Quantifying the shape of barley

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# Quantifying the shape of barley
## using Topological Data Analysis
### <strong>Erik Amézquita</strong>, Michelle Quigley, Tim Ophelders <br> Elizabeth Munch, Dan Chitwood <br> Dan Koenig, Jacob Landis <br> -
### Computational Mathematics, Science and Engineering <br> Michigan State University <br> -
### 2021-02-12

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    <a href="https://cereal.interreg-npa.eu/subsites/CEREAL/Barley_cultivation-Norway_Presentation_2018.pdf" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_norway.jpg"></a>
    <a href="https://www.resilience.org/stories/2020-03-09/the-last-crop-before-the-desert/" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_morocco.jpg"></a>
    <a href="https://ipad.fas.usda.gov/highlights/2008/11/eth_25nov2008/" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_ethiopia.gif"></a>
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    <a href="https://kizilvest.ru/20150827-v-kizilskom-rajone-nachalas-uborochnaya-strada/" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_kizilskoye.jpg"></a>
    <a href="https://www.bloomberg.com/news/articles/2020-09-13/iraq-to-offer-first-ever-barley-exports-as-rains-yield-surplus" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_iraq.jpg"></a>
    <a href="https://thewire.in/agriculture/covid-19-lockdown-crop-harvest-farmers" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_rajasthan.jpg"></a>
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    <p style="text-align: center; font-size: 30px; line-height: 1em;"> <strong> Barley across the world </strong></p>
    <p>Tjøtta (Nordland, Norway)</p>
    <p>Kiliskoye (Chelyabinsk, Russia)</p>
    <p>Marchouch (Rabat, Morocco)</p>
    <p>Bagdad (Iraq) </p>
    <p>Aksum (Tigray, Ethiopia) </p>
    <p>Hanumangarh (Rajasthan, India) </p>
    <p style="font-size:9px;line-height: 1em;">Click on any picture for more details and credits</p>
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# Morphological seed diversity of lines

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    <a href="https://www.nationalgeographic.co.uk/travel/2020/05/photo-story-from-barley-fields-to-whisky-barrels-in-rural-scotland" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_seed_scotland.jpg"></a>
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    <a href="https://www.tibettravel.org/tibetan-culture/highland-barley.html" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_seed_tibet.jpg"></a>
    <a href="https://www.doi.org/10.1007/978-1-4419-0465-2_2168" target="_blank"><img style="padding: 0 0 0 0;" src="../figs/barley_historical_expansion.jpg"></a>
    <p style="font-size: 15px; line-height: 1em"> Barley seeds from Scotland and Tibet. </p>
    <p style="font-size: 15px; line-height: 1em"> Historical expansion of the barley as a crop. </p>
    <p style="font-size:9px;line-height: 1em;">Click on any picture for more details and credits</p>
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# Topological Data Analysis (TDA)

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    <img style="padding: 25px 0 35px 0;" src="../figs/S019_L0_1.gif">
    <p style="font-size: 25px; text-align: center; color: DarkRed;"> Raw Data </p>
    <ul>
      <li> X-ray CT </li>
      <li> Point clouds </li>
      <li> Time series </li>
    <ul>
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    <img src="../figs/ecc_X.gif">
    <p style="font-size: 23px; text-align: center; color: DarkRed;"> Topological Summary </p>
    <ul>
      <li> Euler Characteristic </li>
      <li> Persistence diagrams </li>
      <li> Mapper/Reeb graphs </li>
    <ul>
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    <img src="../figs/svm_mds_ect.gif">
    <p style="font-size: 25px; text-align: center; color: DarkRed;"> Analysis </p>
    <ul>
      <li> Statistics </li>
      <li> Machine learning </li>
      <li> Classification/prediction </li>
    <ul>
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# Classification of 28 lines with SVM

<img src="../figs/avg_accuracy_normalized_size_combined_158_8_laplacedot_12_horz_transp.png" width="700" style="display: block; margin: auto;" />
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