## 2 Materials and Methods
### GGO Segmentation  
In the second step, a novel automated pipeline for the segmentation of GGO areas was developed, combining 2 different techniques: vessel artifacts exclusion and k-means clustering. Both these methods are unsupervised learning techniques and have been chosen due to the limited number of available samples. The decision to avoid supervised methods such as Convolutional Neural Networks (CNNs) is based on the likelihood of including strong biases, even including possible data augmentation strategies. The intensity of pulmonary vessels is very similar to solid components of GGO; therefore, it affects the segmentation, introducing potential false positives [56]. To remove these vessels, we used the vesselness measure, i.e., the presence of multiscale tubular structures. Multiscale Vessel Enhancement Filtering (MVEF) [57] is defined as the likelihood of an image region to contain vessels, and it is estimated using the Frangi filter [58]. The areas with high values of MVEF were identified as vessels and therefore removed from the lung region obtained in the previous step. After the removal of the vessels, we identified the GGO as areas with a common color texture. To identify these regions, we used k-means clustering, grouping voxels by color and texture similarity, and identifying the tissue corresponding to each cluster [59]. Since GGO involves extended areas, it is informative to include neighborhood voxel information. The color contrast between GGO and healthy areas may change between patients; it is, therefore, useful to consider different gamma corrections of the image. We applied a series of image processing filters to obtain a high-dimensional feature space, including all these features for each individual voxel. For each voxel, we estimated a vector of features obtained by the application of the following filters:  
* Gamma corrected image (\(\gamma\) = 1.5);
* Adaptive Histogram Equalized image, in a radius of 3 voxels;
* Median blurred image with a kernel of radius 3 voxels;
* Standard deviation filtered image with a kernel of radius 1 voxels. We used the Adaptive Histogram Equalization algorithm for the image standardization: for each slice, the histogram was equalized considering a volume of 3 voxels. The gamma correction is a non-linear operation used to decode the luminance and enhance the low contrast regions. The median blurring allows considering the information about the neighborhood voxels, reducing the effect of outlier voxels. The last feature is the application of a local standard deviation filter; this filter replaces each voxel value with the standard deviation of its neighborhood. This feature is useful as GGO is characterized by highly heterogeneous gray level regions, allowing to filter out bronchial structures and motion artifacts not removed during the lung segmentation. The k-means clustering is \"isotropic\" in all directions of space and therefore tends to produce round (rather than elongated) clusters. In this situation, leaving variances unequal is equivalent to put more weight on variables with smaller variance. To avoid this, the features were standardized according to the mean and standard deviation estimated on the training dataset. We selected 10 scans and applied the k-means clustering for the estimation of the centroids using the Euclidean metric. The k-means clustering is sensitive to the class balance in the training phase (it might give more prominence to more common present structures). Therefore, for the training phase, we considered only a subset of scans with a reasonable amount of GGO areas, excluding in all the cases the (overrepresented) imagebackground. The k-means cardinality was estimated based on lung anatomy considerations. The resulting clusters were:  
* Healthy lung;
* Edges;
* Remaining vessels;
* Noise;
* GGO.