Image histogram decomposition method for particle sizing - A numerical simulation study

Scanning probe microscopy is a useful tool in nanoscience. The effective application of nanotechnologies in various fields requires a knowledge of the characteristic attributes of nanoparticles such as shape, dimensions and statistical distribution, and a wide spectrum of experimental and theoretical methods based on various principles have been developed to determine these characteristics. Image histograms offer a global overview of the characteristics of an image. Their shape can encode specific statistical properties of displayed objects such as the distribution function in the case of similar and scalable objects. The model of height histogram presented here proposes a method which solves the long-term problem of processing images of extremely dense particle distributions. The method is based on the principle of the superposition of histograms of individual particles whose topographic surface is described by a parametric model. The resulting height histogram is defined by a convolution of the model of the particle histogram with the distribution function of particle size, with this construction forming the basis of the regression model. The parameters of the distribution function can be obtained via the optimization of the model. The method has been tested on artificially generated configurations of particles of various shapes and size distributions. Each of these configurations creates a topographic surface which is transformed into an image, and the heights obtained from the image allow a histogram to be calculated. Firstly, various configurations of particles are simulated without the presence of any disruptive influences. Next, several experimental effects are evaluated separately (for example, the background, particle shape irregularity and particle overlap). The decomposition of the histogram by the regression model on artificially generated images shows the robustness of the method with respect to particle density, partial horizontal overlap, randomly generated backgrounds and random fluctuations in particle shape. However, the method is sensitive to uniform changes in particle shape, a factor which limits its use to particles with known parametric models of their shape which allow the means of their parameters to be estimated.