Using topology to analyze the shape of barley

Euler meets plant science

Erik Amézquita 1,

Michelle Quigley2 Tim Ophelders1 Elizabeth Munch1 Daniel Chitwood2 Jacob Landis3,4 Daniel Koenig3

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


Experimental Design

  • 28 founders (land races). 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.

SVM Classification Results

Shape descriptors No. descriptors Classification accuracy
Traditional 11 51.9% — 54.2%
Topological (ECT + KPCA) 12 43.2% — 45.7%
Combined (Trad + Topo) 23 69.2% — 71.9%

Acknowledgements

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


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: Traditional + ECT + KPCA

  • SVM to classify 3,000 seeds from the 28 founders
  • (80% training vs 20% testing) \(\times\) 50 times
  • 70% classification accuracy

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.