## 1 Introduction  
In recent years, European countries experienced an increase of wildfire events, causing extensive damage from environmental, humanitarian, and economical perspectives [1]. After a wildfire extinction, competent offices of public bodies report the perimeter of the burned areas and the severity of the damage in each burned sub-area. The census of the burned areas is usually adopted (i) for estimating the economical damage, and (ii) for planning a full environment restoration. Europe actively supports wildfire census operations through the Copernicus Emergency Management Service (Copernicus EMS) [2]. The service provides certified information about the hit areas through delineation and grading maps. More precisely, delineation maps determine the boundaries of areas hit by wildfires, while grading maps estimate the severity of environmental damages. The damage level estimation activity, which is used to create the grading maps, is performed by the EMS experts and it consists in assigning to each sub-area of the area hit by a wildfire a numerical severity level between 0 and 4, where 0 is assigned to unburned sub-areas with no damages, while 4 is assigned to the burned areas that have been completely destroyed by the wildfire. The intermediate levels are used to represent burned sub-areas associated with negligible (1), moderate (2), or high (3)damages. For the sake of simplicity, only integer levels are used by domain experts to represent the damage level of each sub-area. However, continuous values between 0 and 4 should be used to obtain more accurate and fine-grained estimations. Currently, EMS experts manually compare pre- and post-wildfire imagery to compute and assign the proper damage level to each hit sub-area. To achieve good results and facilitate the experts work imagery taken in similar conditions are needed. Automatic systems, based on machine learning algorithms, support domain experts to track the evolution of wildfires [3; 4; 5] during the event and to automatically identify burned areas after the wildfire extinction [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. However, to the best of our knowledge, usually the post event estimation of the damage level of the affected areas is a manual activity based on the comparison of pre- and post-UAV or satellite-based imagery of the burned areas and, less frequently, through on-site missions. The estimation process may also leverage on the analysis of the variations occurred in the soil between the compared imagery [21]. To unburden domain experts from this complex and time-consuming activity, we propose a novel deep-learning approach based on a two-step solution that combines a classification algorithm and a regression one. First, a binary classification algorithm is used to automatically label each sub-area as burned or unburned. Then, a regression algorithm is used to assign a severity/damage level between 1 and 4 only to the sub-areas that are labeled as burned sub-areas by the first step. The experimental results show that this two-step approach performs better than a single step approach based only on a regression algorithm. To the best of our knowledge, few attempts have been performed to automatically infer severity/damage maps for burned areas [22] and they are all based on the comparison of pre- and post-wildfire imagery. The quality of these approaches is affected by the used imagery. If the imagery are taken in different conditions the damage level estimation could be affected. Specific preprocessing techniques, and sometimes also a manual selection of imagery by means of the domain expert, are needed to obtain comparable imagery. In the following, we describe the state-of-the-art damage indexes and the manual and automatic approaches that are used to assign a severity/damage level of each sub-area of an area hit by a wildfire.