# Insights into Segmentation Methods Applied to Remote Sensing SAR Images for Wet Snow Detection
## 2 Data and Method
### BERA Bulletins
In this version, the weighting term, according to the area inside the contour, is not taken into account (i.e., \(\
u=0\)) and we assigned the values \(\mu=0.3\), \(\lambda_{1}=\lambda_{2}=1\) to the other coefficients. The iterations were stopped either when a maximal number of iterations was reached (fixed at 200 in this study) or when the root mean square variation between successive iterates of \(\phi\) fell below a specified tolerance (\(5\times 10^{-4}\) in this work). Figure 6: Simplified diagram representing all segmentation methods tested in this work, as well as the corresponding acronyms used in the paper. (b) Random Walker method  
This method (described in [36]) is part of the family of methods based on graph partitioning. The version that we used comes from the python library scikit-image. This algorithm can segment an image into several categories (in our case, presence or absence of wet snow), but it requires a priori knowledge of the elements of each category (called the \"seeds\") before starting the segmentation. Once the seeds have been chosen, the algorithm calculates, for each undetermined pixel, the probability that a \"walker\" starting from this pixel, and moving randomly from one pixel to another, would first reach one of the seeds. This type of random displacement is similar to the anisotropic diffusion mechanism. In this algorithm, the diffusivity coefficient is larger for neighboring pixels having similar values and scattering is more difficult across areas of strong gradients. Computing the above probabilities amounts to solving a sparse linear system of equations corresponding to a discrete Dirichlet problem (several numerical methods are implemented within the scikit-image toolbox, and we chose the conjugate gradient method with Jacobi preconditioner and tolerance fixed to \(10^{-5}\)). A segmented image was obtained by assigning each pixel to the most probable seed. In the following, we denote by RW the Random Walker algorithm. (c) Random Forest method  
It is possible to train an algorithm on a set of segmented images so that it can then recognize the wet snow areas on a new image. We used the supervised learning algorithm by decision (Random Forest), implemented in the python library scikit-learn, and based on the work of [37]. We chose this algorithm because it is one of the most popular in machine learning and requires little preprocessing. However, many other methods could have been tested, such as neural network learning. This algorithm uses randomly constructed decision trees trained on different subsets of data. Each tree taken individually has a weak classification capacity (we call it a weak classifier) close to a random classification. It is the union of these decision trees in a \"forest\" (average of the trees) that has a strong classification capacity. The choice of the number of classifiers is, therefore, an important element and is strongly dependent on the problem. In our case, the number of trees was fixed to 20 (100 by default) and the depth of the trees limited to 10. The efficiency of this algorithm is mainly dependent on the training image sets. In our case, we selected 100 \(\times\) 100 pixel images from our full image time series representing either wet snow or snow-free areas (see Figure 7). We also tested adding a snow edge image to increase the number of pixels categorized as wet snow. In this article, RF1 was the trained version without borders and RF2 was the trained version with edges (See Figure 6 for a simplified scheme of all methods tested in this study). (d) Fixed thresholding  
Many studies have used a threshold of 2-3 dB to separate dry snow or snow-free areas from wet snow. The algorithm employed by [19] used a fixed threshold to map wet snow using a reference image taken under dry snow or frozen ground conditions. Our panel of segmentation methods included the 2 dB threshold, which is commonly used for snow monitoring.