Quantifying the shape of plants

class: center, middle, inverse, title-slide

.title[
# Quantifying the shape of plants
]
.subtitle[
## using Topological Data Analysis
]
.author[
### <strong>Erik Amézquita</strong>, Michelle Quigley, Tim Ophelders <br> Elizabeth Munch, Dan Chitwood <br> Dan Koenig, Jacob Landis <br> -
]
.institute[
### Computational Mathematics, Science and Engineering <br> Michigan State University <br> -
]
.date[
### 2021-07-23<br>-<br>Animated poster available: <code>bit.ly/eccb21_tda</code>
]

---

# Topological Data Analysis

<div class="row">
  <div class="column" style="max-width:25%; font-size: 15px;">
    <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>
  </div>
</div>

---

# Topological Data Analysis

<div class="row">
  <div class="column" style="max-width:25%; font-size: 15px;">
    <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>
  </div>
  <div class="column" style="max-width:40%; padding: 0 25px 0 25px; font-size: 15px;">
    <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>
  </div>
</div>

---

# Topological Data Analysis

<div class="row">
  <div class="column" style="max-width:25%; font-size: 15px;">
    <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>
  </div>
  <div class="column" style="max-width:40%; padding: 0 25px 0 25px; font-size: 15px;">
    <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>
  </div>
  <div class="column" style="max-width:35%; font-size: 15px;">
    <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>
  </div>
</div>

---

# Cross Composite II experiment

.pull-right[
![](../figs/composite_hybrid_mixture.jpg)
]

---

# Cross Composite II experiment

.pull-left[

![](../figs/barley_world.jpg)
- **28 parents/accessions** `\((F_0)\)`
]

.pull-right[
![](../figs/composite_hybrid_mixture.jpg)
]

---

background-image: url("../figs/composite_cross_v_05.svg")
background-size: 400px
background-position: 95% 90%

# Cross Composite II experiment

.pull-left[

![](../figs/barley_world.jpg)

- **28 parents/accessions** `\((F_0)\)`

- Do `\({28 \choose 2}\)` **hybrids** `\((F_1)\)`

- **Self-fertilize** the resulting 379 hybrids `\((F_2\to F_{58})\)`
]

.pull-right[
![](../figs/composite_hybrid_mixture.jpg)
]

---

# Raw Data: X-rays &rarr; Image Processing

<div class="row">
  <div class="column" style="max-width:51%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/x3000_setup.jpg">
    <p style="text-align: center;"> Proprietary X-Ray CT scan reconstruction </p>
  </div>
</div>

---

# Raw Data: X-rays &rarr; Image Processing

<div class="row">
  <div class="column" style="max-width:51%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/x3000_setup.jpg">
    <p style="text-align: center;"> Proprietary X-Ray CT scan reconstruction </p>
  </div>
  <div class="column" style="max-width:17.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S019_L0_1.gif">
    <p style="text-align: center;"> 975 spikes </p>
  </div>
</div>

---

# Raw Data: X-rays &rarr; Image Processing

<div class="row">
  <div class="column" style="max-width:51%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/x3000_setup.jpg">
    <p style="text-align: center;"> Proprietary X-Ray CT scan reconstruction </p>
  </div>
  <div class="column" style="max-width:17.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S019_L0_1.gif">
    <p style="text-align: center;"> 975 spikes </p>
  </div>
  <div class="column" style="max-width:20.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S017_L0_seed_10_0.gif">
    <p style="text-align: center;"> 38,000 seeds </p>
  </div>
</div>

---

# Raw Data: X-rays &rarr; Image Processing

<div class="row">
  <div class="column" style="max-width:51%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/x3000_setup.jpg">
    <p style="text-align: center;"> Proprietary X-Ray CT scan reconstruction </p>
  </div>
  <div class="column" style="max-width:17.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S019_L0_1.gif">
    <p style="text-align: center;"> 975 spikes </p>
  </div>
  <div class="column" style="max-width:20.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S017_L0_seed_10_0.gif">
    <p style="text-align: center;"> 38,000 seeds </p>
  </div>
</div>

<div class="row">
  <div class="column" style="max-width:35%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/seed_orientation1.png">
    <p style="text-align: center;"> Align all the seeds </p>
  </div>
</div>

---

# Raw Data: X-rays &rarr; Image Processing

<div class="row">
  <div class="column" style="max-width:51%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/x3000_setup.jpg">
    <p style="text-align: center;"> Proprietary X-Ray CT scan reconstruction </p>
  </div>
  <div class="column" style="max-width:17.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S019_L0_1.gif">
    <p style="text-align: center;"> 975 spikes </p>
  </div>
  <div class="column" style="max-width:20.5%; color: Navy; font-size: 15px;">
    <img src="../figs/S017_L0_seed_10_0.gif">
    <p style="text-align: center;"> 38,000 seeds </p>
  </div>
</div>

<div class="row">
  <div class="column" style="max-width:35%; color: Navy; font-size: 15px;">
    <img style="padding: 2px 0 2px 0;" src="../figs/seed_orientation1.png">
    <p style="text-align: center;"> Align all the seeds </p>
  </div>
  <div class="column" style="max-width:55%; color: Navy; font-size: 15px;">
    <img src="../figs/boxplot_all_traditional_h.gif">
    <p style="text-align: center;"> Traditional shape descriptors </p>
  </div>
</div>

---

# The Euler Characteristic Transform (ECT)

`$$\chi = \#(\text{Vertices}) - \#(\text{Edges}) + \#(\text{Faces}).$$`

--

- ECT is the record of how the EC changes as we chop/reconstruct a given object in all possible directions.

--

![](../figs/ect_ver2.gif)

--

- [**Theorem _(Turner, Mukherjee, Boyer 2014)_**](https://doi.org/10.1093/imaiai/iau011):  Mathematically speaking, the ECT summarizes all shape information.

---

# Hidden topological shape information

- **Goal:** Classify 28 barley accessions using solely grain morphology information.

- **3121** grains in total

--

.pull-left[
![](../figs/svm_f0_table_umap_results.png)
]

.pull-right[
<img src="../figs/pole_directions_p7_m12_crop.jpg" width="150" style="display: block; margin: auto;" />
]

---

# Hidden topological shape information

- **Goal:** Classify 28 barley accessions using solely grain morphology information.

- **3121** grains in total

.pull-left[
![](../figs/svm_f0_table_umap_results.png)

<img src="../figs/kruskal_wallis_topo_summary.jpg" width="300" style="display: block; margin: auto;" />
]

.pull-right[
<img src="../figs/pole_directions_p7_m12_crop.jpg" width="150" style="display: block; margin: auto;" />
]

---

# Hidden topological shape information

- **Goal:** Classify 28 barley accessions using solely grain morphology information.

- **3121** grains in total

.pull-left[
![](../figs/svm_f0_table_umap_results.png)

<img src="../figs/kruskal_wallis_topo_summary.jpg" width="300" style="display: block; margin: auto;" />
]

.pull-right[
<img src="../figs/discerning_directions.png" width="150" style="display: block; margin: auto;" />

![](../figs/arrow_seed_09_0.gif)
]

---

# Into semi-supervised territory

- Train an SVM with 100% of the founders `\((F_0)\)`

- Classify the progeny `\((F_{18}\text{ and }F_{58})\)` to detect genotype enrichment

--

.pull-left[
![](../figs/histogram_umap_gen1_d158_T16_vert.png)
]

.pull-right[
![](../figs/histogram_umap_gen7_d158_T16_vert.png)
]

---
class: right, bottom, inverse

background-image: url("../figs/acknowledgments.jpg")
background-size: 1000px
background-position: 50% 40%

Grab these slides at [`bit.ly/eccb21_barley`](http://bit.ly/eccb21_barley)