Random-walk Segmentation of Nuclei in Fluorescence Microscopic

Images with Automatic Seed Detection

Tabea Margareta Grace Pakull, Frederike Wirth and Klaus Brinker

Hamm-Lippstadt University of Applied Sciences, Marker Allee 76-78, 59063 Hamm, Germany

Keywords:

Medical Image Analysis, Computer Vision, Fluorescence Microscopy, Cell Nuclei Segmentation,

Random-walk Segmentation.

Abstract:

In personalized immunotherapy against cancer analysis of cell nuclei in tissue samples can provide helpful

information to predict whether the beneﬁts of the therapy outweigh the usually severe side effects. Since

segmentation of nuclei is the basis for all further analyses of cell images, research into suitable methods is

of particular relevance. In this paper we present and evaluate two versions of a segmentation pipeline based

on the established random-walk method. These versions contain automatic seed detection, using a distance

transformation in one of them. In addition, we present a method to select the required hyper-parameter of

the random-walk algorithm. The evaluation using a benchmark dataset shows that promising results can be

achieved with respect to common evaluation metrics. Furthermore, the segmentation accuracy can compete

with a reference CellProﬁler segmentation pipeline, based on the watershed transformation. Based on the

presented pipeline, the random-walk method can also be integrated into more advanced pipelines to further

improve segmentation results.

1 INTRODUCTION

With 10 million deaths caused by cancer in 2020, it

is one of the most common causes of death world-

wide (World Health Organization, 2021). In the ﬁght

against cancer, immunotherapy has become a promis-

ing treatment option by using the body’s immune sys-

tem to ﬁght cancer (Esfahani et al., 2020). The dis-

covery of immune checkpoint inhibitors, which pre-

vent tumor cells from using immune escape mecha-

nisms, was of great importance for research.

There is still insufﬁcient research into which peo-

ple beneﬁt from this kind of treatment. A preselection

is particularly important because the side effects can

be severe and even fatal (Esfahani et al., 2020). As

part of the ImmunePredict research project, we aim

at improving this selection by developing a predic-

tive model based on ﬂuorescence microscopy imag-

ing. The ﬁrst step in analyzing the images is to seg-

ment nuclei to accumulate cellular information for

predicting treatment success in further steps.

For segmentation, different methods were pro-

posed, that can be divided into the categories of

optimization, threshold and machine-learning-based

methods (Abdolhoseini et al., 2019). The latter is usu-

ally considered state-of-the-art and produce promis-

ing results for nuclei segmentation (cf. Liu et al.,

2021; Zaki et al., 2020; Kowal et al., 2020). Neverthe-

less, segmentation of nuclei remains challenging. For

example, overlapping nuclei are typically segmented

less accurately. A common approach is to use hybrid

methods by combining multiple techniques. The wa-

tershed transformation, which was evaluated as a part

of our research project (Wirth et al., 2020), for exam-

ple, can be combined with threshold and model-based

methods (Abdolhoseini et al., 2019) or used for post-

processing (Kowal et al., 2020), to improve segmen-

tation of clustered cell nuclei.

The random-walk algorithm can be widely applied

for image processing (e.g. image fusion, registra-

tion and segmentation) and it has already been ap-

plied successfully for segmentation in the oncologi-

cal ﬁeld (Wang et al., 2019). Besides the model we

use in this paper, proposed by Grady (2006), there are

alternating models to suit different use cases (Wang

et al., 2019). Key points in the improvement of the

algorithm are the preprocessing of input data and the

position of required seeds, that typically need user in-

teraction (Wang et al., 2017). An automatic solution

is necessary to make better use of the algorithm and

to combine it with e.g. deep learning methods.

The aim of this paper is to explore the basic po-

tential of the random-walk method for segmentation

of nuclei in ﬂuorescence images by assessing the per-

formance of two pipeline versions we developed. We

follow an automatic approach by proposing two au-

Pakull, T., Wirth, F. and Brinker, K.

Random-walk Segmentation of Nuclei in Fluorescence Microscopic Images with Automatic Seed Detection.

DOI: 10.5220/0010780400003123

In Proceedings of the 15th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2022) - Volume 2: BIOIMAGING, pages 103-110

ISBN: 978-989-758-552-4; ISSN: 2184-4305

103

tomatic seed detection methods with appropriate pre-

processing for detection and the random-walk algo-

rithm itself, as well as a method to set the hyper-

parameter β (see (1)). This enables the use of our

pipeline separately or in combination with sophisti-

cated techniques.

This paper is organized as follows: We summarize

the concept of segmentation using the random-walk

method in section 2. After that we outline the im-

plementation of our pipeline in section 3, which we

evaluate using a publicly available dataset presented

in section 4 and the metrics listed in section 5. The

results are presented in section 6 followed by the dis-

cussion in section 7. We provide a summary of our

ﬁndings and concluding remarks in section 8.

2 RANDOM-WALK

SEGMENTATION

A random-walk is a stochastic process that can be

used to describe random movements (Grady, 2006).

For segmentation, the random-walk is considered in

at least two dimensions. It operates on an undirected

graph and has a bias, which means that the steps on

this graph have different probabilities represented as

edge weights (Grady, 2006).

The segmentation method used in this paper was

proposed by Grady (2006). Grady (2006) derived a

method for analytically computing the desired prob-

abilities without the need of a rather inefﬁcient sim-

ulation of a random-walk. The result of this method

is an image that is segmented into regions that are as-

signed their own speciﬁc label. It is necessary to as-

sign labels to certain pixels (seeds) in advance. The

remaining pixels are assigned to these labels using the

random-walk algorithm by calculating the probability

that a random-walker that starts at a pixel will ﬁrst

reach a seed with a certain label (Grady, 2006).

The algorithm is based on the conversion of the

image into a graph G = (V, E) that consists of nodes

v ∈ V and edges e ∈ E. To prevent the random-walker

from crossing sharp intensity gradients, the edges are

weighted with a weighting function. As described in

(Wang et al., 2019) different weighting functions have

been proposed. We use the Gaussian weighting func-

tion (see (1)) in our pipeline:

w(e

i, j

) = w

i, j

= e

−β(g

−g

)

(1)

The edge e

i, j

connects the neighboring nodes i

and j. β is the only free parameter in the algorithm.

The intensities of the pixels are denoted as g

and g

The probability with which the random-walker uses

an edge is referred to as w(e

i, j

). Thus, strong inten-

sity gradients yield small probabilities.

The required probabilities are determined by solv-

ing a sparse linear system of equations. For each node

a k-tuple vector x

= (x

, ..., x

) is computed. The ﬁnal

segmentation is determined by assigning each node v

to the label corresponding to argmax(x

The algorithm always comes up with the same

unique result, which depends on the seed selection.

For completely black images or noise, the method

creates a so-called neutral segmentation. For each

seed, the segmented areas then resemble Voronoi cells

(Grady, 2006).

3 IMPLEMENTATION

Our proposed pipeline are based on methods of the

following standard python libraries: NumPy

, SciPy

OpenCV

, scikit-image

and pandas

. Figure 1 shows

a schematic representation of our pipeline.

Figure 1: Schematic representation of the pipeline for seg-

mentation using the random-walk algorithm.

An image is taken from a dataset and prepro-

cessed. Since a distance transformation is optional

in the preprocessing step, there are two versions of

the pipeline, which, however, do not differ in the gen-

eral process. Preprocessing produces one image that

is used in seed detection and a second one that is used

for segmentation. In addition a mask seed detection

is created. As the ﬁrst preprocessing step we reduce

noise in all of three images with the non-local-means

method, the contrast is optimized with the help of

an adaptive histogram equalization and edges are en-

https://numpy.org/ (version 1.18.5)

https://www.scipy.org/ (version 1.5.0)

https://opencv.org/ (version 4.5.1.48)

https://scikit-image.org/ (version 0.16.2)

https://pandas.pydata.org/ (version 1.0.5)

BIOIMAGING 2022 - 9th International Conference on Bioimaging

104

hanced by using a Sobel ﬁlter.

To create the mask we use the Li threshold (Li and

Lee, 1993) after that and then ﬁlter out small objects

to prevent detection of seeds for artifacts in the back-

ground. If the distance transformation is to be used

before seed detection, we apply the Li threshold on an

image with 1.5 times more enhanced edges, only us-

ing strong edges. After the transformation, a Gaussian

ﬁlter is applied and the intensity values get stretched

to cover values from 0 to 255. Without the transfor-

mation, only the last two steps are required after the

edge enhancement.

The image, to which the random-walk algorithm

is applied, demands a different preprocessing. Hence,

we use a background subtraction after noise reduction

and stretch the intensity values as described before.

Lastly, we dim intensity values to 40% of the maxi-

mum intensity to reduce contrast in bright regions.

In the developed pipeline, local maxima are used

as seeds. In order to avoid too many seeds per ob-

ject and yet not set an overall upper limit, only seeds

that are at least ten pixels apart are accepted. The

determined seeds are marked in a labeled image. In

addition, the biggest region of the background, after

dilating the objects in the mask from preprocessing,

is marked as a background seed. If a distance trans-

formation is used, the seeds for the nuclei are dilated

before labeling.

Using the random walker()-method of the scikit-

image library, a segmentation of the image is created.

As post-processing, objects that are larger than a pre-

deﬁned value (here 5000) are removed from the image

and the biggest object is labeled as the background.

4 DATASET

The image dataset BBBC039v1

(Caicedo et al.,

2019), available from the Broad Bioimage Bench-

mark Collection (Ljosa et al., 2012), was used for

evaluating the two pipeline versions. The collection

was published by the Carpenter lab at the Broad Insti-

tute and contains sets of microscopic images. In ad-

dition, the sets contain a ground truth for each image

as well as metadata.

The metadata describes a division into training,

validation and test set consisted of 100, 50 and 50

images respectively. For this paper, these sets were

used as follows: The training dataset was used dur-

ing pipeline development. The validation dataset was

used to determine the β parameter. Finally, the test

dataset is used to evaluate the segmentation accuracy.

https://sites.broadinstitute.org/bbbc/BBBC039

4.1 Image Data

The BBBC039v1 image set contains 200 images in

which nuclei of cell line U2OS can be seen. The hu-

man osteosarcoma cell line U2OS was obtained from

a tumor in the tibia of a 15-year-old girl in 1964 (Ni-

forou et al., 2008). The images were acquired with a

ﬂuorescence microscopy where the DNA was stained

with Hoechst. They have a resolution of 520 × 696

pixels and are stored as 16-bit TIFF ﬁles.

This dataset is rather challenging because of

strong intensity differences within and between the

nuclei. Some of them overlap or touch each other.

The size and shape of nuclei can differ due to a

wide variety of phenotypes, including micronuclei,

toroidal, fragmented, round and elongated nuclei

(Caicedo et al., 2019). The number of nuclei in an

image varies between 0 and 231. All images contain

some noise and a couple of images are almost entirely

ﬁlled with noise. In addition, some images contain

bright artifacts that cover up nuclei or cause strongly

reduced intensity values in surrounding areas. A to-

tal of approximately 23000 nuclei were manually seg-

mented by biologists for this dataset.

4.2 CellProﬁler Pipeline

The Broad Institute has also published a reference

pipeline for the CellProﬁler

software, which is a pos-

sible solution to the segmentation problem.

The preprocessing steps of this pipeline include

morphological operations, background subtraction

and applying a Sobel ﬁlter to enhance edges. A Gaus-

sian ﬁlter is applied to the image and a binary image is

created using a global Li threshold (Li and Lee, 1993).

Even though the typical diameter is speciﬁed with 20

to 80 pixels, objects outside these limits are not dis-

carded. Then, objects are identiﬁed that potentially

contain multiple nuclei. For these objects a distance

transformation is applied and the local maxima of its

output are used as seeds for a watershed transforma-

tion. All maxima that are less than ten pixels apart are

discarded. A smoothing ﬁlter is used to post-process

the segmentation to prevent over-segmentation. Fi-

nally, all holes in the objects are ﬁlled.

5 EVALUATION METRICS

Despite the importance of evaluating a segmentation

algorithm, there is no consensus on how it should be

https://cellproﬁler.org/

Random-walk Segmentation of Nuclei in Fluorescence Microscopic Images with Automatic Seed Detection

105

done (Sonka et al., 2015). As part of the ImmunePre-

dict project, suitable evaluation metrics for supervised

evaluation were selected (Wirth et al., 2020). They

include pixel- and object-based methods. The ground

truth data in the BBBC039v1 dataset are used as ref-

erence (R) for the created segmentations (S).

5.1 Pixel-based Metrics

Pixel-based evaluation can be obtained through cal-

culation of the Rand Index (RI) (Rand, 1971) and

the Jaccard Index (JI) (Jaccard, 1901). They consider

whether pixels of pairs of pixel in R or S are assigned

to the same or to different objects. The intensities in

S are called S

and S

and R

in R. All combi-

nations of pixels are considered as long as i 6= j. The

pairs are divided into the groups A to D according to

following scheme.

A: S

= S

∧ R

= R

C: S

= S

∧ R

6= R

B: S

6= S

∧ R

= R

D: S

6= S

∧ R

6= R

Groups A and D contain pixel pairs for which S

and R agree that pixels of the pair belong to the same

object or not. Conversely, groups B and C contain the

pairs for which there is no agreement in this respect.

The number of pairs in the corresponding groups are

denoted by a, b, c and d. Thus the RI is given by:

RI(R, S) =

a + d

a + b + c + d

a + d





. (2)

Here n denotes the total number of pixels in S and

R respectively. If S and R overlap completely, the in-

dex takes a value of 1. If there is less overlap, the

value is lower.

The above deﬁnition of a, b, c and d is also used

to calculate the JI:

JI(R, S) =

a + d

b + c + d

. (3)

The upper limit for JI depends on the number and

size of nuclei in relation to the image size. Thus, it

only allows a comparison between segmentations that

were created for the same data.

5.2 Object-based Metrics

For object-based metrics, reference objects in R must

be assigned to the objects in S. The object in R is de-

termined with which an object in S shares the most

pixels. On this basis, the maximum of the small-

est distance between two objects can be calculated,

which is called the Hausdorff Distance (HD). This can

be calculated as described by Coelho et al. (2009).

HD(R, S) = maxD(i) : S

6= R

(4)

Where D

is the minimum distance of a pixel i on

the object boundary to a pixel on the boundary of the

reference object. The mean value of all Hausdorff

Distances is used to evaluate an entire image.

Using D

, the Normalized Sum of Distances

(NSD) for each object can also be calculated as de-

scribed by Coelho et al. (2009) as follows.

NSD(R, S) =

∑

6= S

K ∗ D(i)]

∑

(5)

The index i iterates over all pixels of the union of

both objects. As for the HD, the mean value of all

distances in the image is calculated for the NSD of

the whole image.

The Error Counting Metrics (ECM) also belong to

the object-based evaluation methods and count Miss-

ing, Added, Merged and Split objects. They thereby

quantify errors that are intuitively identiﬁed by hu-

man observers (Coelho et al., 2009). For the calcu-

lation of the ECM, a list of assignments of objects in

S to objects in R is used and additionally a list of re-

verse assignments. Here, the background in S and R

represents a separate object. An assignment only hap-

pens if the number of common pixels is greater than

half the number of pixels of the object for which an

assignment is sought. Objects that are signiﬁcantly

larger in S than in R can thus be interpreted as Added

and those that are signiﬁcantly larger in R as Missing.

The four metrics are deﬁned as follows:

• Split: Number of objects in R assigned to more

than one object in S.

• Merged: Number of objects in S assigned to more

than one object in R.

• Added: Number of objects in S assigned to the

background in R.

• Missing: Number of objects in R assigned to the

background in S.

For the BBBC039v1 dataset, an alternative calcu-

lation of the assignments was also proposed, where

the intersection-over-union is calculated and the as-

signments are determined using a threshold (Caicedo

et al., 2019). In comparison the second method marks

objects that are marked as Added as Missing too.

This results in a substantially increased number of

Missing-errors. This is why the previously described

calculation is used in this work; besides, it is also used

in the ImmunePredict project before (Wirth et al.,

2020).

BIOIMAGING 2022 - 9th International Conference on Bioimaging

106

6 RESULTS

Following results were produced using the dataset de-

scribed in section 4. In order to quantify the seg-

mentation success, the evaluation metrics presented

in section 5 are used. In section 3 two pipeline ver-

sions were presented. In order to improve readability,

the version without distance transformation will be re-

ferred to as ’version 1’ and the one with as ’version 2’.

6.1 Selection of the β Parameter

The parameter β (see (1)) plays a crucial role in the

segmentation process. Based on the metrics presented

in section 5 the ratio of pixel- to object-based metrics

(6) is presented as a decision criterion for selection of

β.

Ratio = 10 ∗

JI + RI

HD + NSD +

∑

ECM

(6)

The selection is done by using the validation hold-

out set. Figure 2 shows the average results of version

2 for different β values. The results of version 1 are

very similar, so that the same beta value was selected.

The β values to consider lie within the range of 10 to

200 with equidistant spacing.

The RI and JI initially rise sharply with an in-

crease in the β value and then decline slightly but

steadily, starting from a value of around 50. The

largest average HD is measured for the smallest β

value. After which the value drops sharply. Then it

rises slightly, but falls roughly from a β value of 90.

The NSD values behave similarly to the HD values for

low β values. As the values increase, NSD remains

low for longer and then increase slightly.

The ECM show different trajectories. The av-

erage number of Split-errors is consistently lowest

and almost remains at the same level. The number

of Added-errors is just above this, whereby a falling

trend can be observed up to a β value of 100. For the

Merged-error the numbers decrease slightly with the

increase of β and are more than twice as high as for

the Added-error most of the time. The Missing-error

is the most frequent error for both versions. Its aver-

age number decreases up to a β value of 50 and then

increases with higher values.

The course of the ratio between pixel- and object-

based metrics emerges from the described courses

for the evaluation metrics. For version 1, these val-

ues are consistently lower than those for version 2

because the latter achieves mostly higher values for

pixel-based and mostly lower values for object-based

metrics. The optimal value for β corresponds to the

maximum of the mentioned ratio. For a comparison

of the two versions with the CellProﬁler pipeline (CP

version) the value for β gets ﬁxed to 50.

6.2 Pipeline Comparison

Table 1 compares the average results of the version

1, version 2 and CP version. The values of the pixel-

based metrics are similar for all versions. The CP ver-

sion has the lowest RI, but a higher JI. Both the HD

and NSD are lowest for version 2, whereby version 1

and 2 achieve similar values for these metrics.

Differences between our proposed versions are

noticeable for the ECM. Except for the number of

Split-errors, the values of version 2 are lower than

those of version 1. The CP version causes fewer

Missing-errors compared to the other two versions,

but more than three times as many Added-errors. The

number of Merged- and Split-errors is also highest

for the CP version. Despite fewer Missing-errors, the

sum of all ECM for the CP version is the highest.

This is also reﬂected in the lower ratio value for

the CP version. Version 2 achieves the best metric

scores most of the time, what results in the highest

ratio.

Figure 3 shows example results on the test dataset

for version 1, version 2 and CP version in compari-

son to the ground truth. Segmented nuclei are colored

randomly to facilitate the differentiation of touching

cells. In general, the results for the ECM can be de-

tected. In the segmentations of the CP version, for ex-

ample, more Merged-errors can be recognized. Com-

pared to the ground truth, the missing nuclei can also

be identiﬁed, which are the cause of the high Missing-

error values mentioned.

7 DISCUSSION

As described in section 4, the ground truth used for

evaluation is a manual segmentation. Therefore, the

dataset may be affected by intra- and inter-observer-

variability. We will not analyze these effects further.

The effect of the β parameter (see (1)) on the re-

sulting segmentation causes the trajectories in Figure

2. For higher values, smaller weights between neigh-

boring nodes result in small objects, which leads to in-

crease in NSD, decrease in RI and JI but less Merged-

errors. In return, there might be more Missing-errors.

Smaller β values mean higher weights between nodes

and a signiﬁcant increase in object size, resulting in

a high HD and number of Added-errors. A suitable

choice of parameter balances these effects. During the

development of the pipeline, β was set to 130 (default

value of scikit-image-method). The selection of the

Random-walk Segmentation of Nuclei in Fluorescence Microscopic Images with Automatic Seed Detection

107

Figure 2: Average results of version 2 on the validation dataset for Rand and Jaccard Index, Hausdorff Distance, Normalized

Sum Of Distances, Error Counting Metrics and the ratio between pixel- and object-based metrics for β values from 10 to 200.

Table 1: Results of pipeline version 1 and 2 (β=50) and the CellProﬁler pipeline on test dataset. Results are the average

values of the Rand and Jaccard Index, Hausdorff Distance, Normalized Sum Of Distances and Error Counting Metrics (Split,

Merged, Added, Missing) as well as the ratio between pixel- and object-based metrics. Best results are marked in gray.

Pixel-based Object-based

Version RI JI HD NSD Split Merged Added Missing Ratio

1 0.9778 4.1928 4.7973 0.0684 0.7000 5.7600 1.4400 6.3000 2.7120

2 0.9788 4.1947 4.6611 0.0645 1.1000 5.3200 1.4000 5.7400 2.8293

CP 0.9701 4.2115 5.1847 0.0946 1.3400 6.8600 5.0200 4.3800 2.2648

parameter could be done automatically by determin-

ing the maximum of the ratio of pixel- to object-based

metrics. This leads to β = 50 for the dataset used. As

can be seen in table 1, the ﬁxed value turns out to be

a suitable setting for the whole test set on the aver-

age. The values for pixel-based metrics differ only

slightly between the compared versions. In contrast,

the object-based metrics clearly indicate that our pro-

posed pipeline achieves superior performance. This is

also conﬁrmed by the overall higher ratio values. Be-

fore using the segmentation pipeline on a new dataset,

especially with images from other modalities, it will

still be necessary to redeﬁne the β value and poten-

tially adjust the preprocessing.

Also other segmentation pipelines were evaluated

on the BBBC039v1 dataset. Compared to deep learn-

ing methods as presented in Caicedo et al. (2018),

the proposed pipeline perform a little worse in terms

of Merged- and Split-error. Missing-errors are again

lower for our pipeline, but this may also be due to

the different calculation of the JI. Liu et al. (2021)

have also evaluated several deep learning methods us-

ing this dataset. Their evaluation metrics differ from

those in this paper, which makes a direct comparison

difﬁcult.

The results of the random-walk algorithm signif-

icantly depend on the seed placement. For optimal

segmentation, one seed must be set at a suitable lo-

cation for each nucleus. Because expert knowledge

to set seeds involves a great deal of effort we pro-

posed an automatic approach, described in section

3. Approaches for automatic seed determination for

random walk have already been explored for speciﬁc

problems, such as tumor or liver segmentation, and

different modalities (e.g. 3D CT, 3D MRI) (Wang

et al., 2019). Intensity values of pixels are often used

for seed determination.

We use intensity values to distinguish nuclei from

the background in ﬂuorescence microscopy images.

Due to a combination of thresholds and local max-

ima, appropriate seeds can be selected. By using the

distance transformation, additional information about

the shape of the objects is included. From the results

shown in table 1 it can be concluded that the proposed

seed detection methods are suitable for this setting.

Since the two proposed versions differ only in the use

of a distance transformation before seed detection, it

can be concluded that such a transformation improves

seed detection in cell nuclei images. Yet, it should be

noted that it causes more Split-errors. This type of

error occurs more often for nuclei that have an elon-

gated shape and are notched in the middle. For the

present dataset, this effect occurs only sporadically.

When using the pipeline with other data or methods,

the detection method should then be selected accord-

ing to the prevailing nuclei shapes.

For some images in the dataset segmentation is

particularly challenging. One example are images

BIOIMAGING 2022 - 9th International Conference on Bioimaging

108

Ground truth version 1 version 2 CellProﬁler

Figure 3: Example results for version 1, version 2 and CP version using images of the BBBC039v1 dataset compared with

the ground truth. Cropped images are shown in which the objects are randomly coloured.

that are highly noisy or show artifacts. For the former,

the ground truth for this image is empty and shows

no nuclei. Therefore results for such images are not

included in the evaluation because neither the calcu-

lation of the HD nor the NSD would be possible, as

reference objects are needed for the calculations of

both metrics. This affects two images in training set

and one image in validation set.

Due to different phenotypes, the sizes of the nuclei

can vary greatly. In order not to determine seeds for

artifacts in the image, small objects are ﬁltered out

as described in section 3. The downside of this ap-

proach is that no seeds are determined for a large part

of the micronuclei. These nuclei are either segmented

as part of the background or merged with nuclei in

the neighborhood. The hole inside toroidal nuclei can

also be a challenge for segmentation method because

a strong intensity gradient exists between the hole and

the rest of the nucleus. Due to the random-walk algo-

rithm’s property of creating only smooth segmenta-

tions, the pipeline is robust to these morphologies as

long as only one seed is set per nuclei.

Additionally, the shapes created by touching nu-

clei can inﬂuence the segmentation. Smaller nuclei

can form structures that resemble shapes of larger nu-

clei. After a distance transformation, no adequate

number of seeds can be found because only the nuclei

that have the greatest distance to the background re-

ceive a seed, resulting in more Merged- and Missing-

errors. If the contrast is very low, even cutting out the

transformation only improves the results slightly. The

same effect on ECM applies to images with strong

artifacts, which cause a strongly reduced contrast in

both bright and dark areas. In addition, the number

of Added-errors is higher because some objects are

signiﬁcantly larger than in the ground truth.

The runtime of methods based on the random-

walk is known to depend on the speed with which

the linear system of equations can be solved (Wang

et al., 2019). Our background seed detection can save

runtime because many background pixels are already

labeled. Since the number of these pixels varies, the

variance of the running time per image remains high.

This yields in a runtime of around 3 minutes (64 Bit

Windows, i5-10400 2.90GHz, 16GB RAM) for the

whole test dataset.

Throughout the pipeline, different values (e.g.

maximum object size and minimum distance of seeds)

must be set. These values should be selected accord-

ing to the available metadata. Since different magni-

ﬁcations can be used for microscopy images, a calcu-

lation, e.g. based on the resolution, is not useful.

8 CONCLUSION

In the context of this paper, two versions of a pipeline

were developed which use the random-walk algo-

rithm to segment nuclei. The versions differ in their

seed detection, as the second version uses a distance

transformation. We propose a way of determining the

free parameter of the random walk automatically by

using the ratio of the evaluation metrics.

For a benchmark dataset with ﬂuorescence mi-

croscopy images, both versions achieve good results

with respect to different evaluation metrics. These re-

sults and the comparison with the CP pipeline show

that the developed pipeline is suitable for segment-

ing ﬂuorescence microscopy images of nuclei. Es-

pecially for object-based evaluation metrics, the two

developed versions consistently reliably achieve good

values. The pipeline is robust against different mor-

phologies of the cell nuclei. However, micronuclei

are often missing in the segmentation results because

corresponding seeds are not generated.

Many typical challenges of a medical context are

included in the dataset used. This allows an evalua-

tion of the pipeline in terms of its use in such a setting.

The heterogeneity of the image data poses a challenge

Random-walk Segmentation of Nuclei in Fluorescence Microscopic Images with Automatic Seed Detection

109

for segmentation algorithms and seed detection. The

latter has a great inﬂuence on the quality of the seg-

mentation. The use of local maxima as seeds and the

developed method to determine a background seed is

suitable for the present dataset. The results can be

further improved by a preceding distance transforma-

tion, but results in more Split-errors. However, fur-

ther evaluations on other data sets are needed to make

a more general statement on performance.

Following aspects can also be content of further

research: An extension of the range of intensity val-

ues when handling the images to use the full 16 bits of

the TIFF images instead of 8 bits. Improving the run-

time by using further preprocessing or other solvers

for the system of equations. It is also interesting to

explore how the pipeline can be used for 3D data.

The results of this paper can further serve as a ba-

sis for an integration of the random-walk algorithm

in more sophisticated pipelines based on deep learn-

ing (e.g. as post-processing). We are planning fur-

ther evaluation and testing of this kind of integration.

In addition, the developed pipeline is suitable to pro-

vide reference benchmark results for the evaluation of

other segmentation methods.

ACKNOWLEDGMENTS

This work has been supported by the European Union

and the federal state of North-Rhine-Westphalia

(EFRE-0801303).

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