# Comparing Three Machine Learning Techniques for Building Extraction from a Digital Surface Model
## 1 Introduction  
In recent years, the availability of high-spatial-resolution remote sensing data has fostered the development of research methods and applications in several fields [1], such as urban planning, land monitoring, and environmental risk management [2; 3; 4; 5] (e.g., urbanization delineation, vegetation mapping, flood modeling). The accurate information provided by the high-resolution data has been exploited both in large-scale problems, such as land use and land cover types [6; 7], and small-scale ones, such as the extraction of urban objects: trees, roads, buildings, etc. [8; 9; 10]. Laser imaging detection and ranging (LiDAR) airborne mapping systems supply point clouds datasets containing 3-dimensional x, y, and z points and attributes to produce precise digital terrain model (DTM) and digital surface model (DSM) products--within a gridded or raster data format--in both natural and manmade environments [11]. Automatic building extraction from remotely sensed data is a major area of interest for an extensive range of applications but challenging due to difficulties in extracting precise boundaries because of urban morphology complexity [12]. Different methods have been proposed to address this issue [13], such as methods based on template matching, knowledge, object-based image analysis, and machine learning (ML) [14]. Commonly used template-matching-based approaches for automated buildings and urban objects footprints detection use \"snake\" or active contour model (ACM) [15] improvements [16; 17; 18; 10] andintegration with ML and deep learning (DL) [19]. The approaches based on supervised ML can achieve the best results, especially along with DL [14], a subset of ML based on neural networks with representation learning [20]. Traditional computer vision techniques require manually engineered feature descriptors for the desired object detection, whereas DL models automate the process of feature engineering [21,22]. Generally, classical ML-based object detection methods involve two steps: feature extraction and classifier training. Among features descriptors, histogram of oriented gradients (HOG) [23] features have proven to be effective in describing the edge or local shape information of the urban objects [24,25,26,27,24]. Typical ML algorithms for classifier training include, but are not limited to, the support vector machine (SVM) [7,28,29,30], artificial neural network (ANN) [31,32], including the extreme learning machine (ELM) [33] and AdaBoost. Several successful buildings and urban objects detection approaches are based on DL methods [34,35,36,37,34], such as convolutional networks, and in particular, fully convolutional networks (FCNs) have shown good performance on semantic segmentation [38,39,40,41,42], with correct pixel classification and accurate spatial information [43]. Despite the numerous algorithms proposed, building segmentation based only on the geometric information provided by DSM data is still a complicated task [44,45], mainly because objects with similar morphological characteristics and height can create ambiguity, resulting in position inaccuracy and local under-sampling [35,45]. A simplified method to detect and extract the building footprint based only on a DSM as input without any other additional feature could be beneficial in scenarios where only DSM data are available and a more expeditious solution is desirable (e.g., the rapid assessment of building damage). This paper aims to investigate the capability of three different, popular supervised ML models--namely HOG with SVM, HOG with ELM, and FCN--to detect building footprints using only raster DSM data as input and evaluate their performance on a publicly available benchmark dataset. This empirical comparison may highlight the potential usefulness of expeditious methods and help understand which model performs best in different urban environments.