  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.
