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DatasetsIn this study, datasets from two fundamentally different real-world ecological use cases were employed. The 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 ringsThe first dataset consists of 3585 microscopic images of otoliths (i.e., hearing 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 fish was measured, the sagittal otoliths were removed and microscopic images of two zoom levels ((10times 20) and (10times 10), depending on fish 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). Therefore, a stratified 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 validation set, which is used to estimate the model performance and optimise hyperparameters during training.Figure 6Distribution of the labels (i.e., number of post-settlement rings) of all images in the otolith dataset ((n=3585)).Full size imageAerial images of sealsThe 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 whenever seals were sighted, while flying at a fixed height of approximately 150m, using different 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 efforts. 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). Therefore, as with the otoliths, all 11,087 images were grouped into 20 bins according to their label (Fig. 7, panel A), after which five images were randomly selected from each bin for the test set. Second, images of sufficient quality and containing easily identifiable 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. The dimensions of those cropped images were preserved and, if required, the image-level annotation was modified accordingly. The resulting ‘seal subset 1’ only contains images with zero to 99 seals (Fig. 7, panel B). These 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 refinement was performed (see the section “Dealing with noisy labels: two-step label refinement” below).Figure 7Distribution 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)).Full size imageConvolutional neural networksCNNs are a particular type of artificial neural network. Similar to a biological neural network, where many neurons are connected by synapses, these models consist of a series of connected artificial 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 filter) and each spatial input location and its surroundings. This 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 filter weights (i.e., neurons). After this convolution, an activation function is applied so that the final 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. The 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 convolutional filters per layer or larger filter sizes. A final layer usually projects the intermediate, high-dimensional outputs into a vector of size C (the number of categories) in the case of classification, 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, differentiable functions, the chain rule can be applied to also compute gradients for the intermediate, hidden layers and modify neurons therein backwards until the first layer. This 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 filters and layers).CNNs come in many layer configurations, 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. This 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 consequence, ResNets were the first models that could be trained even with many layers in series and provided a significant increase in accuracy.Model selection and trainingFor 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). These 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 efficiently, as it will already have learned how to recognise common recurring features, such as edges and basic geometrical patterns, which would have to be learned from zero otherwise. Therefore, pre-training reduces the required amount of training data significantly.Figure 8Schematic representation of the CNN used in this study. The classification output layer of the pretrained ResNet18 is replaced by two fully-connected layers. The model is trained with a Huber loss.Full size imageWe modified the ResNet architecture to perform a regression task. To do so, we replaced the classification output layer with two fully-connected layers that map to 512 neurons after the first layer and to a single continuous variable after the second layer23 (Fig. 8). Since the final 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). The Huber loss is more robust against outliers and is defined as follows:$$begin{aligned} {mathscr {L}}(y,{hat{y}})=frac{1}{n}sum _i^{n} z_i end{aligned}$$
(1)
where (z_i) is given by$$begin{aligned} z_i= {left{ begin{array}{ll} 0.5times (y_i-{hat{y}}_i)^2, &{}quad text {if } |y_i-{hat{y}}_i| More

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