All about cracks and shapes

.title[
# All about cracks and shapes
]
.subtitle[
## in a nutshell
]
.author[
### <strong>Erik Amézquita</strong>, Michelle Quigley, Pat Brown<br>Liz Munch, Dan Chitwood <br> — <br> Plant Sciences & Mathematics <br> University of Missouri <br> —
]
.date[
### 2023-10-12 <br> - <br> Preprint available: <a href="https://doi.org/10.1101/2023.09.26.559651">10.1101/2023.09.26.559651</a>
]

---

background-image: url("../../img/endlessforms.png")
background-size: 150px
background-position: 89% 7%

# Plant morphology

<div class="row">
  <div class="column" style="max-width:50%">
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/Cr0B-yFcJZk?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/ikhuvGpJbeA?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
  </div>
  <div class="column" style="max-width:50%">
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/lZXSpPzstF8?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
    <iframe width="375" height="210" src="https://www.youtube-nocookie.com/embed/qkOjHHuoUhA?controls=0" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
  </div>
</div>
<p style="font-size: 24px; text-align: right; font-family: 'Yanone Kaffeesatz'">Check out more 3D X-ray CT scans at <a href="https://www.youtube.com/@endlessforms6756">youtube.com/@endlessforms6756</a></p>

---

# The wal(nu)tzing nutcracker!

<div class="row" style="font-family: 'Yanone Kaffeesatz'; margin: 0 auto; font-size:22px">
  <div class="column" style="max-width:25%;">
    <img src="../figs/IMGA04011.jpg">
    <p style="text-align: center;">149 accessions</p>
  </div>
  <div class="column" style="max-width:42%;">
    <img src="../../barley/figs/x3000_setup.jpg">
    <p style="text-align: center;">1301 (1264) walnuts scanned</p>
  </div>
  <div class="column" style="max-width:33%;">
    <img src="../figs/pat_walnut_crack_detail4.jpg">
    <p style="text-align: center;">Qualitative data for crackability</p>
  </div>
</div>

<div class="row" style="font-size: 22px; font-family: 'Yanone Kaffeesatz'; margin: 0 auto;">
  <div class="column" style="max-width:20%;">
    <img src="../figs/2014SBa_R5_T81_shell_1.gif">
    <p style="text-align: center; margin: 0.5ex;">Shell</p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../figs/2014SBa_R1_T3_001_air.gif">
    <p style="text-align: center;margin: 0.5ex; ">Air</p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../figs/2014SBa_R1_T3_001_vein.gif">
    <p style="text-align: center;margin: 0.5ex; ">Packing tissue</p>
  </div>
  <div class="column" style="max-width:20%;">
    <img src="../figs/2014SBa_R5_T81_meat_2.gif">
    <p style="text-align: center;margin: 0.5ex;">Kernel</p>
  </div>
  <div class="column" style="max-width:20%; padding: 0 0 0 5px">
    <p style="margin:5px 0 0 0; text-align:left">
      &#9656;&ensp;Individuals separated manually<br>
      &#9656;&ensp;Tissues separated with watershed segmentation<br>
      &#9656;&ensp;49 traditional shape and size descriptors
    </p>
  </div>
</div>

---

## Watershed segmentation

![](../figs/2014SBa_R5_T20_001_w.gif)

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## Shape and size phenotypes

]

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# 49 image-based phenotypes!

- Length, width, height
- Raw  and *convex* Volume
- Raw and *convex* surface Area
- *Convexity ratios*
- Sphericity indices

**Kernel and its *main cavity***

- Length, width, height
- Raw  and *convex* total volume
- Volume relative to total and *without air*
- Raw and *convex* surface area
- *Convexity ratios*
- *Sphericity indices*
]

- Absolute and relative total volume
- Absolute and relative *protruding* volume
- Average thickness
- *Average density* relative to kernel
- *Average density* relative to packing tissue

**Air**

- Total and relative volume

***Packing tissue***

- *Absolute and relative total Volume*
- *Relative density to kernel*
]

Italics for phenotypes that I haven't seen measured elsewhere

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## Just to get out of the way

- Two kinds of relative volume

`$$\text{Kernel Volume Ratio}=\frac{V_{\text{kernel}}}{V_{\text{shell}} + V_{\text{kernel}} + V_{\text{packing}} + V_{\text{air}}}$$`

`$$\text{Kernel Airless Volume Ratio}=\frac{V_{\text{kernel}}}{V_{\text{shell}} + V_{\text{kernel}} + V_{\text{packing}}}$$`

- Per-individual vs per-accession

- Morphological phenotypes were averaged based on accession to make them comparable to qualitative data.

- Focus on volume and thickness-related phenotypes

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# The power of allometry: `$\;y = e^bV_N^m$`

Different tissues grow at different rates with respect to each other.

Growth does **not** scale linearly but it follows a power law.

<div class="row" style="color: black; font-size: 20px; font-family: 'Yanone Kaffeesatz'; margin: 0 auto;">
  <div class="column" style="max-width:33%;">
    <img src="../../walnuts/figs/nut_convex_volume_vs_nut_volume.png">
    <p style="padding: 0 2ex 0 0;">Walnut changes dramatically after its diameter is larger than 1.6cm (&frac58;")</p>
  </div>
  <div class="column" style="max-width:33%;">
    <img src="../../walnuts/figs/air_volume_vs_nut_volume.png">
    <p style="margin: 3px 0 0 0; padding: 0 2ex 0 0;">If nut volume increases by 2x, then air volume increases by 2.3x</p>
    <p style="padding: 0 2ex 0 0;">Walnut diameter cannot go beyond 15cm (6")</p>
  </div>
  <div class="column" style="max-width:33%;">
    <img src="../../walnuts/figs/kernel_volume_vs_nut_volume.png">
    <p style="margin: 1.1ex 0 0 0; padding: 0 2ex 0 0;">If nut volume increases by 2x, then kernel volume only increases by 1.8x</p>
  </div>
</div>

There are biophysical constraints at play in walnut development

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## Individual-based correlation

---