## 2 Related Work
### Object Recognition and Relationship Establishment  
As highlighted by [PERSON] et al. [9] and [PERSON] et al. [16], object recognition is a core task in as-built BIM modelling. Beyond geometry, elements extracted from point clouds have to be assigned to several object classes. The attribution of semantic information can be done at various steps in the processing chain. Semantic information can be integrated directly during the segmentation step and/or the geometric modelling of elements so that the search of building elements is guided. As shown above, some approaches integrate knowledge about building structure in order to identify specific elements in point clouds. [PERSON] et al. [38], [PERSON] and [PERSON] [40] and [PERSON] et al. [43] first extract only horizontal planes with the aim of identifying grounds and ceilings. Then, [PERSON] et al. [38] and [PERSON] et al. [43] exploit the fact that walls are located in borders of rooms to extract them. Whereas [PERSON] and [PERSON] [40] use a verticality constraint for the extraction of walls. Buildings generally follow standards and architectural codes linked to the type of building and the construction date. Plenty of buildings, notably office buildings, verify the Manhattan-World (MW) assumption originally defined by [47]. As explained by [PERSON] et al. [37] these buildings have three mutually orthogonal directions. Grounds and ceilings are horizontal (X-Y plane), whereas the walls are vertical and either parallel to the Y-Z or the X-Z planes. [PERSON] and [PERSON] [34] consider the MW assumption in their approach. They use a sweeping method along Y-Z and X-Z planes to extract walls. [PERSON] et al. [37] also take advantage of MW assumption in their processing chain in particular during the fusion of wall planes. Methods based on shape grammars, used more specifically for MW buildings, are studied by [31; 48; 49]. [PERSON] et al. [36] developed an approach in which a scene graph is modified thanks to a structure grammar. When the attribution of semantic information is not coupled with the modelling of the geometry, an a posteriori object recognition has to be performed. The chosen approach depends on the considered elements which are either parametric representations or non-parametric representations [9]. In the context of as-built BIM, one of the challenges for object recognition is that many objects are similar. Several works focus on the use of contextual characteristics to differentiate very close objects. A constraint network is used by [50] to represent a knowledge model. This type of network specifies the relationships between entities. For example, considering a building, this consists in saying that a wall is parallel or orthogonal to another wall and orthogonal to ceiling and floor. [PERSON] et al. [51] combine simultaneously contextual and geometrical characteristics in order to assign an object category to extracted elements. [PERSON] and [PERSON] [21] also suggest to distinguish segmented planar entities based on their characteristics. The characteristics taken into account are the size, the position, the orientation, the topology and the density of points. [PERSON] et al. [19] propose a machine learning algorithm to automatically label planar patches previously extracted as walls, ceilings, or floors. Features of different types of surfaces and the contextual relationships between them are learned to perform the labelling. For non-parametric models, 3D object recognition algorithms may label object instances or recognized classes of objects. They are used whether in urban environments [52], industrial environments [53] or in indoor areas of buildings [54]. The recognition is based on a database of objects which have to be recognized. Shape descriptors are computed for both objects of the database, and the scene containing these objects. Then, a matching step allows to identify objects in the scene. Recognition of object instances is usually performed when objects with known shape and which are repeated in a scene have to be identified.