... | ... | @@ -7,21 +7,18 @@ Most experiments study a model 2 dimensional (2D) granular system composed of ci |
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### 1.1 Detection of the particles (discs) from white light imaging
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For particles of disc shape, a picture with white light transmitted through particles is usually taken to record their positions. The general idea to detect particles then is to . The procedure can be summarized as follows:
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For particles of disc shape, a picture with white light transmitted through particles is usually taken to record their positions. The general idea to detect particles then is to produce a high contrast or a binary image distinguishing between areas occupied by particles and those by background. The procedure can be summarized as follows:
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* From one channel of the white light image, 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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* 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 straight lines caused by the edges of slats, especially for the edges passing through particles in the image. Fig.~\ref{fig-diskpos}(b) shows the result after enhancing the contrast and removing lines inside of the particles.
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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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* 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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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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#### 1.1.1 Thresholding
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#### 1.1.2 Circular Hough transform
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#### 1.1.3 Convolution method
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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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### 1.2 Detection of the particles from UV light imaging
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