## 1 Introduction  
Significant acceleration of the urbanization rate is contributing to a persistent vertical expansion in many cities in order to meet the increasing demand for living and working space [1]. In this context, the three-dimensional form of a city has important implications for a city's sustainability, efficiency, and resilience [2]. Considering the expected urban expansion in the near future across the globe [3], understanding the relation between the three-dimensional urban form, critical infrastructure operations, and quality-of-life measures is one of the most important research and technical challenges. The growing interest in generating 3D city models is motivated by a broad range of applications, such as estimation of solar irradiation, energy demand estimation, classification of building types, visibility analysis, 3D cadastre, visualization for navigation, urban planning, emergency response, computation fluid dynamics, change detection, flooding, archaeology, forest management, and virtual tours [4]. Moreover, a decrease in the cost of remote sensing technology and data storage in recent years has contributed to the expansion of urban morphology studies [4; 5]. In particular, the emergence of airborne laser, a leading technology for the extraction of information about physical surfaces, enables substantial advances of in-depth availability of data on buildings and infrastructure, as well as over large scales. By directly providing measurements of surface heights with high point density and high level of accuracy, light detection and ranging (LIDAR) technology can improve the automation level in accurate and efficient 3D reconstruction of urban models [6; 7; 8; 9]. The 3D information about buildings and related structures that can be retrieved from the data acquired by airborne LIDAR is usually characterized by directness and simplicity. However, practice shows that the massive number of points requires introducing some level of organization into the data before extraction of information can become effective (e.g., aggregating points with similar features into segments in the form of surfaces) [10]. Therefore, producing 3D building reconstruction by manual or semi-automatic methods could be a very time consuming and challenging task. Hence, the generation of 3D building models in a simple and quick way is becoming attractive [11]. Indeed, in the last decade, the automatic 3D reconstruction of buildings from airborne data is an active area of research among photogrammetry, computer graphics, and remote sensing communities [3; 5; 12; 13; 14]. Among the great variety of reconstruction methods from airborne laser scanning (ALS) proposed in literature (see [3] for a complete review), the data-driven polyhedral method is one of the most commonly used rooftop modeling techniques and can be adapted for generating building models with both simple and complex roof topology [5]. Moreover, polyhedron buildings are quite common in urban areas [7]. These methods use a bottom-up approach that begins with the extraction of primitives (e.g., planes, cylinders, cones and spheres), followed by analysing primitive topology in 3D space, extracting and grouping them to form building models. In summary, the problem of building rooftop reconstruction based on a data-driven framework is transformed into a problem of consistency maintenance of topological relationships among rooftop primitives, primitive boundaries or their combinations: The common assumption is that the building has only planar roofs, based on which various model detection methods in pattern recognition can be adopted for building extraction. The 3D reconstruction process from airborne LIDAR data is principally based on the segmentation of the raw data sets into building points; the segmentation refers to the task of dividing data into non-overlap homogeneous regions that constitute the complete data sets [7]. The efficiency and accuracy of the segmentation method results are one of the major challenges in 3D building reconstruction.