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Most experiments study a model 2 dimensional (2D) granular system composed of circular discs as grains. While in cases of studying particle shape effect, discs are replaced by other shapes like ellipses, polygons and crosses \cite{}. With a digital camera, the first and one of the most important information that can be obtained is particle positions and particle orientations. The latter are informative even for circular discs due to existence of inter-particle friction in most experiments. Particle detection and tracking alone provide rich information such as particle configuration and flow field, and are necessary for further measurements like force-bearing contact detection and contact force calculation. In this session, a detailed description for detecting particle positions and orientations and tracking particles in high resolution images will be summarized below. In addition, in images with resolution not high enough to precisely track particles, another method (PIV) will be introduced.
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Position detection and tracking
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* Detection of the particles from white light imaging
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Thresholding
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Circular Hough transform
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Convolution method
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## 1 Position detection and tracking
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* Detection of the particle from UV light imaging
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### 1.1 Detection of the particles from white light imaging
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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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### 1.2 Detection of the particle from UV light imaging
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Though being used most commonly in granular studies, discs are far from grains in reality. Hence there have been numerous studies on granular systems with different shapes other than discs, e.g., ellipses, polygons and star-shape-like particles. Here we choose star particles as an example to illustrate how to detect them from UV light imaging.
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* Tracking
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## 2 Tracking
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### 2.1 Direction measurement
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Direction measurement
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In order to detect particle orientation, we usually put an artificial UV ink bar on the surface of particles.
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* Thresholding
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* Least Squares Fitting for Perpendicular Offsets
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Measurement of the particle flow
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### 2.2 Measurement of the particle flow
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Low resolution imaging does not allow particle detection and finding their positions. However, displacement field of particles can be obtained using [Particle Image Velocimetry (PIV)](https://link.springer.com/article/10.1007/BF00190388). This method, by using correlations between neighboring cells in a coarse-grained grid, can calculate displacement fields between two images. The photo-elastic response images are not accurate enough for PIV. As the intensity of image changes drastically locally, it becomes very noisy for PIV to calculate displacements. To achieve a better precision, one use normal light images (without plorizers)to extract particle's trajectories. Several open-source packages in [Matlab](https://www.mathworks.com/matlabcentral/fileexchange/27659-pivlab-particle-image-velocimetry-piv-tool) or [other programming languages](http://www.openpiv.net/). Figure below shows a sample of PIV technique on unpplarized images. The blue arrows provide the displacement field of the granular medium under shear. The field represents data on a grid, showing mean flow around the points. The grid size chosen here is about the size of smaller particles for better accuracy. This technique can be used to extract local time series and mean flow of particles movements.
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* The trajectories of particles obtained by PIV on unpolarized light images of a sheared granular medium. Blue arrows show the magnitude and direction of displacement field. The top image is an enlarged view of the bottom one:
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