PH-of-Images

This repo contains code used in the paper:

T. Heiss, S. Tymochko, B. Story, A Garin, H. Bui, B. Bleile, and V. Robins. The impact of finite resolution on the persistent homology of images. Proceedings of 2021 IEEE International Conference on Big Data, 2021.

• Published Version
• arXiv Version

Code

The following examples (some of which are used in the paper) are:

1. Concentric Rings - Rings.ipynb
2. Disk with Spots - Disk_With_ManySpots-Simple.ipynb (just compute bottleneck distances), Disk_With_ManySpots-wBounds.ipynb (compute bottleneck distances and theoretical bounds for comparison)

The majority of the code is contained in the two .py files:

• generate_examples.py contains code to generate many example images
  • create_circles_image: 2 dimensional disk (of any resolution)
  • make_checkerboard: Chessboard (of any resolution with any number of squares)
  • make_rings_example: three concentric rings example from the paper (of any resolution)
  • create_diskwithspot: A disk with one spot in the middle (fixed resolution of 2048x2048)
  • create_diskwithmanyspots: A disk with many spots (fixed resolution of 2048x2048)
• utils.py contains functions related to:
  • Image processing: Compute DSEDT (discrete signed Euclidean distance transform), binarize an image based on a threshold, downsample using the averaging technique described in our paper
  • TDA: Use giotto-TDA to compute persistent homology and bottleneck distance.

Figures

The Figs folder contains figures used in the paper as well as the same plots with respect to pixel size (where the high resolution image has pixel size=1), rather than resolution.

Citing

If you use code from this repo, please cite our paper for the methodology as:

@InProceedings{Heiss2021,
author={Teresa Heiss and Sarah Tymochko and Brittany Story and Adélie Garin and Hoa Bui and Bea Bleile and Vanessa Robins},
booktitle={2021 IEEE International Conference on Big Data (Big Data)},
title={The Impact of Changes in Resolution on the Persistent Homology of Images},
year={2021},
pages={3824-3834},
doi={10.1109/BigData52589.2021.9671483}
}

Contact

Feel free to contact us with any questions or issues!