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<script type="text/front-matter">
title: "LSDs"
description: ""
</script>
<body>
<div style="text-align: center;">
<img class="b-lazy"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/small/lsds_header.jpeg"
srcset="assets/img/small/lsds_header.jpeg 320w,
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sizes="100vw"
alt="LSD direction vectors">
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="50%"><figcaption style="text-align: center;">Direction vectors of
the LSDs on a single neuron from the fly visual system. Colors correspond
to the direction in which the neuronal processes travel.</figcaption></td>
</tr></table>
</div>
<dt-article class="centered" id="dtbody">
<dt-byline class="l-page transparent"></dt-byline>
<h1>Local Shape Descriptors for Neuron Segmentation</h1>
<p></p>
<dt-byline class="l-page" id="authors_section" hidden>
<div class="byline">
<div class="authors">
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=Md__FUQAAAAJ&hl=en&oi=ao">Arlo Sheridan</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.salk.edu/science/core-facilities/advanced-biophotonics">Salk Institute</a>
</div>
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=AnU408sAAAAJ&hl=en">Tri M. Nguyen</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.lee.hms.harvard.edu/">Harvard University</a>
</div>
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=gBcB_UUAAAAJ&hl=en">Diptodip Deb</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.janelia.org/lab/turaga-lab">HHMI Janelia</a>
</div>
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=y2s07ssAAAAJ&hl=en">Wei-Chung Allen Lee</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.lee.hms.harvard.edu/">Harvard University</a>
</div>
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=oSGyzt4AAAAJ&hl=en">Stephan Saalfeld</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.janelia.org/lab/saalfeld-lab">HHMI Janelia</a>
</div>
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=V_NdI3sAAAAJ&hl=en">Srini Turaga</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.janelia.org/lab/turaga-lab">HHMI Janelia</a>
</div>
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=_ZLy6tEAAAAJ&hl=en">Uri Manor</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.salk.edu/science/core-facilities/advanced-biophotonics">Salk Institute</a>
</div>
<div class="author">
<a class="name" target="_blank" rel="noopener noreferrer" href="https://scholar.google.com/citations?user=7rqAapgAAAAJ&hl=en">Jan Funke</a>
<a class="affiliation" target="_blank" rel="noopener noreferrer" href="https://www.janelia.org/lab/funke-lab">HHMI Janelia</a>
</div>
</div>
<div class="date"> <div style="color: #2AAFCF;"><a target="_blank"
rel="noopener noreferrer"
href="https://www.biorxiv.org/content/10.1101/2021.01.18.427039v1"
target="_blank">LSD Paper</a></div>
</div>
</div>
</dt-byline>
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<h2>Abstract</h2>
<p>We present a simple, yet effective, auxiliary learning task for the problem of
neuron segmentation in electron microscopy volumes. The auxiliary task
consists of the prediction of Local Shape Descriptors (LSDs), which we combine
with conventional voxel-wise direct neighbor affinities for neuron boundary
detection. The shape descriptors are designed to capture local statistics
about the neuron to be segmented, such as diameter, elongation, and direction.
On a large study comparing several existing methods across various specimen,
imaging techniques, and resolutions, we find that auxiliary learning of LSDs
consistently increases segmentation accuracy of affinity-based methods over a
range of metrics. Furthermore, the addition of LSDs promotes affinity-based
segmentation methods to be on par with the current state of the art for neuron
segmentation (Flood-Filling Networks, FFN), while being two orders of
magnitudes more efficient - a critical requirement for the processing of
future petabyte-sized datasets. Implementations of the new auxiliary learning
task, network architectures, training, prediction, and evaluation code, as
well as the datasets used in this study are publicly available as a benchmark
for future method contributions.</p>
<hr>
<div id="toc_container">
<p class="toc_title">Contents</p>
<ul class="toc_list">
<li><a href="#background">1. Background</a>
<ul>
<li><a href="#connectomics">1.1 Connectomics</a></li>
<li><a href="#neuron_segmentation">1.2 Neuron Segmentation</a></li>
<li><a href="#related_work">1.3 Related Work</a></li>
<li><a href="#contributions">1.4 Contributions</a></li>
</ul>
</li>
<li><a href="#methods">2. Methods</a></li>
<ul>
<li><a href="#local_shape_descriptors">2.1 Local Shape Descriptors</a></li>
<li><a href="#network_architectures">2.2 Network Architectures</a></li>
</ul>
<li><a href="#results">3. Results</a></li>
<ul>
<li><a href="#datasets">3.1 Datasets</a></li>
<li><a href="#accuracy">3.2 Accuracy</a></li>
<li><a href="#throughput">3.3 Throughput</a></li>
</ul>
<li><a href="#discussion">4. Discussion</a></li>
<li><a href="#acknowledgements">5. Acknowledgements</a></li>
<li><a href="#code">6. Code</a></li>
<li><a href="#references">7. References</a></li>
</ul>
</div>
<h2 id="tldr">Tl;dr</h2>
<ul>
<li>
<p>Connectomics is a relatively new field combining neuroscience, microscopy, biology and computer science.</p>
</li>
<li>
<p>The goal is to generate maps of the brain at synaptic resolution. By doing so,
it will hopefully lead to a better understanding of how things work and
subsequently advance medical approaches to various diseases.</p>
</li>
<li>
<p>The datasets required to produce these brain maps are massive since they have
to be imaged at such a high resolution.</p>
</li>
<li>
<p>Manually reconstructing wiring diagrams in the datasets is extremely time consuming and
expensive so there is a great need to automate the process.</p>
</li>
<li>
<p>Reconstructing neurons is challenging because many consecutively correct decisions must be made. Errors can propagate throughout a dataset easily.</p>
</li>
<li>
<p>Methods need to also be computationally efficient and scalable to account
for the size of the data.</p>
</li>
<li>
<p>We present a novel approach to neuron segmentation, Local Shape Descriptors
(LSDs) - a 10-Dimensional embedding used as an auxiliary learning objective
for boundary detection.</p>
</li>
<li>
<p>We find that the LSDs help improve boundaries and subsequent neuron
reconstructions in several large and diverse datasets and are competitive with
the current state of the art, albeit two orders of magnitude faster.</p>
</li>
</ul>
<hr>
<h2 id="background">Background</h2>
<h3 id="connectomics">Connectomics</h3>
<p>Connectomics is an emerging field which integrates multiple domains including
neuroscience, microscopy, and computer science. The overarching goal is to
provide insights about the brain at resolutions which are not achievable with
other approaches. The ability to study neural structures at this scale will
hopefully lead to a better understanding of brain disorders, and subsequently
advance medical approaches towards finding treatments & cures.</p>
<p>The basic idea is to produce "connectomes" which are essentially maps of the
brain. These maps, or "wiring diagrams", give scientists the ability to see how
every neuron interacts through synaptic connections. They can be used to
complement existing techniques <dt-cite
key="schlegel_synaptic_2016,turner-evans_neuroanatomical_2020"></dt-cite> and
drive future experiments <dt-cite
key="schneider-mizell_quantitative_2016,motta_dense_2019,bates_complete_2020"></dt-cite>.</p>
<p>Currently, only Electron Microscopy (EM) allows imaging of neural tissue at a
resolution sufficient to see individual synapses. Unfortunately, by imaging
brains at such high resolution, the resulting data is massive. Let's consider
the fruit fly example. A full adult fruit fly brain (<strong>FAFB</strong>) imaged with
ssTEM <dt-cite key="zheng_complete_2018"></dt-cite> at a pixel resolution of ~4
nanometers and ~40 nanometer thick sections, comprises ~50 teravoxels of data
(neuropil)<dt-cite key="heinrich_synaptic_2018"></dt-cite>. For reference, a
voxel is a volumetric pixel, and the "tera" prefix means 10<sup>12</sup>. So,
one fly brain contains upwards of 50,000,000,000,000 volumetric pixels. To put
that in perspective, <dt-cite key="abbott_mind_2020">Abbott et al.</dt-cite>
argue that, assuming a scale where 1000 cubic microns is equivalent to 1
centimeter, a fruit fly brain would comprise the length of 6 and a half Boeing
747 aeroplanes. This still pales in comparison to a mouse brain which would
require the acquisition of 1 million terabytes of data.</p>
<div style="text-align: center;">
<img class="b-lazy"
id="scale_large"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/large/scale.jpeg" style="margin: auto; width: 100%;"/>
<img class="b-lazy"
id="scale_vertical"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/medium/scale_vertical.jpeg" style="margin: auto; width: 100%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="50%"><figcaption style="text-align: center;">Scale perspective. A
fruit fly brain imaged at synaptic resolution takes up 100's of terabytes of
storage space. It allows us to see fine structures such as neural plasma
membranes (pink arrow), synapses (blue arrow), vesicles (green arrow) and
mitochondria (orange arrow). 3D fruit fly model kindly provided by <a
href="https://scholar.google.com/citations?user=ir1vhA8AAAAJ&hl=en"
target="_blank">Igor Siwanowicz</a></figcaption></td>
</tr></table>
</div>
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<div class="box-content"><div><p>Try navigating the fly brain in an
interactive <a href="https://github.com/google/neuroglancer"
target="_blank">Neuroglancer</a> viewer (click question mark in top right
corner for controls).
Think, Google Earth for brains:</p> </div>
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<p>Okay, now we have the data, so how do we create the wiring diagrams?</p>
<p>To create a wiring diagram, we need to reconstruct all of the neurons and their
synaptic connections. This process can be done manually - which consists of
human annotators navigating these datasets and labeling every neuron and their
synaptic partners using various software <dt-cite
key="saalfeld2009catmaid,boergens_webknossos_2017,berger_vast_2018,zhao_neutu_2018"></dt-cite>.
However, this can become extremely tedious and expensive (<strong>$$$</strong>) given the
size of the datasets. For example, simply reconstructing 129 neurons from
<strong>FAFB</strong> took a team of tracers ~60 days to complete<dt-cite
key="zheng_complete_2018"></dt-cite>. Given that a fruit fly has ~100,000
neurons, purely manual reconstruction of connectomes is obviously infeasible.</p>
<p>Consequently, methods have been developed to automate this process. From here
on, we will focus on the automatic reconstruction of neurons. To see the current
approaches to synapse detection, check <dt-cite
key="kreshuk_who_2015,heinrich_synaptic_2018,huang_fully-automatic_2018,buhmann_automatic_2020">
these papers</dt-cite> out!</p>
<h3 id="neuron_segmentation">Neuron Segmentation</h3>
<p>Neuron segmentation is the current rate-limiting step for generating large
connectomes. Errors in a neuron segmentation can easily propagate throughout a
dataset as the scale increases, which makes it tedious for humans to proofread
the data without advanced tools.</p>
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<label class="box-title" for="seg">Segmentation overview</label>
<label class="box-close" for="acc-close"></label>
<div class="box-content"><div> <p> To better understand the problem of neuron
segmentation, it is necessary to understand what segmentation is. There are a
few ways to detect objects in an image. A standard approach is called
<b>object detection</b> which is a technique used to locate and label objects,
often resulting in fitting a bounding box to each object. This is a good
strategy for finding and tracking objects in an image but it neglects the
volumetric data contained within an object. An alternative method is called
segmentation in which every pixel of an object is assigned to a class. There
are two main techniques: <b>semantic segmentation</b> and <b>instance
segmentation</b>. In semantic segmentation, each pixel is assigned to a
broader class, for example each car in an image would be assigned to a car
class and each animal in an image would be assigned to a animal class.
Conversely, instance segmentation assigns each pixel to a unique label.
Consider the following example:</p>
</div>
<div class="box-content"><div style="text-align: center;">
<img id="shoes" src="assets/img/detection_vs_segmentation_shoes.jpeg" style="margin: auto; width: 100%;"/>
<img id="shoes_vertical" src="assets/img/detection_vs_segmentation_shoes_vertical.jpeg" style="margin: auto; width: 100%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="50%"><figcaption style="text-align: center;">Each shoe in the image
can be located (object detection), each pixel of each shoe can be assigned to
a class indicating the type of shoe (semantic segmentation - soccer cleats,
boots, sneakers), and each pixel can be assigned a unique label indicating the
specific shoe (instance segmentation)</figcaption></td>
</tr></table>
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<p>Neuron reconstruction is an instance segmentation problem because every pixel of
every neuron needs to be assigned a unique label (in contrast to object
detection and semantic segmentation). Take the following example:</p>
<div style="text-align: center;">
<img class="b-lazy"
id="neurons"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/detection_vs_segmentation_neurons.jpeg"
style="margin: auto; width: 100%;"/>
<img class="b-lazy"
id="neurons_vertical"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/detection_vs_segmentation_neurons_vertical.jpeg"
style="margin: auto; width: 100%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="50%"><figcaption style="text-align: center;">Given a raw EM image,
we could simply detect mitochondria (object detection), assign all pixels
containing mitochondria to one class (semantic segmentation), or assign all
pixels of each object to a unique class (instance segmentation). Our goal in
this paper is the latter.</figcaption></td> </tr></table>
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<label class="box-close" for="acc-close"></label>
<div class="box-content"><div><p>An example training batch showing raw data and
the corresponding ground truth labels (unique neurons) which were reconstructed
by a human expert. These labels are used to generate ground truth LSDs which are
then passed into a neural network</p> </div>
<div class="box-content"><div class="responsive-container">
<iframe class="responsive-iframe" src="https://neuroglancer-demo.appspot.com/#!%7B%22dimensions%22:%7B%22d0%22:%5B1%2C%22%22%5D%2C%22d1%22:%5B1%2C%22%22%5D%2C%22d2%22:%5B1%2C%22%22%5D%7D%2C%22position%22:%5B98.5%2C98.5%2C98.5%5D%2C%22crossSectionScale%22:1.0176722261336113%2C%22projectionOrientation%22:%5B-0.21856307983398438%2C-0.4040609300136566%2C-0.18352380394935608%2C0.8690707087516785%5D%2C%22projectionScale%22:484.7402817353436%2C%22layers%22:%5B%7B%22type%22:%22image%22%2C%22source%22:%22zarr://https://raw.githubusercontent.com/LocalShapeDescriptors/LocalShapeDescriptors.github.io/draft/assets/zarrs/fib.zarr/raw%22%2C%22tab%22:%22annotations%22%2C%22annotationColor%22:%22#fb00ff%22%2C%22name%22:%22raw%22%7D%2C%7B%22type%22:%22segmentation%22%2C%22source%22:%7B%22url%22:%22zarr://https://raw.githubusercontent.com/LocalShapeDescriptors/LocalShapeDescriptors.github.io/draft/assets/zarrs/fib.zarr/labels%22%2C%22transform%22:%7B%22matrix%22:%5B%5B1%2C0%2C0%2C52%5D%2C%5B0%2C1%2C0%2C52%5D%2C%5B0%2C0%2C1%2C52%5D%5D%2C%22outputDimensions%22:%7B%22d0%22:%5B1%2C%22%22%5D%2C%22d1%22:%5B1%2C%22%22%5D%2C%22d2%22:%5B1%2C%22%22%5D%7D%7D%2C%22subsources%22:%7B%22default%22:true%2C%22bounds%22:true%7D%2C%22enableDefaultSubsources%22:false%7D%2C%22tab%22:%22source%22%2C%22annotationColor%22:%22#00d9ff%22%2C%22crossSectionRenderScale%22:0.24230351153893748%2C%22colorSeed%22:54670317%2C%22name%22:%22labels%22%7D%5D%2C%22selectedLayer%22:%7B%22layer%22:%22raw%22%7D%2C%22layout%22:%224panel%22%7D"></iframe>
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<p>It would be ideal to directly predict unique labels (i.e neurons) in a dataset.
Unfortunately this requires global information which is difficult because
neurons span large distances. Due to the nature of neural networks, field of
views are not large enough to account for downstream changes in a neuron such as
branching and merging. Consequently, alternative approaches aim to solve the
problem locally.</p>
<h3 id="related_work">Related Work</h3>
<p>Most current approaches to neuron segmentation center around producing boundary
maps which are then used to generate unique objects with post-processing steps.
Consider the following example:</p>
<div style="text-align: center;">
<img class="b-lazy"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/labels.jpeg"
style="display: block; margin: auto; width: 50%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="100%"><figcaption style="text-align: center;">We have four neurons
(A,B,C,D) and we want to assign voxels (squares) to the label they belong to.
Images kindly provided by <a
href="https://scholar.google.com/citations?user=oSGyzt4AAAAJ&hl=en"
target="_blank">Stephan Saalfeld</a>.</figcaption></td>
</tr></table>
</div>
<ul>
<li>Foreground / Background
<ul>
<li>It is often sufficient to assign pixels as either foreground or background
and then perform connected components to label unique objects <dt-cite
key="ciresan_deep_2012"></dt-cite>. This technique can fail for neuron
segmentation because the axial resolution of fine-tip neurites is lower.</li>
</ul>
</li>
</ul>
<div style="text-align: center;">
<img class="b-lazy"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/boundaries.jpeg"
style="display: block; margin: auto; width: 50%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="100%"><figcaption style="text-align: center;">Naively labeling
foreground voxels (white squares) and background voxels (black squares) would
result in the top part of the yellow neuron (B) being falsely labeled as
background.</figcaption></td>
</tr></table>
</div>
<ul>
<li>Nearest-neighbor Affinities
<ul>
<li>One solution is to predict edges between neighboring voxels rather than the
voxels themselves <dt-cite
key="turaga_convolutional_2010,funke_large_2019"></dt-cite>. This ensures
that distal processes receive the same treatment as larger axons. Since
these affinity graphs can be computed locally, they can be parallelized
which leads to performance increases. However, affinities are sensitive to
small errors. A few incorrectly assigned pixels can lead to false merges
during post-processing.</li>
</ul>
</li>
</ul>
<div style="text-align: center;">
<img class="b-lazy"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/affinities.jpeg"
style="display: block; margin: auto; width: 50%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="100%"><figcaption style="text-align: center;">The top part of the
yellow neuron would now be correctly assigned. However, slight changes in
boundary predictions could result in subsequent post-processing
errors.</figcaption></td>
</tr></table>
</div>
<ul>
<li>Long Range Affinities
<ul>
<li>In order to incorporate more context for the receptive field of the network, a larger affinity neighborhood can be used as an auxiliary learning objective <dt-cite
key="lee_superhuman_2017"></dt-cite>. This theoretically helps to improve
the nearest neighbor affinities and the resulting segmentations.</li>
</ul>
</li>
</ul>
<div style="text-align: center;">
<img class="b-lazy"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/longrange.jpeg"
style="display: block; margin: auto; width: 50%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="100%"><figcaption style="text-align: center;">Several increased
neighborhood steps can be used to provide increased context to the nearest
neighbor affinities. This essentially allows the network to see more than it
otherwise would.</figcaption></td>
</tr></table>
</div>
<ul>
<li>MALIS loss
<ul>
<li>The above approaches rely on a Euclidean loss. An alternative loss function
(MALIS) <dt-cite key="turaga_maximin_2009"></dt-cite> penalizes topological
errors by minimizing the Rand Index, a measure of similarity between
clusterings <dt-cite key="rand_objective_1971"></dt-cite>. This method has
been further optimized by constraining the loss to a positive and negative
pass followed by growing a maximal spanning tree on the affinity graph
<dt-cite key="funke_large_2019"></dt-cite>.</li>
</ul>
</li>
</ul>
<div style="text-align: center;">
<img class="b-lazy"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/malis.jpeg"
style="display: block; margin: auto; width: 50%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="100%"><figcaption style="text-align: center;">After predicting
affinities, losses are computed on maximin edges and a maximal spanning tree
(line) is grown to identify maximin edges.</figcaption></td>
</tr></table>
</div>
<ul>
<li>Flood Filling Networks (FFN)
<ul>
<li>The current state of the art approach <dt-cite
key="januszewski_high-precision_2018"></dt-cite> eliminates the need for a
separate post-processing step. After generateing seed points within neurons,
a recurrent CNN iteratively fills each object by predicting which voxels
belong to the same objects as the seeds.</li>
</ul>
</li>
</ul>
<div style="text-align: center;">
<img class="b-lazy"
src=data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==
data-src="assets/img/ffn.jpeg"
style="display: block; margin: auto; width: 50%;"/>
<table style="width: 100%;" cellspacing="0" cellpadding="0"><tr>
<td width="100%"><figcaption style="text-align: center;">Given seed points
inside a neuron (large white square, for example), the network predicts which
voxels belong to the same neuron (white squares) and which belong to different
neurons (black squares).</figcaption></td>
</tr></table>
</div>
<ul>
<li>Other approaches
<ul>
<li>
<p>Deep Metric Learning</p>
<ul>
<li>A relatively new method uses deep metric learning to produce dense voxel
embeddings <dt-cite key="lee_learning_2019"></dt-cite>. Voxels within an
objects are similar in embedding space while voxels across objects are
repelled <dt-fn>This method was introduced after experiment completion and
is therefore not compared against.</dt-fn>.</li>
</ul>
</li>
<li>
<p>Watershed / Agglomeration Variants</p>
<ul>
<li>Other approaches <dt-cite
key="ferrari_mutex_2018,beier2017multicut"></dt-cite> aim to improve
segmentations by targeting the downstream graphs generated during
post-processing rather than the boundary labels <dt-fn>We assess boundary
prediction in this paper and do not consider post-processing
strategies.</dt-fn>.</li>
</ul>
</li>
</ul>
</li>
</ul>