Companion Repository for "Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform"

This is a small list of additional resources for the Euler Characteristic Transform. Please also check out the repository for some sample code. Notice that the examples have been provided with a primary focus on being instructive as opposed to being highly optimized.

Examples

• ect.py: A script for calculating the ECT of meshes, i.e., two-dimensional simplicial complexes. This file was used to create all visualizations in the paper.

• ect_image.py: Renders the output of the script above as an image.

The two scripts are supposed to work in tandem like this:

# Create the ECT of a given mesh (not supplied for licencing reasons)
# using multiple directions and visualize it.
$ python ect.py /tmp/ncc-1701-d.stl > /tmp/ECT.txt
$ python ect_image.py --normalize /tmp/ECT.txt

The ect.py also affords several other creation strategies:

# Create the ECT of a given mesh (not supplied for licencing reasons)
# using a specific direction (x-axis).
$ python ect.py /tmp/ncc-1701-d.stl -d "1,0,0" -e /tmp/x.ply > /tmp/x.txt

Papers

The ECT or its variants has been used in a variety of different applications. Here are some examples (feel free to add more by opening a PR or issue in this repository):

• An Invitation to the Euler Characteristic Transform
• Differentiable Euler Characteristic Transforms for Shape Classification
• Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms
• Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis

Software

• ect
• DECT