| color value interpolation from colorbar [message #64128] |
Thu, 04 December 2008 09:27  |
j.coenia@gmail.com
Messages: 36
Registered: December 2008
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Member |
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Hi,
I have a color-coded medical image.
There is a colorbar on the image, for example a red-to-yellow gradient
valued from 1 to 100.
There is *not* a one-to-one correspondence between the colors in the
colorbar and the colors in the image. There are many more
intermediate reds, oranges, and yellows in the image than in the
colorbar.
What is the correct way to interpolate gradient values to all the
unknown image colors from the discrete colors/gradients defined in the
colorbar?
(The documentation for INTERPOL and INTERPOLATE has not helped me so
far.)
Thanks
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| Re: color value interpolation from colorbar [message #64202 is a reply to message #64128] |
Sat, 06 December 2008 04:44  |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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On Dec 5, 10:50 am, "j.coe...@gmail.com" <j.coe...@gmail.com> wrote:
> I fixed the RGB plot and uploaded it to Picasa:
>
> http://picasaweb.google.com/j.coenia/ColorInterpolation?auth key=H9iPr...
>
> I will look into how the images were made. The colors were
> automatically overlaid on the images by the scanning equipment. Maybe
> I will have to contact the manufacturers.
>
> Someone has given me a brute force HSV color matching function. There
> is no curve fitting involved, but it seems promising. The text below
> is from the header notes:
>
> ; The input colors (sampled from the colorbar) are broken into blocks
> every n colors, and
> ; the extremes of H, S, and V are used to define a cube. All
> possible HSV-tuples
> ; within the cube are selected that correspond to possible colors in
> RGB space, which can
> ; optionally be reduced by a compression factor. The function
> returns a 3xn array of
> ; rgb triples corresponding to the INTERPOLATED colors in the reduced
> rgb colorspace
> ; (num of colors = (256/compression)^3 ).
>
> I'll post the results from this function soon, and I'll try to
> implement Peter's more elegant approach (next week?).
>
> Thanks again.
Looking at the new version, I think the R and G curves are broken
lines, not single curves, in which case I'm not sure how well the
methods that try to fit them to single functions (either polynomials,
like Peter said, or power laws like Paolo suggested) will work. Maybe
you could split the image points by intensity and do the linear method
using either the lower part or the upper part separately, but you
might well get artifacts for colours around the break point.
The good news is, if they really are broken lines then you can make a
huge simplification to my algorithm - instead of using the entire
colour bar, you can reduce it to 3 points: the bottom point, the break
point, and the top point.
-Jeremy.
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| Re: color value interpolation from colorbar [message #64209 is a reply to message #64128] |
Fri, 05 December 2008 07:17 |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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I would fit a*x^b for red and blue and c+dx for blue.
Ciao,
Paolo
Jeremy Bailin wrote:
> On Dec 4, 9:35�pm, "j.coe...@gmail.com" <j.coe...@gmail.com> wrote:
>> Thanks everyone. �Sorry for the delay, I had to generate the requested
>> pics and create a Picasa web album. �If there is a better way to post
>> images to usenet forums, please let me know.
>>
>> Below is the Picasa link to the two images requested by Vince and
>> Paolo, (1) an example frame grab of a scan, and (2) its colorbar RGB
>> plotted against colorbar location:
>>
>> http://picasaweb.google.com/j.coenia/ColorInterpolation?auth key=H9iPr...
>>
>> To answer Jeremy's question, the colorbar length is 140 pixels or so
>> (scaled here from 1 to 100 on the x axis, which is vertical in the
>> scan). �You can see from the plot that the colorbar sampling is
>> "garbagy." �There are two very bright artifacts, at approximately x=20
>> and x=80. �Such outliers can be tossed or smoothed out somehow I
>> think. �For simplicity, I just sampled the values down the vertical
>> center of the colorbar, as the colorbar tends to bleed a little into
>> the dark background near the edges (more errors).
>>
>> Jeremy's answer makes some sense to me. �So is it possible to
>> reasonably guess the color levels in that artery using the colorbar on
>> the side of the scan? �I know there is no scale on the colorbar --
>> I've been instructed to assume linear gradient from 1 to 100.
>> Radiologists and researchers use these colors; can the computer
>> quantify them to extract more meaningful information?
>>
>> Thanks again.
>
> I think that your colour bar is sampled well enough for the approach I
> suggested to work. You'll need to smooth out your R,G,B curves first,
> though - I would first use Peter's suggestion of taking the mean over
> a few columns within the colour bar, and then I'd pass it through a
> median filter to get rid of the artifacts and further smooth it.
>
> I quite like Peter's approach, actually - assuming that the curves can
> be fit to a sufficiently low-order polynomial, which you'll have to
> check. It should be a lot faster, and is definitely more elegant! The
> approach I suggested should work pretty generically for any bizarre
> colour table, but yours looks it would be reasonably well-behaved once
> smoothed.
>
> -Jeremy.
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| Re: color value interpolation from colorbar [message #64210 is a reply to message #64128] |
Fri, 05 December 2008 06:36 |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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On Dec 4, 9:35 pm, "j.coe...@gmail.com" <j.coe...@gmail.com> wrote:
> Thanks everyone. Sorry for the delay, I had to generate the requested
> pics and create a Picasa web album. If there is a better way to post
> images to usenet forums, please let me know.
>
> Below is the Picasa link to the two images requested by Vince and
> Paolo, (1) an example frame grab of a scan, and (2) its colorbar RGB
> plotted against colorbar location:
>
> http://picasaweb.google.com/j.coenia/ColorInterpolation?auth key=H9iPr...
>
> To answer Jeremy's question, the colorbar length is 140 pixels or so
> (scaled here from 1 to 100 on the x axis, which is vertical in the
> scan). You can see from the plot that the colorbar sampling is
> "garbagy." There are two very bright artifacts, at approximately x=20
> and x=80. Such outliers can be tossed or smoothed out somehow I
> think. For simplicity, I just sampled the values down the vertical
> center of the colorbar, as the colorbar tends to bleed a little into
> the dark background near the edges (more errors).
>
> Jeremy's answer makes some sense to me. So is it possible to
> reasonably guess the color levels in that artery using the colorbar on
> the side of the scan? I know there is no scale on the colorbar --
> I've been instructed to assume linear gradient from 1 to 100.
> Radiologists and researchers use these colors; can the computer
> quantify them to extract more meaningful information?
>
> Thanks again.
I think that your colour bar is sampled well enough for the approach I
suggested to work. You'll need to smooth out your R,G,B curves first,
though - I would first use Peter's suggestion of taking the mean over
a few columns within the colour bar, and then I'd pass it through a
median filter to get rid of the artifacts and further smooth it.
I quite like Peter's approach, actually - assuming that the curves can
be fit to a sufficiently low-order polynomial, which you'll have to
check. It should be a lot faster, and is definitely more elegant! The
approach I suggested should work pretty generically for any bizarre
colour table, but yours looks it would be reasonably well-behaved once
smoothed.
-Jeremy.
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| Re: color value interpolation from colorbar [message #64212 is a reply to message #64128] |
Thu, 04 December 2008 20:31 |
Peter Mason
Messages: 145
Registered: June 1996
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Senior Member |
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j.coenia@gmail.com wrote:
> Thanks everyone. Sorry for the delay, I had to generate the requested
> pics and create a Picasa web album. If there is a better way to post
> images to usenet forums, please let me know.
>
> Below is the Picasa link to the two images requested by Vince and
> Paolo, (1) an example frame grab of a scan, and (2) its colorbar RGB
> plotted against colorbar location:
>
> http://picasaweb.google.com/j.coenia/ColorInterpolation?auth key=H9iPrIqxX1c#
>
> To answer Jeremy's question, the colorbar length is 140 pixels or so
> (scaled here from 1 to 100 on the x axis, which is vertical in the
> scan). You can see from the plot that the colorbar sampling is
> "garbagy." There are two very bright artifacts, at approximately x=20
> and x=80. Such outliers can be tossed or smoothed out somehow I
> think. For simplicity, I just sampled the values down the vertical
> center of the colorbar, as the colorbar tends to bleed a little into
> the dark background near the edges (more errors).
>
> Jeremy's answer makes some sense to me. So is it possible to
> reasonably guess the color levels in that artery using the colorbar on
> the side of the scan? I know there is no scale on the colorbar --
> I've been instructed to assume linear gradient from 1 to 100.
> Radiologists and researchers use these colors; can the computer
> quantify them to extract more meaningful information?
Whoever made these images in the first place must have had a system, surely?
But who knows what might have happened in between printing and digitising.
For the plots, did you take a single column of colourbar pixels or did you
average across some of its width? (Averaging, median-filtering or
something like that would clean up some of the noise.)
So anyway the objective is to find a function that maps image_colour to
data_value. Judging from the plot, blue is sort-of linear while red and
green look like the're through some gamma. Along the lines of
R_now=R_orig^0.9 and G_now=G_orig^1.1 (for example). Yuk.
A brute-force solution is to use SVD, for example, to fit a polynomial to
this lot and map it to your data values. Divide your 140-element
colourbar-derived R, G, B arrays by 255.0 and try something like this.
(This has x^2 and x^3 terms for R and G to try to map some curvature.
Maybe you don't need the x^3 terms. Maybe you need more. Maybe you need
a higher term for blue too. I haven't tried this out.)
A=fltarr(8,140)
A[0,*]=1
A[1,*]=R & A[2,*]=G & A[3,*]=B
A[4,*]=R*R & A[5,*]=G*G
A[6,*]=R*R*R & A[7,*]=G*G*G
SVDC, A, W, U, V
CF=SVSOL( U, W, V, (findgen(140)+1.0)/1.4 )
(I might have columns and rows mixed up here. I'm only human.)
CF will have coefficients that you can use to get a data value given some
image pixel's RGB. Get the image pixel's R,G,B, divide by 255, and
calculate image_data_value=CF[0] + CF[1]*R + CF[2]*G + CF[3]*B + CF[4]*R*R +
CF[5]*G*G + CF[6]*R*R*R + CF[7]*G*G*G.
RGB isn't a great colour space for colour matching work and you might have
better luck converting to some form of HSV (hue-saturation-intensity) for
this modelling. You can use IDL's COLOR_CONVERT for this. (Watch out for
wrapping hues. Shouldn't be a problem for red-to-yellow hues as you can
clip any hue above 330, say, to 0.) You might get away with just using
intensity and saturation in this dataset (with a stronger weight on
intensity), or perhaps intensity alone, as long as you know that you will
only query the data values of the coloured bits of imagery (which is an
obvious constraint whatever you do). If you can work with intensity alone
then it'll make the modelling much simpler.
I hope this helps
Cheers
Peter Mason
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| Re: color value interpolation from colorbar [message #64214 is a reply to message #64128] |
Thu, 04 December 2008 18:35 |
j.coenia@gmail.com
Messages: 36
Registered: December 2008
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Member |
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Thanks everyone. Sorry for the delay, I had to generate the requested
pics and create a Picasa web album. If there is a better way to post
images to usenet forums, please let me know.
Below is the Picasa link to the two images requested by Vince and
Paolo, (1) an example frame grab of a scan, and (2) its colorbar RGB
plotted against colorbar location:
http://picasaweb.google.com/j.coenia/ColorInterpolation?auth key=H9iPrIqxX1c#
To answer Jeremy's question, the colorbar length is 140 pixels or so
(scaled here from 1 to 100 on the x axis, which is vertical in the
scan). You can see from the plot that the colorbar sampling is
"garbagy." There are two very bright artifacts, at approximately x=20
and x=80. Such outliers can be tossed or smoothed out somehow I
think. For simplicity, I just sampled the values down the vertical
center of the colorbar, as the colorbar tends to bleed a little into
the dark background near the edges (more errors).
Jeremy's answer makes some sense to me. So is it possible to
reasonably guess the color levels in that artery using the colorbar on
the side of the scan? I know there is no scale on the colorbar --
I've been instructed to assume linear gradient from 1 to 100.
Radiologists and researchers use these colors; can the computer
quantify them to extract more meaningful information?
Thanks again.
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| Re: color value interpolation from colorbar [message #64218 is a reply to message #64128] |
Thu, 04 December 2008 17:00 |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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On Dec 4, 4:35 pm, Paolo <pgri...@gmail.com> wrote:
> So your first step is to "digitize" the color bar:
>
> Create 3 arrays of r,g,b with the colors as a function of pixel size
> and an array x of the pixel index number.
>
> Then, show us a plot of r(x), g(x), b(x)
>
> Ciao,
> Paolo
>
> j.coe...@gmail.com wrote:
>> Thanks. The red-to-yellow colorbar is already on the image -- I don't
>> create it. The map of gradient values to the 3D colorspace would have
>> to be determined from this colorbar, which also has errors in it
>> (garbage in, as Dr. Fanning says.) I suppose this would be an
>> irregular grid of gradient values within the 3D colorspace.
>
>> Basically, there's a color-coded image with a colorbar *on* the
>> image. The colors, even those in the bar, often have errors because
>> they were digitized from analog tape recordings. Still, it is
>> possible to eyeball the images to determine color levels. I want the
>> computer to do something more quantitative than the eyeball analysis.
>
>
How many points do you have on the colour bar? If it's sampled finely
enough, it might be okay to assume a straight line through RGB space
between them. Then you could calculate the minimum distance of any
desired colour from each of those interpolated segments in RGB space
to find the closest segment, and then use its component in the
direction of the segment.
That's only going to work if the input isn't too garbagy - you'll need
points on the colour bar that sample the gradiant quite finely, and
the colours on the image can't be too distant in RGB space from the
locus that the colour bar defines. But if those conditions are met,
this might work.
I'm imagining something like this. You have cbar_r, cbar_g and cbar_b,
each of which contain nbar points and represent data values cbar_data.
To find the best data value for a pixel with colour image_r, image_g
and image_b (untested and unwieldy - can easily be vectorized to work
on the image at once, but I'm too hungry):
; find the closest colourbar point
cbardist2 = (cbar_r-image_r)^2 + (cbar_g-image_g)^2 + (cbar_b-image_b)
^2
cbarmin = min(cbardist2, segment1)
case segment1 of
0: segment2=1
nbar-1: segment2=nbar-2
else: segment2 = (cbardist2[segment1-1] gt cbardist2[segment1+1) ?
(segment1+1) $
: (segment1-1)
endcase
; find component along the segment
from1toi = [image_r-cbar_r[segment1],image_g-cbar_b[segment1],image_b-
cbar_b[segment1]]
from1to2 = [cbar_r[segment2]-cbar_r[segment1],cbar_g[segment2]-cbar_g
[segment1], $
cbar_b[segment2]-cbar_b[segment1]]
projcomp = total(from1toi * from1to2) / (norm(from1to2) * norm
(from1toi))
; interpolate data value
imagedata = cbar_data[segment1]*(1.-projcomp) + cbar_data[segment2]
*projcomp
-Jeremy.
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| Re: color value interpolation from colorbar [message #64311 is a reply to message #64200] |
Mon, 15 December 2008 19:49 |
j.coenia@gmail.com
Messages: 36
Registered: December 2008
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Member |
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I finally posted the results from the HSV color interpolation function
that was supplied to me. I used the colors it found to recolor the
images from red to yellow, instead of the original black-red-yellow,
which was harder to see. These colors were extruded according to
their interpolated gradient values to produce an animation that I
uploaded to Picasa:
http://picasaweb.google.com/j.coenia/ColorInterpolation?auth key=H9iPrIqxX1c#
I think now that this inefficient HSV interpolation function is not
necessary. As Dr. Fanning says, if the images were generated
correctly by the scanner, then originally the colorbar on them should
contain all the image colors. There are more colors (errors) in this
problem because these images are digitized frame grabs from a session
recorded to videotape from an analog source, but the colors should
still be close enough to extract something meaningful.
It might be preferable to just sample the colorbar; find all the
colors in the image; calculate how close the image colors are to the
colorbar colors (in HSV?); then assign corresponding values to the
image colors if they are closer to the nearest colorbar color than
some threshold. This is similar to what was originally proposed by
Jeremy Bailin, although not as elegant as the later fitting methods
described in this thread. There is even the
IDLgrPalette::NearestColor method that will find the nearest color for
you if supplied with both the sampled colorbar and the image color to
match, although I don’t know exactly how it finds the nearest color.
Thanks all.
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