Refining the position of nanoparticles on an image
After locating particles for nanoparticle tracking using gray dilation, we will end up with a lot of false positives (for example, single-pixel noise). In @crocker1996Methods of Digital Video Microscopy for Colloidal Studies they propose calculating the centroid around one of those pixels by performing the following computation:
The equations above are the common centroid calculation in a region. That is why it is important to subtract the background appropriately as done in image restoration for nanoparticle tracking or there would be a bias towards the brighter regions of the image.
Bear in mind that
It is important to note that @crocker1996Methods of Digital Video Microscopy for Colloidal Studies was written before the onset of single-molecule localization microscopy, and therefore the approach may be slightly extemporaneous to today’s approach, but nonetheless valid.
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