Refining the position of nanoparticles on an image

First published: 2024-01-27

Last Edited: 2021-10-04

Number of edits: 12

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:

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

Where

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

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

$$\epsilon$$

represents the variation from the previously identified pixel as the likely center of the particle. In principle, if

$$|\epsilon|>0.5$$

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.

Backlinks

These are the other notes that link to this one.

Five stages of colloidal particle tracking

Discriminating particles for tracking analysis

Linking particle positions to form trajectories

Comment

Share your thoughts on this note

Aquiles Carattino

This note you are reading is part of my digital garden. Follow the links to learn more, and remember that these notes evolve over time. After all, this website is not a blog.