Using topology to analyze the shape of barley

Euler meets plant science

Erik Amézquita 1,

Michelle Quigley2 Tim Ophelders1 Elizabeth Munch1 Daniel Chitwood2 Daniel Koenig3 Jacob Landis3

1 Computational Math, Science & Engineering, Michigan State University
2 Horticulture, Michigan State University
3 Botany and Plant Sciences, University of California, Riverside


Experimental Design

  • Composite cross. 28 founders. 58 generations.

Image processing to measure seeds

  • 3D X-ray CT scan data: 875 barley spikes.
  • 38,000 seeds: generations F0, F18, and F58.
  • Distribution of length, height, width, volume, etc.

Acknowledgements

This work is supported in part by Michigan State University and the National Science Foundation Research Traineeship Program (DGE-1828149).

References

[1] K. Turner, S. Mukherjee, and D. M. Boyer, “Persistent homology transform for modeling shapes and surfaces,” Information and Inference, vol. 3, no. 4, pp. 310–344, Dec. 2014.


Euler characteristic transform (ECT)

\[\chi = \#(\text{Vertices}) - \#(\text{Edges}) + \#(\text{Faces})\]

  • ECT is the record of how the EC changes as we reconstruct a given object in all possible directions.
  • The ECT summarizes all shape information [1].

SVM Results: Traditional + ECT

  • SVM to classify the seeds from the 28 founders
  • (80% training vs 20% testing) \(\times\) 50 times
  • 66% classification accuracy