The properties of materials synthesized with nanoparticles (NPs) are highly correlated to the sizes and shapes of the nanoparticles. The transmission electron microscopy (TEM) imaging technique can be used to measure the morphological characteristics of NPs, which can be simple circles or more complex irregular polygons with varying degrees of scales and sizes. A major difficulty in analyzing the TEM images is the overlapping of objects, having different morphological properties with no specific information about the number of objects present. Furthermore, the objects lying along the boundary render automated image analysis much more difficult. To overcome these challenges, we propose a Bayesian method based on the marked-point process representation of the objects. We derive models, both for the marks which parameterize the morphological aspects and the points which determine the location of the objects. The proposed model is an automatic image segmentation and classification procedure, which simultaneously detects the boundaries and classifies the NPs into one of the predetermined shape families. We execute the inference by sampling the posterior distribution using Markov chain Monte Carlo (MCMC) since the posterior is doubly intractable. We apply our novel method to several TEM imaging samples of gold NPs, producing the needed statistical characterization of their morphology.
"Bayesian object classification of gold nanoparticles." Ann. Appl. Stat. 7 (2) 640 - 668, June 2013. https://doi.org/10.1214/12-AOAS616