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Counting using deep learning regression gives value to ecological surveys

Abstract and Figures

Many ecological studies rely on count data and involve manual counting of objects of interest, which is time-consuming and especially disadvantageous when time in the field or lab is limited. However, an increasing number of works uses digital imagery, which opens opportunities to automatise counting tasks. In this study, we use machine learning to automate counting objects of interest without the need to label individual objects. By leveraging already existing image-level annotations, this approach can also give value to historical data that were collected and annotated over longer time series (typical for many ecological studies), without the aim of deep learning applications. We demonstrate deep learning regression on two fundamentally different counting tasks: (i) daily growth rings from microscopic images of fish otolith (i.e., hearing stone) and (ii) hauled out seals from highly variable aerial imagery. In the otolith images, our deep learning-based regressor yields an RMSE of 3.40 day-rings and an R2 of 0.92. Initial performance in the seal images is lower (RMSE of 23.46 seals and R2 of 0.72), which can be attributed to a lack of images with a high number of seals in the initial training set, compared to the test set. We then show how to improve performance substantially (RMSE of 19.03 seals and R2 of 0.77) by carefully selecting and relabelling just 100 additional training images based on initial model prediction discrepancy. The regression-based approach used here returns accurate counts (R2 of 0.92 and 0.77 for the rings and seals, respectively), directly usable in ecological research.
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Counting using deep learning
regression gives value to ecological
surveys
Jeroen P. A. Hoekendijk1,2*, Benjamin Kellenberger3, Geert Aarts1,4,5, Sophie Brasseur4,
Suzanne S. H. Poiesz1,6 & Devis Tuia3
Many ecological studies rely on count data and involve manual counting of objects of interest, which is
time-consuming and especially disadvantageous when time in the eld or lab is limited. However, an
increasing number of works uses digital imagery, which opens opportunities to automatise counting
tasks. In this study, we use machine learning to automate counting objects of interest without the
need to label individual objects. By leveraging already existing image-level annotations, this approach
can also give value to historical data that were collected and annotated over longer time series
(typical for many ecological studies), without the aim of deep learning applications. We demonstrate
deep learning regression on two fundamentally dierent counting tasks: (i) daily growth rings from
microscopic images of sh otolith (i.e., hearing stone) and (ii) hauled out seals from highly variable
aerial imagery. In the otolith images, our deep learning-based regressor yields an RMSE of 3.40 day-
rings and an
R2
of 0.92. Initial performance in the seal images is lower (RMSE of 23.46 seals and
R2
of
0.72), which can be attributed to a lack of images with a high number of seals in the initial training set,
compared to the test set. We then show how to improve performance substantially (RMSE of 19.03
seals and
R2
of 0.77) by carefully selecting and relabelling just 100 additional training images based on
initial model prediction discrepancy. The regression-based approach used here returns accurate counts
(
R2
of 0.92 and 0.77 for the rings and seals, respectively), directly usable in ecological research.
Ecological studies aim to unravel the interactions between organisms and their environment at various spatial
scales. In order to quantify these intricate relationships, many ecological studies rely on count data: for instance,
during animal surveys, individuals are counted to estimate and monitor population size1,2 or to predict the
spatial distribution of animals3. On smaller scales, counting physical traits is widely used in, for example, plant
phenotyping, where the number of leaves of a plant is a key trait to describe development and growth4,5. e
usage of count data in ecology is also common on microscopic scales, for example to estimate the age of sh by
counting daily growth rings that are visible in otoliths (i.e., hearing stones)6,7.
Irrespective of the scale, counting objects of interest can be tedious and time-consuming, especially when
objects occur in large numbers and/or densities (e.g., wildlife that clusters in colonies8), when they overlap (e.g.,
leaves of plants4,5), or when they are less well-dened and cryptic (e.g., otolith rings6). Historically, many of these
traits were counted directly by eye. Later, objects of interest were photographed, which allowed for optimisation of
the time in the eld (or lab) and repeatability of the counts. Nowadays, many studies increasingly take advantage
of digital photography, allowing for more ecient ways of archiving the data. Crucially, these archived images
can now potentially be used for digital processing and automated counting.
To this end, recent ecological studies have shown promising potential of using computer vision to count
objects of interest from digital imagery9,10: they employ Machine Learning (ML) models, which are trained
on a set of manually annotated (labelled) images to learn to recognise patterns (e.g., colours and shapes), and
eventually objects, in those training images. Once trained, these ML models can be used to automatically recog-
nise similar patterns in new images and perform tasks like species classication, animal detection, and more11.
OPEN
1NIOZ Royal Netherlands Institute for Sea Research, 1790AB Den Burg, The Netherlands. 2Wageningen University
and Research, 6708PB Wageningen, The Netherlands. 3Ecole Polytechnique Fédérale de Lausanne (EPFL),
1950 Sion, Switzerland. 4Wageningen Marine Research, Wageningen University and Research, 1781AG Den
Helder, The Netherlands. 5Wageningen University and Research, Wildlife Ecology and Conservation Group, 6708
PB Wageningen, The Netherlands. 6Groningen Institute of Evolutionary Life Sciences, University of Groningen,
9700 CC Groningen, The Netherlands. *email: jeroen.hoekendijk@nioz.nl
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Most successful ML models belong to the family of Deep Learning (DL)12, in particular Convolutional Neural
Networks (CNNs)13.
Most ecological studies that use computer vision for counting apply CNNs designed for object detection1416.
ese object detectors are trained on images in which every object of interest is annotated individually, most
commonly by a bounding box drawn around the object, or a location point at its centre. Alternatively, objects of
interest can be counted using detectors based on image segmentation17, which require even more extensive anno-
tations, as every pixel in the image must be labelled. Annotating training images for object detection and image
segmentation can therefore be labour-intensive, especially for images where object counts are high. Hence, this
could potentially undermine the time (and cost) reduction advantage promised by ML models in the rst place.
An alternative is to instead annotate training images with a single value that represents the number of objects
in an image. ese image-level annotations pose signicantly reduced annotation time and can directly be used to
train regression-based CNNs. Perhaps more importantly, image-level counts are an oen used annotation format
in ecological studies, for example in cases where objects are manually counted from digital imagery over longer
time series. Furthermore, image-level annotations provide a viable solution for scenarios that are complicated
to annotate otherwise, such as for overlapping objects5, complex and atypically shaped objects like concentric
rings18, or continuous variables like an individual’s size or age19.
In this study we highlight the value of regression-based CNNs for ecological studies. We present a relatively
lightweight DL model for counting objects in digital imagery and evaluate it on two fundamentally dierent real-
world datasets, that were originally collected without the aim of training DL models. e rst dataset consists of
microscopic images of plaice (Pleuronectes platessa) otoliths (i.e., hearing stones) in which concentric rings are
visible. ese rings represent daily growth layers and are used to estimate the age of the sh to reconstruct egg
and larval dri and calculate the contribution of various spawning grounds to dierent settling areas6,7. Plaice
eggs and larvae are transported from their North Sea spawning grounds towards the coast of the North Sea and
into the Wadden Sea (pelagic phase), where they settle (benthic phase). e transition of the pelagic phase to
the benthic phase is visible in the otoliths. For this application, only the post-settlement benthic phase growth
rings (visible directly aer the pelagic phase centre) are counted. e already existing image-level annotations
in this dataset are of high quality and are directly usable for DL applications. e second dataset consists of
aerial images of grey seals (Halichoerus grypus) and harbour seals (Phoca vitulina) hauled out on land, which
are collected from an aircra using a hand-held camera during annual surveys monitoring population size and
distribution8. ese images are highly variable in light conditions, distance towards the seals, focal length and
angle of view. For this second dataset, some of the existing image-level annotations were not directly usable for
DL applications (see “Methods” section). Instead of recounting the seals and correcting the annotations for all
images in this dataset, we propose a multi-step model building approach to handle scenarios where the quality
of existing image-level annotations is insucient to train a CNN. is approach can also be used to adapt the
CNN to dataset variations that appear over time or with new acquisitions conditions.
ese two real-world applications show that regression-based CNNs have the potential to greatly facilitate
counting tasks in ecology. ey allow researchers to reassign valuable resources and scale up their surveying
eort, while potentially leveraging existing image-level annotations from archived datasets directly for the auto-
mation of counting.
Results
For the results reported in this section, we used a pre-trained ResNet-18 CNN20 and modied it for the task of
regression. Aer various experiments with other architectures and hyperparameters (Supplementary S1), we
found that this relatively lightweight (i.e., shallow) ResNet-18, trained with a Huber loss function21 and with the
largest possible batch size (limited by hardware,
n=84
and
n=100
images for the otolith and seal application,
respectively) gave the best performance on the validation set, for both the seal and otolith ring counting applica-
tion. Details on the CNN architecture selection and training are provided in the “Methods” section.
Otolith daily growth rings from microscopic images. For the otolith growth ring counting applica-
tion, the regression CNN was trained on 3465 microscopic images of otoliths. e results are provided inFig.1.
Here, the predicted counts on the randomly selected test set (
n=120
) are plotted against the labels (i.e., the
manual counts of the post-settlement growth rings). e CNN achieved an
R2
of 0.92, an RMSE of 3.40 day-rings
and an MAE of 2.60 day-rings (Table1), which corresponds to an average error of
9.9%
.
Hauled out seals from aerial images. For the seal counting application, the existing image-level annota-
tions were of insucient quality (see “Methods” section) and manual recounting was required before training
the CNN. Instead of recounting all the seals and correcting the annotations for all 11,087 aerial images in the
main dataset, we applied a multi-step model building approach. First, two smaller subsets from the main dataset
were selected, recounted and used for (i) a stratied random test set (
n=100
) and for (ii) training/validation
(named ‘seal subset 1’,
n=787
) (see “Methods” section). Unlike the stratied random test set (which reects
the full distribution of available annotations from the main dataset), the images in ‘seal subset 1’ were selected
(visually) for their high quality, which led to an under-representation of images with a high number of seals
(which were generally of poorer quality). is rst step greatly reduced the number of images that needed to be
recounted and relabelled. Figure2 (open dots, panels A and B) illustrates the predicted counts versus the real
counts of the resulting model. is Step 1 model achieved an
R2
of 0.72, an RMSE of 23.46 seals and an MAE of
10.47 seals on the seal test set (Table1). e next step allowed us to focus on images where the CNN was most
incorrect. Here, the Step 1 model was used to predict counts on the 10,200 remaining images from the main
dataset (that still include noisy labels). To train the model further, the images from the main dataset in which
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the number of seals was most overestimated (
) and most underestimated (
n=50
) with respect to the
original (noisy) labels were selected (‘seal subset 2’), manually recounted and relabelled and used to supplement
‘seal subset 1’. By further tuning the model using this extended training/validation set, the performance on the
test set improved (Fig.2, solid dots, panel A and C), with the model achieving an
R2
of 0.77, an RMSE of 19.03
seals and an MAE of 8.14 seals (Table1). is can be attributed mostly to improved predictions for images with
a higher number of seals. Experiments with a random sampling on the whole distribution of labels (i.e., 787
images randomly selected from ‘seal subset 1’ and ‘seal subset 2’ combined, including images with a high num-
ber of seals) did not lead to better performance of the Step 1 model (see Supplementary S3). us, the two-step
strategy allowed us to signicantly improve the model performance on the seals with only 100 images to be re-
annotated, thereby reducing labelling eorts to a minimum.
In the test set, a total of 3300 seals were annotated. With our multi-step approach, the predicted total number
of seals on the test set increased from 2372 (71.9% of the total) to 2986 (90.5%) for the Step 1 and Step 2 model,
respectively.
Visualising counts. Class activation maps (CAM)22,23 of images from the test sets were used to further
examine model performance. ese heatmaps represent the regions of the original image that contributed the
most to the nal prediction of the CNN. e heatmaps of the otolith images (Fig.3) were less informative than
those of the the seal images. However, they illustrate that areas with more contrasting post-settlement rings were
highlighted, while the accessory growth centre (containing pre-settlement growth rings that are not targeted by
this application) did not seem to contribute to the prediction (i.e., it remained darker). is underlines that the
model is indeed focusing on the task of counting post-settlement growth rings.
For most seal images, the heatmaps show that the regions containing seals contributed the most to the nal
prediction. Unlike the cryptic concentric otolith rings, seals are clearly picked up by the model, according to
the heatmaps (Fig.4).
Figure1. Numerical results on the otolith test set (
n=120
), where the labels (i.e., manual counts of post-
settlement growth rings) are plotted against the predicted counts. e dotted line corresponds to the optimum
y=x
.
Table 1. Numerical performance of the proposed method on the randomly selected test sets for both
applications. e performance of the seal counting application increased aer ne-tuning the Step 1 model
using ‘seal subset 2’ (Step 2 model).
Otolith Seals
Rings Step 1 model Step 2 model
R2
0.92 0.72 0.77
RMSE 3.40 23.46 19.03
MAE 2.60 10.47 8.14
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Discussion
e regression-based CNN presented here performed well when trained on the two fundamentally dierent
datasets. is was achieved without making any modications to the architecture of the CNN between the two
cases, except for training hyperparameters like the learning rate and number of epochs (see “Methods” section).
By automating the counting tasks, the processing time of newly acquired images is dramatically reduced: pro-
cessing 100 images using our trained CNN takes less than a minute, while manual processing the same amount
of images is estimated to require at least one hour for the seals and three hours for the otoliths.
e accuracies reported here are directly usable in ecological research. For harbour seals, a correction factor
of 0.68 is routinely used to extrapolate the survey counts to a population size estimate24. e 95% condence
interval of this correction factor is [0.47,0.85]. In other words, the uncertainty in the population size estimate is
minus 21% or plus 17%, which is substantially larger than the 9.5% underestimate in the total predicted counts
of our Step 2 model. For the ring counting application, a coecient of variation between multiple human experts
was not available for daily growth rings of plaice. However, these are reported for yearly growth rings of Green-
land halibut as 12%25 and 16.3%26, which is higher than the reported 9.9% average error obtained by our deep
counting regression approach.
e two datasets feature dierent challenges regarding both the quality of the existing annotations and the task
complexity. In the case of the otoliths, the existing annotations were of good quality and could be used directly
to train the model. ese image-level annotations provide a solution to label the complex concentric growth
rings, which would be extremely dicult to annotate using other approaches, such as bounding boxes. A DL
regression-based approach was applied in previous research to count otolith growth rings18, which achieved a
higher accuracy on their test-set (MSE of 2.99). However, the tasks considered in that study were radically dier-
ent from ours: in their paper, Moen and colleagues18 considered year rings, which are less cryptic than the post
settlement day rings considered in this paper. Furthermore, our model was trained with fewer images (
n=3585
instead of
n=8875
), to make predictions on a wider range of counts (1 to 63 day-rings instead of 1 to 26 year-
rings). Finally, we evaluated the performance using a stratied random test set, which covers the ensemble of
Figure2. Numerical results on the seal test set (
n=100
), where the labels (i.e., the manual counts of hauled
out seals) are plotted against the predicted counts. e black dotted lines resemble
y
=
x
. (A) e accuracy
of the model trained on ‘seal subset 1’ (white dots) strongly improved aer ne-tuning using training subset 2
(black dots). (B,C) Zoomed in (range 0-30) on predicted counts made by the Step 1 model (B) and the Step 2
model (C).
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the distribution of possible values, while Moen and colleagues used a non-stratied test set, therefore reducing
the number of occurrences of rare out-of-distribution cases in the test set.
In the case of the seals, the counting task was complex due to the high variability of the images (e.g., light-
ing conditions, distance from the seals and angle of view). Additionally, some of the existing count labels were
not directly usable for training a CNN (see “Methods” section). However, this provided an opportunity to
Figure3. Examples of images (le) and CAMs (right), with good performance from the ring test set.
Figure4. Examples of images (le) and CAMs (right), with good performance from the seal test set. Notice
that in the top example some birds are visible (yellow dotted line), which are not counted by the model, which
has specialised on seals.
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demonstrate the use of an iterative approach, in which the required re-annotation eorts could be minimised
and focused on images where the model performed poorly. e CNN was rst trained using only a subset
containing recounted high quality images (‘seal subset 1’). As is common among DL applications, the resulting
Step 1 model performed relatively poorly when it needed to make predictions that fell outside the range of the
training images. is was the case for images in which a high number of seals were visible and/or when the seals
appeared smaller (i.e., were photographed from a larger distance or a smaller focal length was used). e poor
performance on these type of images could be attributed to ‘seal subset 1’ containing only images with clearly
visible seals, ranging from zero to 99 individuals (see “Methods” section). By using the Step 1 model predic-
tions to guide the selection of images that need to be reviewed, a relatively small number of images (‘seal subset
2’) was selected from the remaining images in the main database, to supplement ‘seal subset 1’. is multi-step
approach allows to focus on images with a large potential for improvement for the Step 2 model: many of the
images in ‘seal subset 2’ contained a high number of seals and/or seals that appeared smaller. is approach can
therefore also be used to cope with dataset variations that appear over time or with new acquisitions conditions.
e high variability in the seal dataset (i.e., distance towards seals, angle of view and zoom level) suggests that
a regression-based approach based on this data can also provide solutions for scenarios where the objects of
interest move through a three-dimensional space (e.g., ocks of birds, schools of sh), provided that the model
is trained with a wide variety of input data covering the expected variations.
In contrast with an object detection approach, it is not possible to evaluate the predicted location of single
objects in our regression-based approach, as the predictions are given as image-level counts. However, by using
CAMs as presented here, model decisions can be visualised and used to evaluate the model performance in more
detail. In case of the seals, these heatmaps were used to further compare the performance of the Step 1 and Step
2 model on the test set. e Step 2 model generally performed better, especially for images where seals appeared
smaller (e.g., Fig.5, case A). For some images however, the model predictions deteriorated. is was for instance
the case for an image with birds presents adjacent to the seals, which contributed to the predicted counts for
the Step 2 model (Fig.5, case B). For some images that were particularly dicult (e.g., due to blur or extremely
small seals), the Step 2 model remained unable to count seals adequately (Fig.5, case C).
For future applications, automated counts based on the regression approach presented here could poten-
tially be further improved by changing the survey design to have lower variability in the images. In the case of
the seals for instance, this could be obtained by photographing the seals from a more constant distance with a
single focal length, although in practice this might be challenging. For existing data sets, the model could also
deliberately be exposed to more appearance variability. is could for instance be done by resorting to un- or
semi-supervised domain adaptation routines27. is requires no or only a few extra annotated images but result
Figure5. Examples of CAMs for cases with unsatisfactory performance. e rst column shows the unedited
aerial images, where the red dotted line marks the area where the seals are visible. e second and third columns
show the heatmaps when predictions are made using the Step 1 and Step 2 model, respectively. For case (A)
(small seals) the performance increased, but is still unsatisfactory, as seals remain only partially detected. For
case (B) the performance decreased as birds (yellow dotted line) start to contribute to the predictions, while for
case (C) (blurry and extremely small seals) the performance was poor for both models.
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in more robustness of the model to the appearance variations inherent in the data. Alternatively, in cases such as
the seals, where many images remain unused due to noisy labels, the iterative approach presented in this study
could be repeated, which is expected to further improve the models performance.
In many computer vision disciplines, regression-based CNNs similar to the one employed here are com-
monly used for counting tasks, especially when the objects of interest occur in high densities and high numbers,
such as human crowds28,29 or buildings30. ey have also been used in some ecological applications, particularly
when the objects of interest are hard to annotate using bounding boxes, for instance in the case of overlapping
plant leaves5,31,32. Wildlife counting is a domain that is typically addressed with spatially explicit object detection
approaches14,15. Few other works have addressed this task using regression-based CNNs33,34, but they either had
no explicit focus on wildlife detection34 or used it to approximate spatial locations33. Nonetheless, proceeding
with a regression approach permits to process surveys where only global counts are provided, rather than precise
annotations of individuals that would be required by object detection approaches. But even in the presence of
individual annotations, the regression approach remains competitive in terms of nal counts: when compared
to a traditional deep object detection approach (Faster R-CNN35) on a manually annotated subset of the seals
dataset, our regression approach remained more accurate (details in Supplementary S2). Furthermore, it took
approximately one hour to obtain the image-level annotations required to train the regression-based CNN,
while it took over 8 hours to create the individual bounding boxes required to train the Faster R-CNN model.
Our study illustrates how a relatively lightweight regression CNN can be used to automatically count objects
of interest from digital imagery in fundamentally dierent kinds of ecological applications. We have shown that it
is well-suited to count wildlife (especially when individuals occur in high densities) and to count cryptic objects
that are extremely dicult to annotate individually. Previous ecological studies have shown that by automating
detection tasks, time and resources can be reassigned, allowing for an increase in sampling eort14. By using
annotations at the image-level, labelling eorts and costs can be reduced. Finally, a unique advantage of using
a regression-based approach is that it has the potential to leverage already existing labels, collected without the
aim of DL applications, thereby reducing labelling eorts and costs to zero.
Methods
Datasets. In this study, datasets from two fundamentally dierent real-world ecological use cases were
employed. e objects of interest in these images were manually counted in previous studies2,8,36,37, without the
aim of DL applications.
Microscopic images of otolith rings. e rst dataset consists of 3585 microscopic images of otoliths (i.e., hear-
ing stones) of plaice (Pleuronectes platessa). Newly settled juvenile plaice of various length classes were collected
at stations along the North Sea and Wadden Sea coast during 23 sampling campaigns conducted over 6 years.
Each individual sh was measured, the sagittal otoliths were removed and microscopic images of two zoom
levels (
10 ×20
and
10 ×10
, depending on sh length) were made. Post-settlement daily growth rings outside
the accessory growth centre were then counted by eye6,7. In this dataset, images of otoliths with less than 16 and
more than 45 rings were scarce (Fig.6). erefore, a stratied random design was used to select 120 images to
evaluate the model performance over the full range of ring counts: all 3585 images were grouped in eight bins
according to their label (Fig.6) and from each bin 15 images were randomly selected for the test set. Out of the
remaining 3465 images, 80% of the images were randomly selected for training and 20% were used as a valida-
tion set, which is used to estimate the model performance and optimise hyperparameters during training.
Aerial images of seals. e second dataset consists of 11,087 aerial images (named ‘main dataset’ from now
onwards) of hauled out grey seals (Halichoerus grypus) and harbour seals (Phoca vitulina), collected between
2005 and 2019 in the Dutch part of the Wadden Sea2,36. Surveys for both species were performed multiple times
each year: approximately three times during pupping season and twice during the moult8. During these periods,
seals haul out on land in larger numbers. Images were taken manually through the airplane window when-
Figure6. Distribution of the labels (i.e., number of post-settlement rings) of all images in the otolith dataset
(
n=3585
).
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ever seals were sighted, while ying at a xed height of approximately 150m, using dierent focal lengths (80-
400mm). Due to variations in survey conditions (e.g., weather, lighting) and image composition (e.g., angle of
view, distance towards seals), this main dataset is highly variable. Noisy labels further complicated the use of this
dataset: seals present in multiple (partially) overlapping images were counted only once, and were therefore not
included in the count label of each image. Recounting the seals on all images in this dataset to deal with these
noisy labels would be a tedious task, compromising one of the main aims of this study of reducing annotation
eorts. Instead, only a selection of the main dataset was recounted and used for training and testing. First, 100
images were randomly selected (and recounted) for the test set. In the main dataset, images with a high number
of seals were scarce, while images with a low number of seals were abundant (Fig.7, panel A). erefore, as with
the otoliths, all 11,087 images were grouped into 20 bins according to their label (Fig.7, panel A), aer which
ve images were randomly selected from each bin for the test set. Second, images of sucient quality and con-
taining easily identiable were selected from the main dataset (and recounted) for training and validation, until
787 images were retained (named ‘seal subset 1’). In order to create images with zero seals (i.e., just containing
the background) and to remove seals that are only partly photographed along the image borders, some of these
images were cropped. e dimensions of those cropped images were preserved and, if required, the image-level
annotation was modied accordingly. e resulting ‘seal subset 1’ only contains images with zero to 99 seals
(Fig.7, panel B). ese 787 images were then randomly split in a training (80%) and validation set (20%). In
order to still take advantage of the remaining 10,200 images from the main dataset, a two-step label renement
was performed (see the section “Dealing with noisy labels: two-step label renement” below).
Convolutional neural networks. CNNs are a particular type of articial neural network. Similar to a
biological neural network, where many neurons are connected by synapses, these models consist of a series of
connected articial neurons (i.e., nodes), grouped into layers that are applied one by one. In a CNN, each layer
receives an input and produces an output by performing a convolution between the neurons (now organised into
a rectangular lter) and each spatial input location and its surroundings. is convolution operator computes a
dot product at each location in the input (image or previous layer’s output), encoding the correlation between
the local input values and the learnable lter weights (i.e., neurons). Aer this convolution, an activation func-
tion is applied so that the nal output of the network can represent more than just a linear combination of the
inputs. Each layer performs calculations on the inputs it receives from the previous layer, before sending it to the
next layer. Regular layers that ingest all previous outputs rather than a local neighbourhood are sometimes also
employed at the end; these are called “fully-connected” layers. e number of layers determines the depth of the
network. More layers introduce a larger number of free (learnable) parameters, as does a higher number of con-
volutional lters per layer or larger lter sizes. A nal layer usually projects the intermediate, high-dimensional
Figure7. Distribution of the labels (i.e., number of seals) in (A) the seal main dataset (
n
=
11,087
), (B) ‘seal
subset 1’ (
n=787
) and (C) ‘seal subset 2’ (
n=100
).
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outputs into a vector of size C (the number of categories) in the case of classication, into a single number in
the case of regression (ours), or into a custom number of outputs representing arbitrarily complex parameters,
such as the class label and coordinates of a bounding box in the case of object detection. During training, the
model is fed with many labelled examples to learn the task at hand: the parameters of the neurons are updated
to minimise a loss (provided by an error function measuring the discrepancy between predictions and labels; in
our case this is the Huber loss as described below). To do so, the gradient and its derivative with respect to each
neuron in the last layer is computed; modifying neurons by following their gradients downwards allows reducing
the loss (and thereby improving model prediction) for the current image accordingly. Since the series of layers
in a CNN can be seen as a set of nested, dierentiable functions, the chain rule can be applied to also compute
gradients for the intermediate, hidden layers and modify neurons therein backwards until the rst layer. is
process is known as backpropagation38. With the recent increase of computational power and labelled dataset
sizes, these models are now of increasing complexity (i.e., they have higher numbers of learnable parameters in
the convolutional lters and layers).
CNNs come in many layer congurations, or architectures. One of the most widely used CNN architecture
is the ResNet20, which introduced the concept of residual blocks: in ResNets, the input to a residual block (i.e.,
a group of convolutional layers with nonlinear activations) is added to its output in an element-wise manner.
is allows the block to focus on learning residual patterns on top of its inputs. Also, it enables learning signals
to by-pass entire blocks, which stabilises training by avoiding the problem of vanishing gradients39. As a con-
sequence, ResNets were the rst models that could be trained even with many layers in series and provided a
signicant increase in accuracy.
Model selection and training. For the otolith dataset, we employed ResNet20 architectures of various
depths (i.e., ResNet18, ResNet34, ResNet50, ResNet101 and ResNet152, where the number corresponds to
the number of hidden layers in the model, see Supplementary S1). ese ResNet models were pretrained on
ImageNet40, which is a large benchmark dataset containing millions of natural images annotated with thousands
of categories. Pre-training on ImageNet is a commonly employed methodology to train a CNN eciently, as it
will already have learned how to recognise common recurring features, such as edges and basic geometrical pat-
terns, which would have to be learned from zero otherwise. erefore, pre-training reduces the required amount
of training data signicantly.
We modied the ResNet architecture to perform a regression task. To do so, we replaced the classication
output layer with two fully-connected layers that map to 512 neurons aer the rst layer and to a single continu-
ous variable aer the second layer23 (Fig.8). Since the nal task to be performed is regression, the loss function
is a loss function that is tailored for regression. In our experiments we tested both a Mean Squared Error and
a Smooth L1 (i.e., Huber) loss21 (see Supplementary S1). e Huber loss is more robust against outliers and is
dened as follows:
where
zi
is given by
where
ˆy
is the value predicted by the model, y is the true (ground truth) value (i.e., the label) and n is the batch
size. Intuitively, the Huber loss assigns a strong (squared) penalty for predictions that are close to the target
(1)
L
(y,ˆy)=1
n
n
i
z
i
(2)
z
i=
0.5 ×(yi−ˆyi)
2
, if |yi−ˆyi|<
1
|yi−ˆyi|−0.5, otherwise
Figure8. Schematic representation of the CNN used in this study. e classication output layer of the
pretrained ResNet18 is replaced by two fully-connected layers. e model is trained with a Huber loss.
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value, but not perfect (i.e., loss value
<1
) and a smaller (linear) penalty for predictions far o, which increases
tolerance towards potential outliers both in prediction and target.
Computations were performed on a Linux server with four Nvidia GeForce GTX 1080 Ti graphics cards.
e CNNs were trained using the FastAI library23 (version 2.0.13) in PyTorch41 (version 1.6.0). FastAI’s default
settings were used for image normalisation, dropout42, weight decay and momentum23, and a batch size of 84
images was used for the otolith dataset. Whenever an image was used in a model iteration during training, a series
of transformations was applied randomly to it for data augmentation (including resizing to
1040 ×770
pixels,
random horizontal ips, lighting, warping, zooming and zero-padding). When using image-level annotations,
only limited degrees of zooming can be used, otherwise objects of interest might be cut out of the image, making
the image-level annotations incorrect. For the same reason, images were squeezed instead of cropped whenever
necessary to account for dierent image dimensions. Various Learning Rates (LR) and Batch Sizes (BS) were
evaluated (see Supplementary S1). A LR nder43 was used to determine the initial LR values, and FastAIs default
settings for discriminative LR were applied23. In discriminative LR, a lower LR is used to train the early layers of
the model, while the later layers are trained using a higher LR. For this purpose, our model was divided into three
sections (the pretrained part of the network is split into two sections, while the third section comprised the added
fully-connected layers), that each had a dierent LR (specied below) during training. Additionally, we applied
‘1cycle training’23,44. Here, training is divided into two phases, one where the LR grows towards a maximum, fol-
lowed by a phase where the LR is reduced to the original value again. Firstly, only the two fully-connected layers
added for regression (i.e., the third section) were trained for 25 epochs (of which the best performing 24th epoch
was saved) with an LR of
5e2
, while the rest of the network remained frozen. Aer this, the entire network was
unfrozen and all layers were further tuned using a discriminative LR ranging from
9e7
to
9e5
, for another
50 epochs, of which the best performing epoch was saved (50th epoch). e same model architecture, training
approach and hyperparameters were used for the seal images, with the following exceptions. e batch size was
100 and images were resized to to
1064 ×708
pixels. First, only the added layers were trained (analogue to the
rings), with an LR of
3e2
, for 50 epochs (of which the best performing 45th epoch was saved). Aer this, the
entire network was unfrozen and further tuned for 50 epochs (of which the best performing epoch, the 49th,
was saved), using a discriminative LR ranging from
3e4
to
3e2
.
For both the otolith and seal cases, the trained models were evaluated on their respective test sets (described
above). ese test sets represent unseen data that is not used during the training and validation of the model.
R2
, RMSE and MAE were used as performance metrics, and predicted counts were plotted against the labels.
Additionally, Class Activation Maps (CAM) were made to aid with interpreting the models predictions22,23.
Dealing with noisy labels: two-step label renement. In order to take advantage of the additionally
available noisy data during training, a two-step approach was employed that avoids the need to recount tens of
thousands of seals. By using the Step 1 model (trained using ‘seal subset 1’) predictions, an additional 100 images
were selected (and recounted) from the remaining main dataset (see “Results” section). For 35 images, the seals
were not clearly identiable by eye (i.e., they appeared too small) and the image was discarded and replaced by
the next most poorly predicted image. ese resulting 100 images (named ‘seal subset 2’, Fig.7, panel C) were
expected to include cases with noisy labels, but also cases that were challenging for the model to predict (e.g.,
images with a high number of seals). Aer this, the entire model (i.e., all layers) was retrained using ‘seal subset
1’ supplemented with ‘seal subset 2’, randomly split in a training (80%) and validation set (20%), for an additional
50 epochs using the same hyperparameters as before, except for the LR. Various LR were evaluated and a dis-
criminative LR ranging from
1e5
to
1e3
gave the best performance on the validation set, in the 48th epoch.
Data availability
e data used in this study are open-source and publicly available. Code and data associated with this study can
be obtained at https:// doi. org/ 10. 25850/ nioz/ 7b. b0c.
Received: 18 August 2021; Accepted: 10 November 2021
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Acknowledgements
e authors would like to thank Peter Reijnders, André Meijboom, Hans Verdaat and Jessica Schop for their
help collecting the aerial seal images, Hans Witte and Henk van der Veer for their work on the otoliths and to
Dainius Masiliunas for his assistance with the server.
Author contributions
S.B. and S.P. collected the data, J.H., G.A., S.B., B.K. and D.T. conceived the experiments, J.H. and B.K. conducted
the experiments and analysed the results. All authors wrote and reviewed the manuscript.
Funding
is study was funded by Nederlandse Organisatie voor Wetenschappelijk Onderzoek (project ALWPP.2017.003).
Competing interests
e authors declare no competing interests.
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Additional information
Supplementary Information e online version contains supplementary material available at https:// doi. org/
10. 1038/ s41598- 021- 02387-9.
Correspondence and requests for materials should be addressed to J.P.A.H.
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... Linear regression models were examined to compare the Fiji and Ilastik counts as predictors of human counts. This analysis was performed in other biological studies that examined machine learning count accuracy versus human-performed counts [18]. However, when the residuals of the linear models were tested for this citrus phloem study, they did not meet the assumptions of linearity and homogeneity of variance. ...
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