You could try treating the data as repeated measures of the
same object. Then you could calculate a single paired t-test for the
entire data set. If the test is significant, the hypothesis that the
mean difference is zero could be rejected. In the sort of tomographic
imaging that I'm familiar with, this is dangerous because individual
points in each image are correlated with other points as a consequence
of the image reconstruction methods. Another simple statistic is a z-
score map (difference between test image and mean of a standard data
set)/(std dev of a standard data set). That is an easy way to see if
an image is consistent with a calibration data set, but again will
require the proper Bonferroni corrections to avoid high error rates.
Mike
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| Re: correlation between images [message #66078 is a reply to message #65922] |
Mon, 06 April 2009 08:46 |
David Fanning
Messages: 11724
Registered: August 2001
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Senior Member |
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Wox writes:
> I'm just trying to find out whether there is a more robust/objective
> image comparison method.
I know there is, although I don't know what it is.
My son is an intellectual property specialist for
a company that represents photographers and sells
images. They hire an Israeli company to search the
web for images that have not been paid for.
Whatever software they are using (and they don't say,
naturally) is VERY good. They can find images that
have been flipped, re-colored, resized, clipped,
and manipulated in other various ways. I'm pretty
sure they are not relying totally on RMS difference. ;-)
Cheers,
David
--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.dfanning.com/
Sepore ma de ni thui. ("Perhaps thou speakest truth.")
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| Re: correlation between images [message #66079 is a reply to message #65922] |
Mon, 06 April 2009 08:13 |
Wout De Nolf
Messages: 194
Registered: October 2008
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Senior Member |
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On Mon, 6 Apr 2009 07:35:46 -0700 (PDT), Mike
<Michael.Miller5@gmail.com> wrote:
> What about just using the RMS difference between the two images?
Whenever I use cross-correlation, RMS difference, mutual information,
Kullback-Leibler distance,...(there seem to be thousands) it always
comes down to this: you have a measure for image difference (i.e. a
number) which should be ideally close to 1 (or some other value,
dependent on what you used). When it's "close enough", the images
match.
But what is "close enough"? I guess nobody knows. Therefor I tried
Brian's approach of dividing in subimages and not only put a threshold
on the correlation coeff (or RMS or whatever) but also check whether
the subimages are located (+/- x pixels) at their original position
after the cross-correlation loop. (This can go wrong when parts of the
images a just noise.)
Another way to solve the "close enough" problem is statistical
hypothesis testing of the Pearson correlation coeff.
(http://davidmlane.com/hyperstat/B62955.html)
However this would only allow me to say that R is significantly
different from zero (if p-value <= 0.05 that is) so there is some
correlation. Fisher's z' transformation of R should allow testing H0:
R=x but this doesn't work for x=1 because z=Inf and p-value=0 (i.e. R
always significantly different from 1). So this approach doesn't work
(or I'm missing something).
I'm just trying to find out whether there is a more robust/objective
image comparison method.
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| Re: correlation between images [message #66081 is a reply to message #65922] |
Mon, 06 April 2009 02:56 |
Wout De Nolf
Messages: 194
Registered: October 2008
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Senior Member |
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On Fri, 03 Apr 2009 09:43:28 -0500, "C.E. Ordonez" <nerdzoo@gmail.com>
wrote:
> Another possibility is the use of "mutual information" in a manner as
> applied to image registration. For example, see F. Maes, et al.,
> "Multimodality image registration by maximization of mutual
> information," IEEE Trans. Med. Imaging, Vol. 16, No. 2, 1997, pp187-198.
> Also,
> http://ranger.uta.edu/~hchen/CSE6392_2005spring/references/M I_survey_maes.pdf
Interesting. But if I use the "mutual information" (0 when image1 and
image2 are indepent and 1 when they are dependent, right?) instead of
the cross-correlation coefficient, how do I benefit from that?
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| Re: correlation between images [message #66091 is a reply to message #65922] |
Fri, 03 April 2009 07:43 |
C.E. Ordonez
Messages: 10
Registered: May 2004
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Junior Member |
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Wox wrote:
> Hi all,
>
> I have two images and I want to check (statistically) whether they are
> "the same" and show it to others so they will believe me :-).
>
>
> I'm still not satisfied though. Does anyone use another statistical
> method to compare images? (I tried IDL's c_correlate but I can't
> figure out what the result means...)
>
>
> Thanks
>
> Wox
Another possibility is the use of "mutual information" in a manner as
applied to image registration. For example, see F. Maes, et al.,
"Multimodality image registration by maximization of mutual
information," IEEE Trans. Med. Imaging, Vol. 16, No. 2, 1997, pp187-198.
Also,
http://ranger.uta.edu/~hchen/CSE6392_2005spring/references/M I_survey_maes.pdf
-Caesar
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| Re: correlation between images [message #66096 is a reply to message #65922] |
Fri, 03 April 2009 05:01 |
Wout De Nolf
Messages: 194
Registered: October 2008
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Senior Member |
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So this is what I came up with so far (see code below) thanks to
Brian's suggestions.
To say whether 2 images are "the same", I subdivided "img2" in
subimages. For each subimage I try to find its best correlating
position in "img1" with a loop over c_correlate while shifting the
subimage over img1.
The criteria for "images are the same" are:
1. A correlation tollerance level (Rtol=0.9): each subimage must
correlate better than Rtol with some part of img1
2. The subimage positions in img1 must be regularly aligned with
respect to eachother within a pixel tollerances
(shifttol=0.01*imgsize)
I have a question for you: when the criteria above are met, would you
believe the images are the same? If not, do you have a better
suggestion?
If you wonder what images I'm talking about, it ain't all roses like
in the example. I have a distribution map of the copper content in a
fragment of a painting. The second distribution map represents the
azurite content (azurite is a copper containing pigment). Both should
be the same (correlated) if there are no other copper containing
pigments present (or if the other pigments are mixed with azurite, so
having the same distribution). I want to prove that this is the case.
CODE:
;------------------------
pro test
path = Filepath(Subdir=['examples', 'data'], 'rose.jpg')
read_jpeg, path, img, /true
img = 0.3*Reform(img[0,*,*]) + 0.59*Reform(img[1,*,*]) +
0.11*Reform(img[0,*,*])
kernelSize = [10,10]
kernel = REPLICATE((1./(kernelSize[0]*kernelSize[1])), $
kernelSize[0], kernelSize[1])
img2= CONVOL(img, kernel, /CENTER, /EDGE_TRUNCATE)
print,image_equal(img,img2,/outid)
end;pro test
;------------------------
function
image_equal,img1,img2,npix=npix,shifttol=shifttol,Rtol=Rtol, outid=outid
; Image offsets or scales don't matter
; npix: subimage pixels for cross-correlation
; shifttol: subimage shift tollerance
; Rtol: cross-correlation tollerance
s1=size(img1,/dim)
s2=size(img2,/dim)
msize=s1[0]<s1[1]<s2[0]<s2[1]
if not keyword_set(npix) then npix=fix(msize*0.4)>10 ; 40% of the size
npix<=msize
if n_elements(shifttol) eq 0 then shifttol=(msize*0.01)>1 ; 1% of the
size
if not keyword_set(Rtol) then Rtol=0.9
; Subimages in img2
nsub=s2/npix
nx=nsub[0]
ny=nsub[1]
x0=npix*indgen(nx)
x1=[x0[1:*],s2[0]]-1
y0=npix*indgen(ny)
y1=[y0[1:*],s2[1]]-1
; img2 subimages in img1
xoff=lonarr(nsub)
yoff=xoff
xyccor=fltarr(nsub)
if keyword_set(outid) then img2recon=img1*0
; Cross-correlate subimages of img2 with img1
for i=0,nx-1 do $
for j=0,ny-1 do begin
sub=img2[x0[i]:x1[i],y0[j]:y1[j]]
ssub=size(sub,/dim)-1
; Number of sub-shifts in img1
noffx=s1[0]-ssub[0]
noffy=s1[1]-ssub[1]
ccor=fltarr(noffx,noffy)
; Correlate sub with img1
for k=0,noffx-1 do $
for l=0,noffy-1 do $
ccor[k,l]=c_correlate(sub,img1[k:k+ssub[0],l:l+ssub[1]],0)
; Sub image offset and cross-correlation
mccor=max(ccor,moff)
k=moff mod noffx
l=moff/noffx
xoff[i,j]=k
yoff[i,j]=l
xyccor[i,j]=mccor
if keyword_set(outid) then begin
img2recon[k,l]=sub
print,'Progress: ',(i*ny+j+1.)/(nx*ny)*100,'%'
endif
endfor
; Check whether img2 and img1 are equal
bsame=total(xyccor lt Rtol,/pres) eq 0
bsame and= total(rebin(total(xoff,2)/ny,nx,ny)-xoff gt shifttol,/pres)
eq 0
bsame and= total(rebin(reform(total(yoff,1),1,ny)/nx,nx,ny)-yoff gt
shifttol,/pres) eq 0
if keyword_set(outid) then begin
window
tvscl,img1,0
tvscl,img2,1
tvscl,img2recon,2
tvscl,img2-img2recon,3
xyouts,0.1,0.7,'img1',/normal,color=100
xyouts,0.3,0.7,'img2',/normal,color=100
xyouts,0.5,0.7,'reconstructed img2',/normal,color=100
xyouts,0.7,0.7,'img1 - reconstructed img2',/normal,color=100
isurface,xyccor
endif
return,bsame
end;function image_equal
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| Re: correlation between images [message #66097 is a reply to message #65922] |
Fri, 03 April 2009 00:45 |
Wout De Nolf
Messages: 194
Registered: October 2008
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Senior Member |
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On Thu, 2 Apr 2009 13:56:56 -0700 (PDT), Brian Larsen
<balarsen@gmail.com> wrote:
> Run this as I think its pretty fun.
> Download this image:
> http://technabob.com/blog/wp-content/uploads/2008/03/apple_l ogo_rainbow_fruit.jpg
>
> then run the following code:
> ; .run image_registration
> read_jpeg, 'apple_logo_rainbow_fruit.jpg', img, /true
> tv, img[1, *, *]
> size = size(img, /dimen)
> cut_size = 50
> sub = img[*, 140:190, 300:350]
> ans = fltarr(size[1:2])
> FOR i = 0UL, size[1]-cut_size-1, 10 DO BEGIN
> FOR j = 0UL, size[2]-cut_size-1, 10 DO BEGIN
> ans[i, j] = c_correlate(sub, img[*, i:i+cut_size, j:j+cut_size],
> 0)
> tv, sub, i, j, /true
> tv, img[1,i:i+cut_size, j:j+cut_size], i, j
> ENDFOR
> ENDFOR
> ind=where(ans eq max(ans))
> wheretomulti, ans, ind, col, row
> tv, img[1, *, *]
> tv, sub, col, row, /true
> END
I like it :-). c_correlate starts making sense to me.
Nevertheless, c_correlate has essentially the same problem as
correlate doesn't it (i.e. the Anscombe problem).
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| Re: correlation between images [message #66101 is a reply to message #65922] |
Thu, 02 April 2009 13:56 |
Brian Larsen
Messages: 270
Registered: June 2006
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Senior Member |
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OK, so I was on much the same telecom three times today and needed to
occupy myself...
This is an example "related" to what you are working on.
Run this as I think its pretty fun.
Download this image:
http://technabob.com/blog/wp-content/uploads/2008/03/apple_l ogo_rainbow_fruit.jpg
then run the following code:
; .run image_registration
read_jpeg, 'apple_logo_rainbow_fruit.jpg', img, /true
tv, img[1, *, *]
size = size(img, /dimen)
cut_size = 50
sub = img[*, 140:190, 300:350]
ans = fltarr(size[1:2])
FOR i = 0UL, size[1]-cut_size-1, 10 DO BEGIN
FOR j = 0UL, size[2]-cut_size-1, 10 DO BEGIN
ans[i, j] = c_correlate(sub, img[*, i:i+cut_size, j:j+cut_size],
0)
tv, sub, i, j, /true
tv, img[1,i:i+cut_size, j:j+cut_size], i, j
ENDFOR
ENDFOR
ind=where(ans eq max(ans))
wheretomulti, ans, ind, col, row
tv, img[1, *, *]
tv, sub, col, row, /true
END
This is fun as it funds just the right place. To be smart one would
iteratively move different numbers of pixels. As I new the answer I
was able to take large steps and get the right answer, but this gave
the same answer taking 1 pixel steps but takes too long.
Cheers,
Brian
------------------------------------------------------------ --------------
Brian Larsen
Boston University
Center for Space Physics
http://people.bu.edu/balarsen/Home/IDL
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| Re: correlation between images [message #66111 is a reply to message #65922] |
Thu, 02 April 2009 10:54 |
Brian Larsen
Messages: 270
Registered: June 2006
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Senior Member |
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> The KS-test (and co.) is another idea. However I'll have to think
> about whether it makes sense. Wouldn't it always pass when the images
> contain the same objects, only in other areas of the image?
Yea, its sure might. I guess that I dont know enough about the images
you are taking about to say for certain. One thought might be to
difference the focal image and one that is the "same" and KS test that
again the difference between the focal and one that is "different".
But maybe I';m way off here...
Cheers,
Brian
------------------------------------------------------------ --------------
Brian Larsen
Boston University
Center for Space Physics
http://people.bu.edu/balarsen/Home/IDL
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| Re: correlation between images [message #66120 is a reply to message #65922] |
Thu, 02 April 2009 07:38 |
Brian Larsen
Messages: 270
Registered: June 2006
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Senior Member |
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Now the details of actually how to do this escape me for now. But a
few ways that come to mind as statistically convincing are:
- compute the cross correlation of the images in chunk showing that
each chuck is cross correlated
- Create a difference image and compare the fluctuation in the
difference to the fluctuations of the image itself or if they are
statistically different from "chunk" to "chunk"
- one might be able to dream about a Kolmogorov–Smirnov test showing
that the distributions of the 2 images are the same, or that the
difference is normal or something like that.
But really I think you are best off beating your head on c_correlate
until it makes sense.
Cheers,
Brian
------------------------------------------------------------ --------------
Brian Larsen
Boston University
Center for Space Physics
http://people.bu.edu/balarsen/Home/IDL
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