11institutetext: Centre for Image Analysis, Department of Information
Technology and SciLifeLab BioImage Informatics Facility, Uppsala University,
Sweden
$*$ These authors contributed equally
11email: {axel.andersson, andrea.behanova, carolina.wahlby,
<EMAIL_ADDRESS>
# Cell segmentation of in situ transcriptomics data using signed graph
partitioning

Axel Andersson*  Andrea Behanova  Carolina Wählby  Filip Malmberg

###### Abstract

The locations of different mRNA molecules can be revealed by multiplexed in
situ RNA detection. By assigning detected mRNA molecules to individual cells,
it is possible to identify many different cell types in parallel. This in turn
enables investigation of the spatial cellular architecture in tissue, which is
crucial for furthering our understanding of biological processes and diseases.
However, cell typing typically depends on the segmentation of cell nuclei,
which is often done based on images of a DNA stain, such as DAPI. Limiting
cell definition to a nuclear stain makes it fundamentally difficult to
determine accurate cell borders, and thereby also difficult to assign mRNA
molecules to the correct cell. As such, we have developed a computational tool
that segments cells solely based on the local composition of mRNA molecules.
First, a small neural network is trained to compute attractive and repulsive
edges between pairs of mRNA molecules. The signed graph is then partitioned by
a mutex watershed into components corresponding to different cells. We
evaluated our method on two publicly available datasets and compared it
against the current state-of-the-art and older baselines. We conclude that
combining neural networks with combinatorial optimization is a promising
approach for cell segmentation of in situ transcriptomics data. The tool is
open-source and publicly available for use at https://github.com/wahlby-
lab/IS3G.

###### Keywords:

Cell segmentation in situ transcriptomics tissue analysis mutex watershed.

##  1 Introduction

Over the past years, a large number of techniques for spatially resolved
multiplexed in situ transcriptomics (IST) have been developed [6, 10, 1, 2, 8,
5]. These techniques enable the mapping of hundreds of different mRNA
molecules directly within tissue samples, allowing the dissection and analysis
of cell type heterogeneity while preserving spatial information. These
techniques produce large gigapixel-sized images of tissue sections with
millions of different spatial biomarkers for various mRNA molecules. A single
experiment can pinpoint the location of hundreds of different types of mRNA
molecules with sub-micrometer resolution. The many different types of targeted
mRNA molecules, as well as a large number of detected molecules, make visual
exploration and analysis challenging. To alleviate, and compute quantitative
statistics, a range of tools, as described below, have been developed for
grouping the mRNA molecules into groups, such as cells, cell types, or tissue-
level compartments.

###  1.1 Tools for analyzing IST data

The analysis of IST data typically starts by assigning mRNA molecules to
localized cells. By examining the composition of molecules within cells, it
becomes possible to define and analyze different cell types and their spatial
organization [22, 11, 3, 19]. Traditionally, cells are located in a nuclear
stained image complementary to the IST experiment using techniques such as
Stardist [21], Cellpose [18], or the distance-transform watershed approach.
Subsequently, the mRNA molecules are assigned to the detected nuclei based on
their proximity in space. However, assigning molecules to cells solely based
on their spatial proximity to the nucleus may not be optimal due to irregular
cell shapes and the asymmetric distribution of detected mRNAs around the
nuclei. Moreover, there are situations where clusters of mRNA molecules
belonging to a cell are detected in the IST experiment, but the corresponding
nucleus lies outside the imaged region of interest. Additionally, if the
quality of the nuclear image is poor and the nuclei are not clearly visible,
it further complicates the assignment process. In such cases, cell detection
based on nuclear staining is not optimal.

To improve the assignment of molecules to already detected cells, Qian et al
[17] created a probabilistic cell typing method, pciSeq, where prior known
information regarding the molecular composition of different cell types is
utilized when assigning molecules and typing cells. Similarly, Prabhakaran et
al. [16] introduced Sparcle, a method where mRNAs are assigned to cells
through a relatively simple "assign" and "refine" algorithm. However, both
Sparcle and pciSeq require that the location of cells is known beforehand.
Petukhov et al. [15] introduced Baysor, an extensive probabilistic model that
both detects the location of cells and assigns molecules to the cell.
Alternatively, there are methods that overcome assigning molecules to cells by
simply ignoring the cells, and instead assigning molecules to spatial bins
[12, 20, 13], or using deep learning to learn more abstract features [14, 4,
9]. Such methods allow the user to easily identify regions of similar
molecular compositions (corresponding to semantic segmentation), but
statistics on a per-cell level (requiring instance segmentation) are difficult
to compute.

###  1.2 Contribution

Localizing cells and assigning the right molecules to cells is a crucial task
in IST. In this context, we introduce In Situ Sequencing SEGmentation (IS3G),
a novel tool that jointly identifies the location of cells and assigns mRNA
molecules to them, without the need for prior knowledge of cell location or
cell type molecular compositions. IS3G operates solely on local mRNA
composition and identifies cells by partitioning a signed graph, making it
possible to segment cells without relying on nuclear staining. Our results
demonstrate that signed graph partitioning can be used to efficiently segment
IST data without seeds for cell location or cell types.

##  2 Methodology

In brief, IS3G utilizes a small neural network to classify whether two mRNA
molecules originate from the same cell or not. The posterior probabilities of
the classifier are used to determine the strength of attractive (positive) and
repulsive (negative) edges in a signed graph. Using a mutex watershed [23],
this graph is then partitioned into components that correspond to individual
cells, enabling the accurate assignment of molecules to their respective
cells.

###  2.1 Compositional features

The neural network used to predict the attractive and repulsive edge strengths
is trained on local compositions of mRNA molecules. In this section, we
explain how to extract such features. We start by setting the notation. In an
IST experiment, the $i$’th detected mRNA molecule can be described with two
attributes: a position $p_{i}\in\mathbb{R}^{D}$ and a categorical label
$l_{i}\in\mathbb{L}$, where $D$ is the number of spatial dimensions (usually
two or three) and $\mathbb{L}$ is the set of targeted mRNA molecules. The
categorical label of a molecule can be represented as a one-hot-encoded
vector, i.e., $e_{i}\in\\{0,1\\}^{|\mathbb{L}|}$. The local composition of
mRNA molecules in a neighborhood around the $i$’th mRNA can thus be computed
by simply counting the labels among the $k$ nearest neighbors,

$x_{i}=\sum_{j\in\mathcal{N}(p_{i})}e_{j},$ (1)

where $\mathcal{N}(p_{i})$ refers to the $k$ nearest neighbors to the $i$’th
molecule. The parameter $k$ depends on the molecular density and must be tuned
so that the compositional features describe molecular patterns on a cellular
scale. We found that setting the value of $k$ to roughly one third of the
expected molecular count per cell works well. The compositional features
$x_{i}$ will serve as the input to our model used for computing the strength
of our attractive and repulsive edges.

Figure 1: Explanatory overview of the method. The top row: (a) Visualization
of the distribution of molecules within three cells, where each color
represents a different type of mRNA molecule. (b) Attractive edges connect
molecules over short distances, whereas repulsive edges connect molecules over
greater distances. The weight of the attractive edges indicates the desire
that the two molecules belong to the same cell, whereas the weight of the
repulsive edges indicates a desire that the molecules belong to two different
cells. Panel (b1-b3) describes how the edge weights are computed. First,
compositional vectors are computed for a pair of molecules (b1). The pair of
compositional vectors, ($x_{i}$, $x_{j}$), are respectively fed through an
encoder, transforming the vectors into latent representations ($z_{i}$,
$z_{j}$) (b2). The Euclidean distance between the latent vectors is fed
through a classifier, attempting to classify whether the pair of latent
vectors are from the same cell or not. The posterior probabilities of the
classifier are used to set the strength of the attractive and repulsive edges
(b3-b4). The signed graph is partitioned using a mutex watershed. The
connected components defined by the active attractive edges are labeled
individual cell instances (b5,c.)

To predict the edge strengths between molecules, we train a small Siamese
neural network to classify whether two molecules belong to the same cell or
not. The network consists of an encoder and a classifier. First, the
compositional features are computed for each of the pairs according to Eq. 1.
The pair of features, $(x_{i},x_{j})$, are respectively encoded by the encoder
into latent vectors $(z_{i},z_{j})$ using a simple neural network with two
fully-connected layers with ELU activations. Next, the Euclidean distance
between the two latent vectors is computed,
$\Delta_{i,j}=\|z_{i}-z_{j}\|_{2}$. Based on the distance between the vectors,
the network attempts to classify whether the sampled molecule pair belongs to
the same cell or not. The classifier consisted of a single fully connected
layer ending with a Sigmoid function. The posterior probability, $y_{ij}$, is
then used as the attractive and repulsive ($y_{ij}-1)$ edge strengths.
However, compositional features ($x_{i}$) computed in regions with low
concentrations of mRNA molecules are inherently more sensitive to small
molecular variations than compositional features computed in high-
concentration regions. We, therefore, scale edge weights by the density factor
$\rho_{ij}=\mathrm{min}(\|x_{i}\|_{1},\|x_{j}\|_{1})$ to give edges between
pairs of mRNA molecules in low concentration regions lower weight than pairs
in high concentration regions.

The weights of the encoder and classifier are jointly optimized by minimizing
the binary cross entropy using the Adam optimizer [7]. Training data is
generated stochastically using the heuristic that two molecules separated by a
distance less than $R_{\mathrm{cell}}$ are labeled as belonging to the same
cell, whereas molecules separated by a distance larger than
$2R_{\mathrm{cell}}$ are labeled to belong to two different cells. We trained
the network for a maximum of 300 epochs, where one epoch was reached when we
sampled the same number of molecule pairs as the total number of molecules in
the dataset. However, 300 epochs were never reached since we employed an early
stopping procedure. If the loss was non-decreasing for more than 15 epochs,
the training would terminate. The model with the lowest loss was saved and
used for computing edge strengths. A batch size of 2048 was used for all
experiments.

###  2.2 Graph construction and partitioning

In the previous section, we explained how a neural network can be used to
compute attractive and repulsive edge strengths. In this section, we will
define our set of attractive and repulsive edges. We define our set of
attractive edges, $E^{+}$, by assuming that molecules separated by a short
distance are likely to belong to the same cell. Specifically, $E^{+}$ is
created by connecting each molecule to all of its five nearest neighbors.

Next, we define our set of repulsive edges between molecules separated by a
distance larger than $2R_{\mathrm{cell}}$ and less than $6R_{\mathrm{cell}}$.
To save memory, each molecule is only connected with a repulsive edge to $15$
randomly selected neighbors within the interval. The repulsive edge weights
are set to $-\infty$ for edges between molecules separated by a distance
larger than $4R_{\mathrm{cell}}$.

Finally, we use the procedure from the previous section to compute the
strength of the edges, leaving us with a graph with signed edge weights. The
graph is finally partitioned using a mutex watershed into components
corresponding to different cells.

The methodology is shown as an illustrative example in Fig. 1.

###  2.3 Pre and Post processing

To speed up the segmentation we first remove markers in low-density regions,
as these markers are likely extracellular. We identify these markers
automatically by computing the distance to the 15’th nearest neighbor. The
distance is then clustered using a Gaussian mixture model. Markers belonging
to the component with the larger mean are deemed extracellular and removed.
After the segmentation, we discard cells with fewer than $n_{\mathrm{min}}$
number of molecules.

###  2.4 Visualization

The segmented cells can be visualized in two ways: by assigning a color to
each marker based on the cell it belongs to, or by outlining the segmented
cell with a contour. To generate the contours, we employ an algorithm similar
to the one described in [15]. For each cell, we calculate the marker frequency
within small spatial bins placed on a regular grid. This process is repeated
for all detected cells, resulting in a multi-channel count image. Each pixel
in the image represents the marker count in a bin for a specific cell. The
count image is spatially smoothed using a Gaussian filter and then transformed
into a 2D labeled mask by identifying the index of the maximum value across
the channels. Each label in the mask thus corresponds to detected cells. Next,
we find the contours of each cell in the labeled mask. The contour pixels for
each cell are finally filtered by taking the longest path of the minimum
spanning tree connecting the points.

##  3 Experiments

We perform experiments on two publicly available datasets: An osmFISH [1] and
an In Situ Sequencing (ISS) [17] dataset and compare with authors’ original
segmentation as well as Baysor [15] — the current state-of-the-art.

###  3.1 osmFISH

We first studied the osmFISH dataset [1]. This dataset consists of around two
million molecules of 35 different types. Also included in this dataset is a
segmentation produced by the original authors [1], here referred to as the
Codeluppi method. We ran IS3G using $R_{\mathrm{cell}}=8~{}\mathrm{\mu m}$ and
$k=35$. We also ran Baysor [15] on the dataset, using the parameters provided
in their osmFISH example. Baysor can be seeded with prior information
regarding the nuclei segmentation (as described in [15]), as such, we run
Baysor both with and without such a prior. For each cell segmentation method,
we filter out cells containing fewer than $n_{\text{min}}=30$ molecules.
First, we look at the number of cells detected by each of the methods as well
as the fraction of assigned molecules. This is shown in Fig. 2a and Fig. 2b
respectively. As seen, IS3G finds roughly the same number of cells as Baysor
and Baysor with prior, but significantly more than the original publication
[1].

Figure 2: Results of various segmentation techniques applied on osmFISH
dataset. The total number of detected cells and the fraction of molecules
assigned cells are shown in a and b respectively. Cells detected by IS3G are
paired with cells detected by other methods. The distribution of Dice indices
of the paired cells is shown in c. The dashed line represents the median Dice
index. Panel d shows a zoomed out view of the DAPI image (100 $\mu$m scale
bar), with zoom-ins showing the distribution of gene markers (e) and IS3G
segmented cells (f). A series of segmentation examples are shown in d.
Presented techniques are IS3G, Codeluppi, Baysor, and Baysor with DAPI.

.

Next, we wanted to investigate if we find cells in the same location as the
other methods. To do this we first matched our detected cells with the other
methods’ detected cells based on Sørensen–Dice index (Dice index). If two
cells identified by two methods contain exactly the same molecules, the Dice
index is one, and zero if no molecules overlap between the two cells. We match
the cells between the two methods by maximizing the average Dice score across
all detected cells using the Hungarian algorithm. Fig. 2c shows the
distribution of Dice indices between matched cells detected using IS3G versus
Baysor, Baysor with prior and Codeluppi et al. [1]. The median Dice index
between IS3G detected cells matched with Baysor detected cells was 0.8.
Finally, Fig. 2d shows some examples of the segmentation done by the different
methods. The full dataset with segmentation results from all the mentioned
techniques can be found here: https://tissuumaps.scilifelab.se/osmFISH.html

Figure 3: Results of various segmentation techniques applied on ISS dataset.
The total number of detected cells and the fraction of molecules assigned
cells are shown in (a) and (b) respectively. Cells detected by IS3G are paired
with cells detected by other methods. The distribution of Dice indices of the
paired cells is shown in (c). The dashed line represents the median Dice
index. Panel (d) shows the DAPI image of the whole data set (1 mm scale bar)
with highlighted zoom-in sections showing gene markers (e) and IS3G segmented
cells (f). A series of segmentation examples are shown in (g). Presented
techniques are IS3G, pciSeq, Baysor, and Baysor with prior.

###  3.2 In Situ Sequencing

Secondly, we studied the dataset by Qian et al [17]. This dataset comprises
around 1.4 million detected molecules of 84 different types. As for post-
processing, we filter out cells containing fewer than $n_{\text{min}}=8$
molecules. We used an $R_{\mathrm{cell}}=10~{}\mu\text{m}$ and $k=8$. Fig. 3a
shows the number of cells detected by IS3G, Baysor, Baysor with prior, and
pciSeq. We note that IS3G finds roughly the same number of cells as Baysor and
Baysor prior, and significantly more than pciSeq.

Fig. 3c shows the distribution of Dice indices when matching molecules
assigned to our segmented cells with the other methods. The dashed lines
indicate the median. Finally, Fig. 3d shows some examples of the segmentation
done by the different methods. The full dataset with segmentation results from
all the mentioned techniques can be found here:
https://tissuumaps.scilifelab.se/ISS.html

##  4 Discussion

We have presented a simple technique for segmenting cells in IST data. IS3G
differs from other approaches that need prior cell segmentation, seeds, or
predetermined cell types. Instead, IS3G directly extracts features from the
data by utilizing a simple neural network. We tested IS3G on two datasets, and
it achieved performance comparable to the current state of the art, see Fig.
2c and Fig. 2c, showing that signed graph partitioning can be used to
efficiently segment cells in IST data.

The deep learning model used to predict edge weights is very basic and likely
not optimal. It was trained on "already aggregated data," which refers to
compositional features obtained by computing the weighted frequency of
molecules in circular neighborhoods, see Eq 1. A graph neural network may be
more suitable for this application since it can also learn the weights used in
the aggregation.

IS3G requires that the user provides a rough estimate of the cell radius,
i.e., $R_{\mathrm{cell}}$. This parameter governs the bandwidth of the
Gaussian kernel used when computing the compositional features. However, here
we have assumed that the size of each cell is approximately the same. In
practice, we have noticed that the size of the cells, or more precisely, the
size of the mRNA point-cloud surrounding the cells, can vary between cells.
Potentially, the segmentation could be improved by considering an adaptive
bandwidth or using a graph-neural network that can extract features across
multiple scales.

While not used explicitly herein, the mutex watershed algorithm provides a
convenient way to specify mutually exclusive constraints between specific
types of markers. This could be particularly beneficial in regions where it is
difficult to differentiate between cells based solely on mRNA composition but
a clear distinction can be made based on their nuclei. In such scenarios, IS3G
may identify cells with multiple nuclei. However, if the user has
supplementary markers indicating the position of nuclei, infinitely repulsive
edges can be incorporated between these markers to explicitly ensures that
each cell contains only one nucleus.

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