# Automatic Building Height Estimation: Machine Learning Models for Urban Image Analysis
## 2 Background  
Research on the seismic vulnerability of buildings using imagery to extract basic parameters such as height or facade material is increasing worldwide [7]. Surveys are traditionally performed manually through visual inspection, which is time consuming and expensive. A current trend is moving towards the automation of these processes, as in the recently published VULMA model, which performs surveys automatically through a categorical classification machine learning model [10]. The reviewed experiences involve taking an image of the facade of a single building and applying the required labels using a classifier model. In real-world applications using street view images, multiple buildings and other elements such as the street are visible; hence, the classifier model would not function correctly, as it is not able to focus on the building of interest. A building is defined in the INSPIRE scheme [11] as a construction, above and below ground, for the purpose of accommodating people, animals and things, or production and distribution of goods or services, this construction being a permanent structure on the ground. In the definition of a building, one or many BuildingParts are characterised, as each of the constructed areas in a cadastral parcel having homogeneous volume, either above and/or below ground. A BuildingPart element hosts the attributes related to height, namely, number of floors above ground, below ground level height in meters, and number of floors below ground [11]. As building heights are usually available through INSPIRE in Europe, new techniques were developed for automatic building height estimation, in part to aid data collection for cadasters in cities without data. Using ESA's Sentinel 1 and 2 data series and particularly Synthetic Aperture Radar (SAR) data [12; 13], it was possible to extract building height data automatically on a large scale [13] with an error of less than 5 m for average-height buildingsbut much larger error for higher buildings. Satellite techniques were improved using multi-view satellite imagery [14] achieving an error of around 2 m. Aerial imagery [15] and Aerial Laser Imaging Detection and Ranging (LIDAR) can be used to measure building heights [16], although this approach is expensive and requires manual work; thus, the viability of using it for large-scale data collection is questionable. Other recently developed methods use street-view imagery, that is, driver-view images taken from a car. The image is segmented using machine learning methods, and the top corners of the buildings are detected. The horizontal distance from the camera to the building is then calculated using the camera position and a database such as Openstreetmap, which registers the x and y coordinates of the corners of the building [17] and building rooflines [18]. Having determined certain parameters such as camera height, estimation of three vanishing points and the detection of the vertical lines of a building with the help of semantic segmentation, the height can be computed by considering the perspective of the image [19]. The relative error obtained using this method is 5%. Finally, the height can be obtained through trigonometry. Spherical images allow other more complex geometrical methods to be used which do not require 2D external corner coordinates [20]. In the field of computer vision, substantial advances have been made in recent years with regard to image classification tasks using new machine learning models such as the vision transformer [21] or its version for semantic segmentation [22]. These models are developed by large companies and contain a large number of parameters; hence, they are difficult to train. Other simpler models developed recently for image classification are RestNexts [23; 24]. With regard to semantic segmentation, very good results have been achieved with HRNets [25], a model which processes an image in multiple resolutions.