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* From one channel of the white light image that has the highest contrast between particles and background, a mapping of the intensities to new values by suppressing low and high intensities is employed to increase the contrast of the image.
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* Then a low-pass filter is applied to the Fourier transform of the image to remove noises or default impurities by setup from the background.
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* Then a low-pass filter is applied to the Fourier transform of the image to remove noises or default impurities by setup from the background and increase contrast.
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* Finally a circular Hough transform is applied to the gray scale image in Fig.~\ref{fig-diskpos}(b) to find centers and diameters of the discs. The transform is an algorithm computing the curvature at each pixel point based on the image gray scale gradient. The curvature will automatically give the center and radius. Then a voting process rules out fake circles and combines circles with close enough centers and similar radii.
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* Finally, if it is possible to binarize the image (1 for particles and 0 for background), then a convolution method is recommended. There are several methods to binarize an image: [imbinarize function in Matlab with a fixed threshold](https://www.mathworks.com/help/images/ref/imbinarize.html), [adaptive thresholding](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.420.7883&rep=rep1&type=pdf), and [otsu method](https://ieeexplore.ieee.org/document/4310076). After image binarization, . If it is too difficult to binarize the image, a circular Hough transform is recommended to be applied to the gray scale image to find centers and diameters of the discs. The circular Hough transform is an algorithm computing the curvature at each pixel point based on the image gray scale gradient. The curvature will automatically give the center and radius. Then a voting process rules out fake circles and combines circles with close enough centers and similar radii.
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The procedure described above with results at each step is illustrated in the figure below.
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![Fig_DisksPos](uploads/fa70a6add46ab4038df159167cede62e/Fig_DisksPos.png)
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