1, 2, 3 – counting and sizing particles
One of the most frequent image analysis tasks that I am asked to do involves some kind of measurements on particles or pores: counting them, sizing them, measuring their orientation and shape, figuring out the distance between particles, and even separating conjoined particles. Sometimes you need to measure actual particles, but particles can be defined loosely - maybe you really want to be analyzing domain sizes of a particular component, which can easily be done with particle analysis software. In any case the proper particle analysis capability will enable you to measure important properties including their density, dimensions, and dispersion.
The key part in a successful particle analysis is having a mechanism to separate out the particles from your background. Probably the most common detection method – and the one I use most often – is a threshold based method where there is image contrast between your particles and the samples. See for example below where I have imaged a rubber sample with silica nanoparticles with AFM.
The height channel is on the right and the phase channel, which is collected simultaneously, is on the left. I also included a histogram below each image. The histogram bins the number of pixels of a particle z value in the image in the specified bin size. So you can see that the x axis for the histogram on the left is in units of height (nm) while the x axis on the histogram on the right is in units of degrees of phase angle. The histograms give us a very quick and easy way to observe the distribution of z values in your image.
We can easily observe that there is a single peak in the height image histogram (left) while the phase image histogram shows 2 peaks. That is because the particles in the phase image (dark) are easily differentiated from their background. Although we can make out by eye the little bright particles in the height image that are the ones we want to make measurements on, we have no way of thresholding them out from the background rubber material. Fortunately, the phase image is suitable for thresholding, and so below you can see in below where I have thresholded in blue the particles on the histogram and the corresponding phase image.
There are other algorithms for selecting out particles from the background including a watershed algorithm, which is designed for height data and requires clear grain boundaries. It can detect particles such as the one below.
There is even morphology based detection where algorithms look for a particle shape (e.g. a circle).
The final aspect of particle counting that I want to comment on is recent advances in algorithms that can separate out conjoined particles. So for my silica nanoparticles in the above images, if I just thresholded out the particles and had the software calculate the particles, I would get an image where each “particle” is colored by a different color. You can see that the software is able to distinguish actually very few individual particles and mostly finds particle aggregates since the particles are joined.
By implementing a “shrinking and expanding” algorithm that shrinks each aggregate a prescribed amount to check if multiple particles are composing the aggregate, I can achieve a much more successful particle identification.
And now for each particle, the software can calculate a host of parameters and associated statistics related to the various dimensions, shape, orientation, and proximity of the particles. All the image analysis I have shown here has been done with SPIP Image Metrology, a powerful third party software designed for processing and analysis of all microscopy images including AFM, SEM, and TEM. It has a very easy-to-use interface and among the most powerful particle analysis capabilities available.
Dalia Yablon, Ph.D.