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* Finally, there are two ways to detect particles, depending on the image contrast quality. (1) 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, a convolution is applied between the image and a pre-set disk mold whose diameter is approximately 3/4 of that of the smallest particle. The resulted convoluted image can be binarized by a threshold of 99.5% of the peak convolution value, resulting in a collection of isolated white bulbs. Centers of these bulbs correspond to the centers of particles, and their areas are related to particle diameters, which can be pre-assigned. (2) 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 (only part of the actual image is shown here for visual purpose).
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![Fig_DisksPos](uploads/1f3859809a9b1f5661df534624b4b43d/Fig_DisksPos.png)
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![Fig_DisksPos](uploads/9cf6df8ae5262520547c047bc1826386/Fig_DisksPos.png)
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The convolution method is fast in computation, but requires high contrast image and has low tolerance for light noises inside of particles. By contrast, the circular Hough transform method has high tolerance for light noises inside of particles and are robust for particles that are deformed from a circular shape, however, is computationally expensive.
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