# Insights into Segmentation Methods Applied to Remote Sensing SAR Images for Wet Snow Detection
## 2 Data and Method
### BERA Bulletins
However, it is important to note that the use of a fixed threshold, as  
Figure 7: Training image set for the Random Forest algorithm, without snow edge areas. The images are 100 \(\times\) 100 pixel sub-areas extracted from the 22 April 2018 SAR image. reported by [28], is not universally applicable and may lead to detection errors, depending on factors such as snow surface roughness and liquid water content. Since most segmentation methods include, by definition, a step of image filtering, we evaluated the fixed thresholding method with and without filtering the images with a simple Gaussian filter. The application of this filter consists of computing, in each pixel of the image, the average of the neighbouring pixels, weighted by the distance to the central pixel. The further away the pixels are, the smaller the impact of their values on the central value. By construction of the Gaussian filter, 95 % of the value assigned to the central pixel came from pixels located at a distance of 2\(\sigma\), \(\sigma\) being a distance in pixels that we provided as a parameter to the Gaussian filter. Figure 8 shows the effect of Gaussian filtering on the fixed thresholding segmentation result with different \(\sigma\) values. By comparison with the optical image of 20 April 2018, we chose the \(\sigma=5\) option. The segmentation results with Gaussian filtering are noted 2 dBF and those without filtering are noted 2 dB. Figure 6 shows a simplified scheme of all methods tested in this study. (e) [PERSON]'s adaptive thresholding  
[PERSON]'s method [13] is basically the same as the fixed threshold method, except the threshold is defined for each image from the histogram of the image value distribution. This algorithm is implemented in the python library scikit-image ([[https://github.com/scikit-image/scikit-image](https://github.com/scikit-image/scikit-image)]([https://github.com/scikit-image/scikit-image](https://github.com/scikit-image/scikit-image)) accessed on 1 January 2021). The selected threshold is the one that minimizes the intraclass variance defined by:  
\[\sigma_{w}^{2}=\sigma_{0}^{2}\sum_{i=0}^{t-1}p(i)+\sigma_{1}^{2}\sum_{i=t}^{L -1}p(i), \tag{2}\]  
where \(t\) is the threshold, \(\sigma_{0}^{2}\) the variance of values lower than \(t\), \(\sigma_{1}^{2}\) represents variance of values greater than \(t\), \(p(i)\) is the probability of occurrence of value \(i\) (histogram class) and \(L\) the number of histogram classes. As for the fixed thresholding, [PERSON]'s method was applied both with and without Gaussian filtering (\(\sigma=5\)). Hereafter, [PERSON]'s method with Gaussian filtering is denoted by OtsuF. (f) RGB color adaptative thresholding  
We also tested a methodology recently developed to detect avalanche debris and wet snow using a color space segmentation technique [38; 39]. The method involves the use of SAR images acquired at different winter dates and the careful selection of 1 or 2 reference images. The technique relies on the use of the Hue Saturation Value (HSV) color space to store SAR images from different dates where the H(ue) dimension represents the color, the S (saturation) dimension represents the dominance of this color, and the V (value) dimension represents the brightness. The HSV color space is particularly relevant for identifying contrasts in images. Therefore, the color detection algorithm seeks the position of the color and its luminance. The detection of wet snow is equivalent to detecting shades of a specific color (which represent areas where there is a drop in values of backscatter). Figure 8: Wet snow maps over Belledonne massif using a 2 dB fixed threshold and different Gaussian filtering distances \(\sigma\). In addition, tests were performed using late April 2018 data. There were two main steps we followed. Firstly, an RGB composition was made with 2 or 3 images (R: Reference-image1, G: image day D, B: reference-image2). RGB is for Red, Green, Blue, and colors are represented in their proportions of red, green, and blue.