Using topology to analyze the shape of barley

10.1093/insilicoplants/diab033

Euler meets plant biology

Erik Amézquita 1,

Michelle Quigley2 Tim Ophelders3 Elizabeth Munch1 Daniel Chitwood2 Jacob Landis4 Daniel Koenig5

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


Barley 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 # descr F1 Score
Traditional 11 0.55 ± 0.019
Topological (ECT + UMAP) 12 0.74 ± 0.016
Combined (Trad + Topo) 23 0.86 ± 0.010
  • SVM to classify 3,000 seeds from the 28 founders
  • (75% training vs 25% testing) \(\times\) 50 times
  • Up to 84% classification accuracy

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 [2].

Semi-supervised learning

  • Train with 100% of the founder seeds
  • Classify 6000 unlabeled seeds from F58
  • Three morphologies are enriched through time.
  • Similar conclusion with genomic analysis!

References

[1] EJA, M. Quigley, T. Ophelders, J. Landis, D. Koenig, E. Munch, D. Chitwood (2022) "Measuring hidden phenotype: quantifying the shape of barley seeds using the Euler characteristic transform," in silico Plants, 4(1) diab033

[2] K. Turner, S. Mukherjee, D. M. Boyer (2014) "Persistent homology transform for modeling shapes and surfaces," Information and Inference, 3(4) 310–344.