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# Tracking individual particles over several frames

One of the characteristics of our measurements on the Faraday experiment is that is is a closed system, in the sense that the mushroom spores never leave our field of view, and we therefore should be able to track the particles for as long as we like. The average density of particles (1 particle per ) is so low, compared to the typical distance that a particle travels between two images (approximately at low amplitudes), that there is little or no reason to doubt which particle is which in the next image.

The principle in this algorithm is to locate all particles in the frames in question, and then identifying the sets of positions that are the most probable particle tracks - one position in each image for each track. It is very important to be aware that the definition of what kind of tracks are most probable can influence which tracks are detected by the algorithm. The two definitions of the probability of a track have worked with, are minimal acceleration and minimal velocity. The latter of these favours Brownian motion-like tracks , whereas the former favours ballistic tracks . Both assumptions were tried on some of the data, and there was no significant difference in the results obtained in the two cases. The steps in the algorithm are listed in figure 4.1.

If you want to improve the detection of tracks, you could use the particle size, measured as total area or total intensity, to identify particles (if you work with particles of different sizes).

The optimal algorithm for locating all clusters of pixels in an image, where you have separated the pixels in two classes, can be found in  [17]. Each cluster of neighbouring pixels with an intensity above the threshold is considered to be one particle. This means that if two particles happen to get so close together that they form one cluster of pixels on the image, they will be processed as one particle.

Figure 4.1: Algorithm for composing particle tracks from sequences of particle positions.

The expected position can be derived from the velocity (equivalent to minimal acceleration), or just be identical to the position from the previous frame (equivalent to minimal velocity).

This algorithm worked quite well for the Faraday experiment with certain limitations.

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