# Insights into Segmentation Methods Applied to Remote Sensing SAR Images for Wet Snow Detection
## 2 Data and Method
### BERA Bulletins  
To further evaluate the overall weather conditions over our study period, we used the information from the BERA bulletins (Bulletin d'Estimation du Risque d'Avalanche), provided daily in winter by the snow forecasters of Meteo-France. These bulletins combine data from model outputs, observations of different types and human expertise to provide information about the state of the snowpack for the French massifs (23 massifs in the Alps, 21 in the Pyrenees and two massifs in Corsica). Figures 3-5 provide the available information for the six massifs included in the 31 TGL tile (the massifs of Belledonne, Chartreuse, Bauges, Maurienne, Vanoise, Grandes-Rousses and Beaufortin) with the continuous snow limit for the northern and southern orientations of each massif (Figures 3 and 4) and the rain-snow limit in cases of precipitation for the Grandes-Rousses massif (Figure 5). The rain-snow line curve indicated frequent rainy weather and rain-on-snow events over the study period. This data helped to infer wet snow occurrences, and Sentinel-1's wet snow products could be synthesized into altitude-time-orientation diagrams at the scale of each massif, following the method presented by [26]. The resulting graphs could then be conveniently compared to the BERA bulletins. Figure 4: Same as Figure 3 but for snow limits for the southern orientations. Figure 5: Snow–rain limit for the Grandes-Rousses massif as derived from the BERA bulletins for the 2017–2018 season. Figure 3: Snow limit for the northern orientations for six French massifs (Belledonne, Chartreuse, Bauges, Maurienne, Vanoise, Grandes-Rousses and Beaufortin) as derived from the BERA bulletins for the 2017–2018 season. (a) Chan-Vese method  
The Chan-Vese method (called CV hereafter), detailed in [35], belongs to the family of contour evolution segmentation methods. It provides a contour \(C\) separating the image into two sub-areas which are as homogeneous as possible. This is achieved by minimization of the cost function  
\[ \begin{split} F&=\mu\cdot Length(C)+\
u\cdot Area( inside(C))\\ &\qquad+\lambda_{1}\int_{inside(C)}|u_{0}(x,y)-c_{1}|^{2}dxdy\\ &\qquad+\lambda_{2}\int_{outside(C)}|u_{0}(x,y)-c_{2}|^{2}dxdy, \end{split}  \tag{1}\]  
where \(C\) is the contour to be determined and \(u_{0}(x,y)\) is the value of the pixel with coordinates \(x\) et \(y\). The constants \(c_{1}\), \(c_{2}\), which depend upon \(C\), are mean values inside and outside \(C\), respectively. The parameters \(\lambda_{1},\lambda_{2},\mu>0\) and \(\
u\in\mathbb{R}\) are fixed by the user. The CV algorithm belongs to the class of level-set methods, i.e., the contour \(C\) corresponds to the level curve of a function \(\phi\) vanishing on \(C\) (and having different signs at both sides). The cost function \(F\) is expressed as a function of \(\phi\), regularized, and minimized iteratively using a gradient descent. As iterations go on, the contour becomes closer to the structure to be segmented. The CV method has several advantages. The level-set approach is appropriate to handle possible topological changes of the contour, while the latter evolves towards the final segmenting contour. It is based on the minimization of an energy defined by \(F\), which can be supplemented by ad-hoc terms, depending on the application, possessing several tunable parameters. The parameters \(\lambda_{1}\), \(\lambda_{2}\) facilitate weighting the variance of each sub-area. The parameter \(\mu\) has an impact on the length of the contour. The smaller \(\mu\) is, the longer and more tortuous the interface can be. This allows one to better track the details (with the risk of increasing noise), while a higher value of \(\mu\) tends to smooth the contour. The \(\
u\) parameter can be used to increase or decrease the area inside the contour. In this paper, we used the version of the CV algorithm available in the Scikit-Image python library.