Subrata Kundu | Searcharxiv

arXiv2019

The Statistical Face of a Region under Monsoon Rainfall in Eastern India

A region under rainfall is a contiguous spatial area receiving positive precipitation at a particular time. The probabilistic behavior of such a region is an issue of interest in meteorological studies. A region under rainfall can be viewed as a shape object of a special kind, where scale and rotational invariance are not necessarily desirable attributes of a mathematical representation. For modeling variation in objects of this type, we propose an approximation of the boundary that can be represented as a real valued function, and arrive at further approximation through functional principal component analysis, after suitable adjustment for asymmetry and incompleteness in the data. The analysis of an open access satellite data set on monsoon precipitation over Eastern India leads to explanation of most of the variation in shapes of the regions under rainfall through a handful of interpretable functions that can be further approximated parametrically. The most important aspect of shape is found to be the size followed by contraction/elongation, mostly along two pairs of orthogonal axes. The different modes of variation are remarkably stable across calendar years and across different thresholds for minimum size of the region.

stat.AP↗

arXiv2013

Bayesian object classification of gold nanoparticles

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.

stat.AP↗