1. Introduction

2. Thresholding

3. Deep Neural Networks

3.1. CNN (Convolutional Neural Network)

Convolutional Neural Networks (CNNs) are a type of model in the field of deep learning, particularly useful at processing data with a grid shape, such as images. Central to CNNs are convolutional layers, which exploit spatial information by capturing the local relationships among pixels through the use of filters. In a convolutional layer, traditional neuron weights are replaced with filters. These filters compute new values for each pixel by considering the local relationships with its neighbors. The architecture is designed to progressively abstract higher-level features from the raw input in the initial layers to more abstract representations in deeper layers, making CNNs particularly powerful for tasks like image classification.

Figure 1. Illustration of the convolutional operation, visualized through a 3x3 kernel applied to an input image, that produces a feature map highlighting detected patterns. This process, core of CNNs, enables the network’s to automatically learn spatial relationships of features [14].

Figure 1. Illustration of the convolutional operation, visualized through a 3x3 kernel applied to an input image, that produces a feature map highlighting detected patterns. This process, core of CNNs, enables the network’s to automatically learn spatial relationships of features [14].

3.2. Segmentation Models: An Overview

The standard CNN architecture can’t be directly used for image segmentation. In fact, as shown in Figure 2 the fully connected layers link the pooling layers to a 1D output, which loses spatial context. To retain the spatial context in the output layer, other segmentation specific architectures have been proposed in the literature. The Fully Convolutional Network (FCN) introduced in [15] utilizes pre-existing CNN architectures designed for classification tasks (such as AlexNet, VGG, etc.). These architectures are adapted into fully convolutional networks and their learned representations are transferred to the segmentation task through fine-tuning. FCNs introduced the idea of replacing fully connected layers with convolutional layers, to produce pixel-wise predictions for segmentation. The architecture consists of an encoder path, which downsamples the input image to extract features, and a decoder path, which upsamples the features to produce the segmentation map. FCNs have been effectively applied in tasks such as flood segmentation, as demonstrated in [16].

Figure 2. Abstract view of a CNN architecture for classification tasks. Following convolutional and pooling layers, the network typically ends with fully connected layers that integrate these learned features into predictions or classifications, outputting a one-dimensional array corresponding to the classes [14].

Figure 2. Abstract view of a CNN architecture for classification tasks. Following convolutional and pooling layers, the network typically ends with fully connected layers that integrate these learned features into predictions or classifications, outputting a one-dimensional array corresponding to the classes [14].

Figure 3. Architecture example of a CNN for image classification and its equivalent FCN architecture with the same backbone for semantic segmentation. KKCs = 4 refers to the number of output classes (channels) probabilities for pixel wise predictions. We can see that in the FCN, the fully connected layers are replaced by convolutions to produce pixel-wise predictions [17].

Figure 3. Architecture example of a CNN for image classification and its equivalent FCN architecture with the same backbone for semantic segmentation. KKCs = 4 refers to the number of output classes (channels) probabilities for pixel wise predictions. We can see that in the FCN, the fully connected layers are replaced by convolutions to produce pixel-wise predictions [17].

In 2015, a novel paper [18] proposed the U-Net architecture which builds upon the ideas introduced by FCNs but adds the concept of skip connections. The idea behind it is that each encoder and decoder layer is symmetrically linked with a skip connection, that is achieved by concatenating the output from encoding layers to corresponding decoding layers. The goal was to provide a more detailed segmentation mask by exploiting global and local features of an image. This concept, initially proposed in [18], was further reproposed a few months later by a new model architecture called ResNet (Residual Nets) [19]. ResNet builds upon the concept of skip connections from Unet [18] but approaches it from a different angle. ResNet [19] solves a common issue encountered in deep neural networks: as the network gets deeper with more layers, the gradient (used to update the weights based on the error) diminishes significantly during backpropagation, leading to difficulties in updating the weights of earlier layers. This is known as the gradient vanishing problem. Recent advances in segmentation combine the power of ResNet deep features extraction into the Unet Encoder, which significantly improve the segmentation performance. This hybrid architecture has been applied for sea-land optical segmentation in [20], demonstrating that replacing ResNet into the Unet architecture significantly improves feature representation. This enhancement, together with fully connected Conditional Random Fields (CRFs) as post-processing predictions refinement, leads to more accurate delineation of coastlines and better-preserved regions in sea-land segmentation tasks as shown in [20].

4. Unsupervised Models for Flood Segmentation

5. Novelty

6. Materials and Methods

6.1. Dataset Creation

The Copernicus Programme, through Sentinel satellites, provides free access to satellite data, including Sentinel-1 SAR data. Pre-processing steps are necessary to improve image quality. The article in [29] discusses the challenges and necessary steps involved in preprocessing Sentinel-1 Ground Range Detected (GRD) data. MMFlood [25] uses the Sentinel Hub API, which aggregates multiple satellite data, enabling real-time processing and access to specific AOIs within seconds, thus avoiding extensive preprocessing.

A significant challenge in building the training dataset is the precise and reliable delineation of flood areas, as most flooded pixels are usually selected manually or adjusted based on operator knowledge. The Sen1Floods11 dataset [24] comprises Sentinel-1 and Sentinel-2 data, with 446 labeled 512x512 chips covering 11 flood events, but it does not consider various flood types and relies on human intervention, introducing potential errors. MMFlood [25] uses the Copernicus Emergency Management Service (EMS) to retrieve flood delineations in vector files for their dataset, consisting of 8,522 labeled 512x512 patches from Sentinel-1, covering 95 flood events globally. EMS has operated since 2021, providing maps for environmental disasters based on a closed-source algorithm and then reviewed by humans, but their labels are not always accurate.

Following the approach in [25], we use the Sentinel Hub API to directly obtain satellite products. We then pair Sentinel-1 and Sentinel-2 images to create a new dataset, SAR-Optical, for training our model. Since the dataset only contains uni-temporal flood and permanent water patches, we create a new dataset derived from the MMFlood dataset [25], enhanced with pre-flood images, which we call MMFlood-CD (change detection). This will be used to qualitatively assess the model performance on flood events through change detection.

6.1.1. Images Acquisition and Preprocessing

With the use of Sentinel Hub API, we can specify the pre-processing steps directly in the parameters of the requests. In our experiments we use Ground Range Detected (GRD) imagery, which preserves signal amplitude while eliminating phase information and reducing speckle noise through multi-look processing [29]. All the images are provided with a spatial resolution of 20 m and a pixels spacing of 10 m, and have a 32-bit floating point precision. As per preprocessing steps, we apply calibrations and thermal noise removal as outlined in the standard workflow proposed in [29]. Moreover, we apply Radiometric Terrain Correction (RTC) and Orthorectification using the MapZen Digital Elevation Model to more accurately geocode the images. We purposely avoid applying speckle filtering, based on the hypothesis, aligned with the findings of [25], that CNNs models inherently possess the capabilities to smooth images to extract relevant information.

6.1.2. SAR-Optical

The SAR-Optical dataset contains paired SAR and Optical patches, and it is used to train the SAR model using the Optical ground truth. The image pairing was not straightforward, since it’s unusual to have both Optical and SAR images taken on the same day, we made sure that the Optical image acquisitions were taken within a maximum of three days after the flood event. This is a good compromise that allows a balanced number of samples while accounting for rapid changes in floods. Clouds may obstruct the regions of Interest (ROIs), therefore we selected only those that don’t have clouds and that have at least 0.01% of water pixels. The Optical ground truth is derived from the SCL layer contained in the Sentinel-2 L2A Optical product, provided directly by Copernicus. Their layer automatically classifies various land covers such as water, land, clouds, etc., and is consistently updated. We extracted only the water classification from this layer to generate a binary raster image that marks pixels as 1 where water is present and 0 where it is not. Unlike the approach taken by DeepAcqua [27], we opt for the SCL layer as it presents a more reliable alternative to the NDWI calculation, which can occasionally miss water regions.

Figure 4. Summary of the preprocessing steps involved to prepare the GRD and Optical products applied directly in Sentinel Hub. The API accounts for both data retrieval and preprocessing.

Figure 4. Summary of the preprocessing steps involved to prepare the GRD and Optical products applied directly in Sentinel Hub. The API accounts for both data retrieval and preprocessing.

6.1.3. MMFlood-CD

The MMFlood-CD dataset contains the same flood events delineations and naming conventions of MMFlood dataset [25], with the addition of pre-flood images. This dataset is utilized solely for a qualitative visual comparision of our SAR model with the EMS ground truth, included in MMFlood-CD. Given that the objective of the SAR model is to detect water, regardless of it being floodwaters or permanent water, we take advantage of both pre- and post-flood images and use a change detection module to detect flood. A more detailed explaination of this process can be found in Section 6.4.

In the following table a summary of the 3 datasets discussed in the previous sections with a comparison highlighting the differences.

Table 1. Dataset Comparison

Table 1. Dataset Comparison

Dataset	N. Events	Ground Truth	Pre-Flood Images	Labels
MMFlood	1,748	EMS	No	Flood
MMflood-CD	1,748	EMS	Yes	Flood
SAR-Optical	823	SCL Optical	No	Water and Flood

6.2. Training Pipeline

The task of flood delineation involves categorizing each pixel within an image as either flood or non-flood (background). Specifically, we define a collection of image pairs, x, where each pair, $x_s$, consists of SAR images with uniform dimensions $H\times W$. These images are paired with corresponding labels, $y\in Y$, also of the same dimensions, derived from optical images that serve as the ground truth. For every pixel i, its label $y_i$ can be either 0 or 1, with 0 indicating non-flood (background) regions and 1 indicating flood-affected areas. The goal of binary segmentation training is to develop a model, $f_{\theta }$, parameterized by $\theta$, which accurately predicts flood pixels across the image, mapping the input, SAR image, to a corresponding label, $f_{\theta }:X\to {\mathbb{R}}^{H\times W}$. Here, ${\mathbb{R}}^{H\times W}$ denotes the output of the model, represented by a matrix of size $H\times W$ containing the raw scores (logits). These scores are subsequently converted into probabilities using a SoftMax function. Further details on SoftMax functionalities can be found in Section 6.4. The model is trained on the labels from the SAR-Optical dataset, which contains SAR images paired with the Optical ground truth. The Optical SCL Layer transfers the knowledge to the SAR model through a weighted cross-entropy function that minimizes the difference in the distributions of the two models output, making the SAR model predictions as close as possible to the Optical one.

Figure 5. The paired Optical and SAR image, to facilitate the understanding of the SAR-Optical dataset structure. The dataset contains paired Optical and SAR images. The Optical image contains the SCL band from Sentinel-2 mission, Copernicus. This band provides a classification of the water extent which will be used as ground truth to train the SAR model.

Figure 5. The paired Optical and SAR image, to facilitate the understanding of the SAR-Optical dataset structure. The dataset contains paired Optical and SAR images. The Optical image contains the SCL band from Sentinel-2 mission, Copernicus. This band provides a classification of the water extent which will be used as ground truth to train the SAR model.

Figure 6. Diagram to facilitate the understanding of the MMFlood-CD (CD stands for change detection) dataset structure. The dataset contains the same flood events delineation from MMFlood but with the addition of pre-flood. It also contains the EMS ground truth, that will be used just to qualitatively compare our model with their performance

Figure 6. Diagram to facilitate the understanding of the MMFlood-CD (CD stands for change detection) dataset structure. The dataset contains the same flood events delineation from MMFlood but with the addition of pre-flood. It also contains the EMS ground truth, that will be used just to qualitatively compare our model with their performance

Figure 7. Diagram of the training pipeline. The SAR model is trained on the paired SAR-Optical dataset. The predictions generated from the Optical Model are used as ground truth for the SAR Model, with the use of a Cross-Entropy Loss function.

Figure 7. Diagram of the training pipeline. The SAR model is trained on the paired SAR-Optical dataset. The predictions generated from the Optical Model are used as ground truth for the SAR Model, with the use of a Cross-Entropy Loss function.

6.2.1. Loss Functions for Data Imbalance

We observed a significant imbalance with a water-to-land ratio of 1:11. To tackle this imbalance without altering the dataset with down sampling or up sampling techniques, we opted for specific loss functions that mitigate this issue by adjusting the weights between water and non-water classes. We explored two specific loss functions for this purpose: Focal Tversky Loss [30] and Weighted Cross-Entropy Loss.

6.2.1.1. Weighted Cross-Entropy Loss

The Weighted Cross-Entropy Loss is an adaptation of the standard Cross-Entropy Loss, introducing a weighting factor to account for class imbalances. This is particularly useful in datasets where one class is significantly more frequent than the other, which can lead to a model bias towards the majority class. The weighted version is defined as:

$$WeithedCrossEntrophyLoss=-\sum _{i=1}^N{w}_i·y_i·log\left(p_i\right)$$

Here, w represents the weight assigned to the positive class. This weight is typically set inversely proportional to the class frequencies, meaning that a higher weight is assigned to the less frequent class. This adjustment aims to amplify the loss contributed by the minority class, encouraging the model to pay more attention to correctly classifying these instances.

6.2.1.2. Focal Tversky Loss

In our experiments, inspired from previous studies [25,31] we also explored the Focal Tversky Loss [30], which unlike the traditional Cross-Entropy Loss, aims directly at optimizing the Intersection over Union (IoU) score, aligning closely with our segmentation objectives. The Focal Tversky Loss is defined as:

$$FTL={(1-TI)}^{\frac{1}{\gamma }}$$

Here, $TI$ represents the Tversky index, and $\gamma$ is a modulating factor parameter that diminishes the influence of easily classified examples, thereby making the model focus more on hard to classify examples. The Tversky index $TI$ is a generalization of the IoU metric that introduces two parameters, $\alpha$ and $\beta$, to control the relative importance of false positives and false negatives. Specifically, is given by:

$$TI=\frac{TP}{TP+\alpha FP+\beta FN}$$

In this formula, $TP$, $FP$, and $FN$ stand for true positives, false positives, and false negatives, respectively. This loss is specifically designed to account for the imbalance in the labels, in this case between water and non-water classes, by applying a dynamic balancing mechanism. The weighting factor $\alpha \in \left[0,1\right]$ for water and $\beta$ for non-water moderates the significance of respective pixels, with a higher $\alpha$ emphasizing water pixels

6.4. Change Detection Module for Flood Analysis

Our model is designed to identify areas covered by water, without specifically distinguishing between flooded and non-flooded regions. To highlight the extent of flooding, we compute the difference between the predictions made before and after the flood event, through the pre- and post-flood images. The model’s predictions are first processed through a SoftMax function to convert the raw logits from the output layer into probabilities. The SoftMax function in simple terms, is a mathematical operation that transforms a vector of real-valued logits into a vector of probabilities by exponentiating each logit and then normalizing those values. It ensures that the output values are in the range (0, 1) and sum up to 1, making them a valid probability distribution. After applying the SoftMax function, we calculate the difference between the post-flood and pre-flood predictions probabilities. Pixels with a difference exceeding a predetermined threshold, empirically set at 0.5, are classified as flooded, while those below this threshold are identified as not flooded. Mathematically this methodology can be expressed as follow:

Figure 8. Example of how SoftMax converts the raw logits from a vector output to probabilities ranging between 0-1.

Figure 8. Example of how SoftMax converts the raw logits from a vector output to probabilities ranging between 0-1.

Let $Z_{water}\left(i,j\right)$ and $Z_{nowater}\left(i,j\right)$ , represent the SoftMax outputs for the classes "water" and "non-water" at each pixel location $\left(i,j\right)$, where i and j denote the pixel coordinates in terms of width and height, respectively. The SoftMax function ensures that for any given pixel, the sum of these probabilities equals one, such that:

$$Z_{water}\left(i,j\right)+Z_{nowater}\left(i,j\right)=1$$

Let’s denote the pre- and post-flood scenarios as $f_{pre}\left(i,j\right)$ and $f_{post}\left(i,j\right)$. The difference between the post-flood and pre-flood predictions indicated as $\Delta f$, is computed as:

$$\Delta f\left(f_{pre},f_{post}\right)=f_{post}\left(i,j\right)-f_{pre}\left(i,j,\right)$$

A pixel is classified as "flooded" if $\Delta f>0.5$ ; otherwise, it is classified as "not flooded". This methodology ensures that the classification is based on a probabilistic approach, with the threshold value determining the sensitivity of flood detection. Rather than relying solely on absolute binary values of 0 and 1, this approach is expected to be more robust and can be tuned through a threshold, so that it can capture water pixels classified with lower probabilities.

7. Experiments and Results

7.0.2. Models benchmark results

Comparison with the Otsu thresholding baseline and different model combinations with encoders and decoders.

Figure 9. Diagram to facilitate the understanding of the inference pipeline in the MMFlood-CD dataset.

Figure 9. Diagram to facilitate the understanding of the inference pipeline in the MMFlood-CD dataset.

Table 2. Model benchmark results

Table 2. Model benchmark results

Model Architecture	Accuracy	Recall	IoU
Otsu Thresholding	0.78 ± 0.03	0.51 ± 0.02	0.27 ± 0.0
Unet	0.86 ± 0.03	0.82 ± 0.04	0.62 ± 0.01
Unet + ResNet50	0.96 ± 0.02	0.95 ± 0.02	0.72 ± 0.02
Unet + DenseNet201	0.85 ± 0.01	0.83 ± 0.01	0.63 ± 0.03
Unet + VGG19	0.79 ± 0.05	0.78 ± 0.04	0.59 ± 0.03

7.1. Results on SAR-Optical Dataset

This section analyzes the performance of the top model, Unet + ResNet50, often surpassing the ground truth predictions from the Optical layer, used to train the model itself. During the EMSR442-0-6 flood event, despite cloud cover obscuring the Optical ground truth, the SAR model successfully identified the water regions. Additionally, the model excels in EMSR280-4-17 event by distinguishing snow-covered areas, which typically appear similar to water in SAR images. Here’s a detailed explanation of the labels in the images:

• SAR Image – The input SAR image.
• Optical (SCL) Ground Truth – Optical ground truth from Sentinel-2 SCL layer, provided by Copernicus.
• Model Prediction - The model prediction (presence of water, whether it’s due to flooding or permanent sources).

Figure 10. Performance Analysis of EMSR258-13-1 Permanent Water in Albania.

Figure 10. Performance Analysis of EMSR258-13-1 Permanent Water in Albania.

Figure 11. Performance Analysis of EMSR407-1-4 Flood Event in the United Kingdom. Event Date: November 12, 2019 at 21:15.

Figure 11. Performance Analysis of EMSR407-1-4 Flood Event in the United Kingdom. Event Date: November 12, 2019 at 21:15.

Figure 12. Performance Analysis of EMSR277-2-0 Flood Event in Greece. Event Date: March 29, 2018 at 11:27.

Figure 12. Performance Analysis of EMSR277-2-0 Flood Event in Greece. Event Date: March 29, 2018 at 11:27.

Figure 13. Performance Analysis of EMSR501-0-3 Flood Event in Albania. Event Date: February 12, 2021 at 16:50.

Figure 13. Performance Analysis of EMSR501-0-3 Flood Event in Albania. Event Date: February 12, 2021 at 16:50.

Figure 14. Performance Analysis of EMSR442-0-6 Flood Event in Norway. Event Date: June 13, 2020 at 10:30.

Figure 14. Performance Analysis of EMSR442-0-6 Flood Event in Norway. Event Date: June 13, 2020 at 10:30.

Figure 15. Performance Analysis of EMSR280-4-17 Flood Event in Sweden. Event date: April 21, 2018 at 15:15.

Figure 15. Performance Analysis of EMSR280-4-17 Flood Event in Sweden. Event date: April 21, 2018 at 15:15.

Overall, the model has demonstrated great performance. An example is shown in flood event EMSR442-0-6. Illustrated in Figure 14, this event highlights a section of water missing from the Optical (SCL) ground truth due to cloud cover obstruction. However, given SAR capacity of penetrating through clouds, the model was able to accurately detect those flood areas.

Figure 16. RGB image of the EMSR442-0-6 flood event, from the Optical Sentinel-2 Satellite. It demonstrates the presence of cloud cover.

Figure 16. RGB image of the EMSR442-0-6 flood event, from the Optical Sentinel-2 Satellite. It demonstrates the presence of cloud cover.

Another notable performance is seen in the flood event EMSR280-4-17. As illustrated in Figure 15, this event demonstrates the model’s capability to identify and exclude snow-covered areas. In SAR images, regions covered in snow closely resemble water, making them indistinguishable to the human eye. However, the model successfully distinguished these areas avoiding the misclassification of snow as water.

Figure 17. RGB image of the EMSR280-4-17 flood event, from the Optical Sentinel-2 Satellite. It demonstrates the presence of snow

Figure 17. RGB image of the EMSR280-4-17 flood event, from the Optical Sentinel-2 Satellite. It demonstrates the presence of snow

An example where the model underperforms the Optical, SCL ground truth, is given by the flood event in EMSR258-13-1. As shown in Figure 10, it’s evident that the model predictions are less accurate along the borders, likely due to the lower resolution of SAR resolution compared to the Optical ground truth.

7.2. Results on MMFlood-CD Dataset

In the following section is shown a visual comparison of the model prediction on flood events included in the MMFlood-CD dataset, using the trained model on SAR-Optical and the ground truth provided by EMS. Here’s a detailed explanation of the labels in the images:

• EMS Prediction - Ground Truth EMS to be compared against our model.
• SAR Model Prediction - The final flood prediction of our SAR Model.
• Pre-Flood Prediction - The pre-flood model predictions of water.
• Post-Flood Prediction- The post-flood model prediction of water.
• SAR Image Post-Flood - The SAR raw image post-flood.
• SAR Image Pre-Flood - The SAR raw image pre-flood.

Note that a lower IoU indicates that the EMS ground truth and the SAR-Optical Model predictions don’t closely match, either due to our SAR model or the EMS ground truth error.

Figure 18. Comparative Analysis of the EMSR265-14-6 Flood Event in France. Event Date: January 23, 2018, at 19:17. Acquisition Date: January 25, 2018, at 05:59.

Figure 18. Comparative Analysis of the EMSR265-14-6 Flood Event in France. Event Date: January 23, 2018, at 19:17. Acquisition Date: January 25, 2018, at 05:59.

Figure 19. Comparative Analysis of the EMSR332-2-1 Flood Event in Italy. Event Date: November 1, 2018, at 21:08. Acquisition Date: November 2, 2018 at 05:18.

Figure 19. Comparative Analysis of the EMSR332-2-1 Flood Event in Italy. Event Date: November 1, 2018, at 21:08. Acquisition Date: November 2, 2018 at 05:18.

Figure 20. Comparative Analysis of the EMSR314-2-2 Flood Event in Nigeria. Event Date: September 18, 2018, at 21:27. Acquisition Date: September 22, 2018 at 17:44.

Figure 20. Comparative Analysis of the EMSR314-2-2 Flood Event in Nigeria. Event Date: September 18, 2018, at 21:27. Acquisition Date: September 22, 2018 at 17:44.

Figure 21. Comparative Analysis of the EMSR-319-3-4 Flood Event in Tunisia. Event Date: September 29, 2018, at 17:42. Acquisition Date: October 3, 2018 at 17:11.

Figure 21. Comparative Analysis of the EMSR-319-3-4 Flood Event in Tunisia. Event Date: September 29, 2018, at 17:42. Acquisition Date: October 3, 2018 at 17:11.

Figure 22. Comparative Analysis of the EMSR-342-6-1 Flood Event in Australia. Event Date: February 1, 2019, at 04:45. Acquisition Date: February 5, 2019 at 19:43.

Figure 22. Comparative Analysis of the EMSR-342-6-1 Flood Event in Australia. Event Date: February 1, 2019, at 04:45. Acquisition Date: February 5, 2019 at 19:43.

Figure 23. Comparative Analysis of the EMSR-399-0-0 Flood Event in Vietnam. Event Date: October 28, 2019. Acquisition Date: October 28, 2019 at 22:45.

Figure 23. Comparative Analysis of the EMSR-399-0-0 Flood Event in Vietnam. Event Date: October 28, 2019. Acquisition Date: October 28, 2019 at 22:45.

The model has demonstrated great performance in this qualitative evaluation. Despite the inability to directly compare its performance with an alternative ground truth, we can easily discern areas where the EMS model might fail by examining both pre- and post-flood SAR images. Figure 18, Figure 19, and Figure 21 are possible examples where the EMS model may have misses certain flood areas, detecting them only partially compared to our model. In Figure 20, EMS model appears to miss a rapid flood event that our model correctly detects. Figure 21 is the only instance where both the EMS and our SAR model produce matching predictions.

8. Conclusions

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