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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 \cite{peng07jcise}. 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. The final result of particle identification is shown in Fig.~\ref{fig-diskpos}(c), where blue circles indicate particle centers and radii given by the algorithm with errors smaller than $0.02$ times the particle diameter.
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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/6491e90d5a82e94667fa462d1b6d5f9a/Fig_DisksPos.png)
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![Fig_DisksPos](uploads/fa70a6add46ab4038df159167cede62e/Fig_DisksPos.png)
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#### 1.1.1 Thresholding
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