Refining the position of nanoparticles on an image

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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:

$$\begin{pmatrix}\epsilon_x \ \ \epsilon_y \end{pmatrix}=\frac{1}{m_0}\sum_{i^2+j^2\le w^2}\begin{pmatrix}i\ j\end{pmatrix}A(x+i, y+j)$$


$$m_0 = \sum_{i^2+j^2\le w^2} A(x+i, y+j)$$

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

represents the variation from the previously identified pixel as the likely center of the particle. In principle, if
then we should move the likely candidate to a new region and recalculate the position.

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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Aquiles Carattino
Aquiles Carattino
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