# Statistical Inference for Porous Materials using Persistent Homology.

## Abstract

We propose a porous materials analysis pipeline using persistent homology. We rst compute persistent homology of binarized 3D images of sampled material subvolumes. For each image we compute sets of homology intervals, which are represented as summary graphics called persistence diagrams. We convert persistence diagrams into image vectors in order to analyze the similarity of the homology of the material images using the mature tools for image analysis. Each image is treated as a vector and we compute its principal components to extract features. We t a statistical model using the loadings of principal components to estimate material porosity, permeability, anisotropy, and tortuosity. We also propose an adaptive version of the structural similarity index (SSIM), a similarity metric for images, as a measure to determine the statistical representative elementary volumes (sREV) for persistence homology. Thus we provide a capability for making a statistical inference of the uid ow and transport properties of porous materials based on their geometry and connectivity.

- Authors:

- Univ. of Georgia, Athens, GA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1414662

- Report Number(s):
- SAND-2017-13586R

659552

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE

### Citation Formats

```
Moon, Chul, Heath, Jason E., and Mitchell, Scott A..
```*Statistical Inference for Porous Materials using Persistent Homology.*. United States: N. p., 2017.
Web. doi:10.2172/1414662.

```
Moon, Chul, Heath, Jason E., & Mitchell, Scott A..
```*Statistical Inference for Porous Materials using Persistent Homology.*. United States. doi:10.2172/1414662.

```
Moon, Chul, Heath, Jason E., and Mitchell, Scott A.. Fri .
"Statistical Inference for Porous Materials using Persistent Homology.". United States.
doi:10.2172/1414662. https://www.osti.gov/servlets/purl/1414662.
```

```
@article{osti_1414662,
```

title = {Statistical Inference for Porous Materials using Persistent Homology.},

author = {Moon, Chul and Heath, Jason E. and Mitchell, Scott A.},

abstractNote = {We propose a porous materials analysis pipeline using persistent homology. We rst compute persistent homology of binarized 3D images of sampled material subvolumes. For each image we compute sets of homology intervals, which are represented as summary graphics called persistence diagrams. We convert persistence diagrams into image vectors in order to analyze the similarity of the homology of the material images using the mature tools for image analysis. Each image is treated as a vector and we compute its principal components to extract features. We t a statistical model using the loadings of principal components to estimate material porosity, permeability, anisotropy, and tortuosity. We also propose an adaptive version of the structural similarity index (SSIM), a similarity metric for images, as a measure to determine the statistical representative elementary volumes (sREV) for persistence homology. Thus we provide a capability for making a statistical inference of the uid ow and transport properties of porous materials based on their geometry and connectivity.},

doi = {10.2172/1414662},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Dec 01 00:00:00 EST 2017},

month = {Fri Dec 01 00:00:00 EST 2017}

}