How should I apply mathematical correction of the gray levels consisting of subtracting the 2nd degree polynomial that best fits (least square method) the homogeneous (low variance) areas of the gray-level image

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How should I apply mathematical correction of the gray levels consisting of subtracting the 2nd degree polynomial that best fits (least square method) the homogeneous (low variance) areas of the gray-level image

dksamuel
Respected ImageJ users, i read in the paper
Color (and 3D) for Scanning Electron Microscopy, doi:10.1017/12
S1551929518000482

how they had done

applying mathematical correction of the gray levels. This
type of image processing consists of
subtracting the 2nd degree polynomial
that best fits (least square method) the
homogeneous (low variance) areas of
the gray-level image. In the corrected
image, each color represents a different
mineral phase that can yield a quantitative
volume fraction.

How can I do this in ImageJ, I would like to do this work in black and
white Scanning Electron Microscope Images. Thanks, with regards,
Dr.D.K.Samuel, IIHR, Bangalore, India

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Re: How should I apply mathematical correction of the gray levels consisting of subtracting the 2nd degree polynomial that best fits (least square method) the homogeneous (low variance) areas of the gray-level image

Gabriel Landini
On Monday, 14 May 2018 07:53:29 BST you wrote:

> applying mathematical correction of the gray levels. This
> type of image processing consists of
> subtracting the 2nd degree polynomial
> that best fits (least square method) the
> homogeneous (low variance) areas of
> the gray-level image. In the corrected
> image, each color represents a different
> mineral phase that can yield a quantitative
> volume fraction.
>
> How can I do this in ImageJ, I would like to do this work in black and
> white Scanning Electron Microscope Images. Thanks, with regards,

Have a look here. There are some links to polynomial fittings too:

http://imagejdocu.tudor.lu/doku.php?
id=howto:working:how_to_correct_background_illumination_in_brightfield_microscopy

Cheers

Gabriel

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Re: How should I apply mathematical correction of the gray levels consisting of subtracting the 2nd degree polynomial that best fits (least square method) the homogeneous (low variance) areas of the gray-level image

Michael Schmid-3
In reply to this post by dksamuel
Hi Duleep,

first you need a selection of the low-variance areas. Duplicate the
image, use Process>Filters>Variance, smooth it a bit and threshold to
get the low-variance regions. Use Edit>Selection>Create selection and
add it to the ROI manager.

Then you can take the original image, apply the selection from the ROI
Manager (click on it), and use the "Fit Polynomial" plugin to subtract a
polynomial, where the fit is done only in the selected area:
   http://imagejdocu.tudor.lu/doku.php?id=plugin:filter:fit_polynomial:start

All these operation s should be done one floating-point (32-bit) images;
if you have different bit depth, use Image>Type to convert to 32 bits
before starting.

Note that this approach works for a very limited class of images only;
there must be a low-variance phase dominating the image. If you have
e.g. a bright low-variance area at the left and a low-variance area from
a different phase (dark) at the right, it will fail.
I tried with the image in Fig. 1 of the article you have mentioned and
the background crated by this algorithm was not good enough for for
segmentation based on the pixel value. I had to manually select the
areas of the majority phase before running "fit polynomial".
(You can apply 'fit polynomial' several times without losing anything,
so the algorithm might be a first step, then it becomes easier to see
which areas belong to the same physe. Eventually, you will reach a state
where you can threshold the majority phase, create a selection from it,
correct it manually, and run "fit polynomial" again).

One more thing you could try is not subtracting the background but
dividing by it (before duplicate the image before "fit polynomial" and
use it's "Output Fit" option, then use Process>Image Calculator). This
might produce better results than subtracting a background.

Michael
________________________________________________________________
On 14/05/2018 08:53, Duleep Samuel wrote:

> Respected ImageJ users, i read in the paper
> Color (and 3D) for Scanning Electron Microscopy,
> doi: 10.1017/S1551929518000482
>
> how they had done
>
> applying mathematical correction of the gray levels. This
> type of image processing consists of
> subtracting the 2nd degree polynomial
> that best fits (least square method) the
> homogeneous (low variance) areas of
> the gray-level image. In the corrected
> image, each color represents a different
> mineral phase that can yield a quantitative
> volume fraction.
>
> How can I do this in ImageJ, I would like to do this work in black and
> white Scanning Electron Microscope Images. Thanks, with regards,
> Dr.D.K.Samuel, IIHR, Bangalore, India
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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