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\begin{document}

\title{ROBUST METRICS OF CONNECTIVITY}



\author[1,1]{Yaokun Wu}%
\author[1,1]{Siddharth Misra}%
\author[1,1]{Rui Liu}%
\affil[1]{Texas A\&M University}%


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  \date{May 18, 2024}


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\begin{abstract}
Connectivity of material constituents govern the transport, mechanical,
chemical, thermal, and electromagnetic properties. Energy storage,
recovery and conversion depends on connectivity of material
constituents. High-resolution microscopy image of a material captures
the microstructural aspects describing the distribution, topology and
morphology of various material constituents. In this study, six metrics
are developed and tested for quantifying the connectivity of material
constituents as captured in the high-resolution microscopy images. The
six metrics are as follows: geobody connectivity metric based on
percolation theory, Euler number based on integral geometry, indicator
variogram based on geostatistics, two-point cluster function,
connectivity function, and travel-time histogram based on fast marching
method. The performances of these metrics are tested on 3000 images
representing six levels of connectivity. The metrics are also evaluated
on the organic constituent captured in the scanning electron microscopy
(SEM) images of organic-rich shale samples. The connectivity function
and travel-time histogram based on fast-marching method are the most
robust and reliable metrics. Material constituents exhibiting high
connectivity result in large values of average travel time computed
using fast-marching method and average connected distance computed using
connectivity function. The proposed metrics will standardize and
speed-up the analysis of connectivity to facilitate the characterization
of properties and processes of energy-relevant materials.%
\end{abstract}%



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