2.2.3. Changes in Relation to the 3D Cadastre Model

To link the Cadastre to the detected changes, we assumed that every space subdivision in the point clouds was represented in the object description of the spatial unit in the LADM, considering that an interactive refinement on the space subdivision from the previous step was necessary to group some of the subdivisions, according to the 3D Cadastre legal spatial units. For example, a group of offices that belonged to the same owner had an invisible boundary that should be interactively corrected. LADM represents legal spaces in spatial units. Spatial units were refined into two specializations [38].

(1) Building units, as instances of class:

LA\_LegalSpaceBuildingUnit. A building unit concerns the legal space, which does not necessarily coincide with the physical space of a building. A building unit is a component of the building (the legal, recorded, or informal space of the physical entity). A building unit may be used for different purposes (e.g., living or commercial) or it can be under construction. An example of a building unit is a space in a building, an apartment, a garage, a parking space, or a laundry space.

(2) Utility networks, as instances of a class:

LA\_LegalSpaceUtilityNetwork. A utility network concerns legal space, which does not necessarily coincide with the physical space of a utility network.

The LADM class LA\_BAUnit (Figure 10) allowed the association of one right to a combination of spatial units (e.g., an apartment and a parking place).

**Figure 10.** Basic classes of the LADM [38].

A basic administrative unit (LA\_BAUnit) in LADM is an administrative entity, subject to registration, consisting of 0 or more spatial units, against which (one or more) homogeneous and unique rights (e.g., ownership right or land use right), responsibilities, or restrictions are associated to the whole entity, as included in a land administration system. In LADM, each space is represented as a spatial unit and then uses a LADM class LA\_BAUnit to associate those spatial units to a legal unit. The type of building units were individual or shared. An individual building unit is an apartment and represents a legal space. A building contains individual units (apartments), a shared unit with a common threshold (entrance), and a ground parcel. Each unit owner holds a share in the shared unit and the ground parcel.

Every spatial unit in LADM was modelled with GM\_MultiSurface. 2D parcels were modelled by boundary face string (LA\_BoundaryFace). The representation of 3D spatial units was done by boundary face (LA\_BoundaryFace), and for the storage a GM\_Surface was used (see Figure 11). However, in our approach, we are aiming to keep the point clouds until the last step for spatial analysis. Therefore, we just used the calculated features, such as volume, area, and neighboring units, to insert them as classes in the LADM. All spatial attributes and legal issues, such as rights, restrictions, and responsibilities, could be associated between point clouds and LADM. The measured spaces were important because, apart from the floor space, the volumes are also known. This is relevant for valuation purposes of the individual spaces in apartments.

Figure 12 illustrates the LADM representation of an apartment—in this case, owned by a party (right holder) named Frank. This party has an individual space and a share (1/100) in the common or shared space. Individual and shared spaces (including the ground parcel) compose the building as a whole.

**Figure 11.** Mixed use of boundary face strings and boundary faces defining both bounded and unbounded 3D volumes: Annex B in [38].

**Figure 12.** An apartment building in Land Administration Model (LADM) and its legal space [38].

The limiting factor of associating detected space changes to the LADM is that the LADM only provides an abstract representation of 3D objects with no direct mapping to an implementation. There are also specialized data structures, such as CityGML or IndoorGML, which can be used to store 3D data as specified in the LADM model. The issue here is that these data structures are primarily designed for visualization and indoor navigation and not for the management of rights of legal spaces. This becomes more apparent when looking at the definition of primal and dual spaces. The primal space is used to represent semantic subdivisions (e.g., a room, a corridor) and the dual space is used to represent the navigability of the primal space. For the proper management of legal space in a database and to properly determine which changes in the layout of a building affect legal spaces, additional information is needed to be stored in the database, namely, a direct relationship between visible and invisible subdivisions of space and the legal objects in the 3D Cadastre.

Given today's database technology, the available option for the implementation of 3D legal spaces and their corresponding topological relationships is a GM\_PolyhedralSurface [53]. A PolyhedralSurface datatype is defined as a collection of polygons connected by edges which may enclose a solid. When using such a data structure, it is possible to define a subdivision in a building as the primal space and a legal object as the dual space. This way, properties can be assigned to, for example, walls to define whether it corresponds to a legal boundary or not (or where in the wall the boundary is). Similarly, properties can be assigned to invisible space subdivisions that define a change in the rights of the spaces. In this scenario, the dual of an edge is a face and the dual of a face is solid, which will represent a LA\_BAUnit. A database implementation of the topological relationships of a PolyhedralSurface as required by a 3D Cadastre can be based on dual half-edges [54,55]. With this approach, each face is stored as an array of half-edges and can be associated with a set of attributes. These attributes can be defined as a result of the face detection from the point-cloud analysis. Since each face is associated to a legal object, it is possible to support the update of the 3D Cadastre by directly updating changes detected in the latest point cloud epoch on the database structure of the 3D Cadastre. This has to be followed by an update on the rights of the legal objects which will require the intervention of the cadastral expert responsible for mutations and transaction in the land administration system.

## **3. Results and Discussion**

The proposed method is tested on two datasets. One dataset has a smaller amount of clutter and the shape of the building has a regular structure. Therefore, the separation of walls is easier. To challenge the robustness of our method with a complex structure and more furniture, a dataset

with arbitrary wall layout and glass surfaces is selected (ITC restaurant, Figure 12). The details of the datasets for each epoch are in Table 2.

**Table 2.** The details of the datasets and two case studies. The first and second rows belong to the first case study. The table shows the number of points and scanning device per dataset. The fourth column shows the number of changed rooms before and after the renovation of the building. The fifth column shows the items which are identified as changes.


First, the datasets from two different epochs were co-registered using the iterative closest point ICP algorithm (Figure 13). Then the changes between two epochs were identified in 2D and 3D, as explained in the methodology (Section 2.2). The classification algorithm separated the permanent changes from non-permanent changes and then we intersected the permanent changes with the reconstructed spaces from two epochs (Figures 14 and 15). In this way, the changes in the rooms in the second epoch of both datasets can automatically be identified. To identify the relation of physical changes with the 3D Cadastre, a user adds the ownership of the spaces as an attribute to each space. For example, the spaces which have the same rights and ownership obtain the same label and form a new physical space (Figure 16). Then it is possible to connect them to the basic class of the LA\_Spatial Unit in the LADM and update the spatial unit class in the LADM.

In dataset 2 (ITC restaurant), part of the curtain was identified as the permanent change because the curtains were covering the walls and they were detected as a permanent structure. However, this can be the inaccuracy of the classification method, for identifying the changes in the space is not problematic because it has a slight change in the space partitioning.

**Figure 13.** The figure shows the top view of two epochs of our use case. The floor and ceiling are removed for a clear visualization. (**a**) The data is collected by a Riegl terrestrial laser scanners (TLS) [45] (rooms A and B in yellow) and is co-registered with the data collected by the Viametris system [56]. (**b**) The second epoch is also collected by the Viametris system and the walls in the red rectangles are removed.

**Figure 14.** The figure represents the changes in the detected permanent structure and then the spaces. (**a**) and (**b**) show the changes in the walls (black rectangles). The red transparent rectangle is for the orientation between two images. (**c**) and (**d**) show the detected walls in orange and space partitions in random colors. The black rectangles show how the room changed after removing a wall.

**Figure 15.** The top view of the spaces and permanent changes. (**a**) Epoch one, walls are in green and four spaces in random colors. (**b**) After removing walls, two rooms in epoch one are merged with the large space in brown color, and, in total, it forms two spaces with the rest of the interiors. (**c**) Detected permanent changes are shown in red. (**d**) The spaces from the second epoch are intersected with the permeant changes to identify the changes in the space.

The important parameter for the detection of changes is the distance threshold (d) to identify the changes from the differences caused by noise and registration errors. We set this parameter slightly larger than the sum up of the sensor noise coming from the scanning device and the residuals coming from the ICP algorithm (less than 10 cm). In our experiments, we set this threshold on 20 cm, which implies that we cannot detect changes which are smaller than 20 cm. For planar segmentation of the point clouds, the smoothness parameter for a surface growing algorithm is important, which depends on the noise and point spacing in the data. We set the smoothness threshold to 8 cm because the noise from MLS systems (Viametris and Zeb-Revo) is around 5 cm. The smoothness parameter was set slightly larger than the sensor noise and point spacing. The point spacing was 5 cm, which meant we could subsample point clouds to reach 5 cm point spacing. The parameters for detecting the permanent structure were chosen according to [23]. Segments with more than 500 supporting points were selected for creating the adjacency graph and smaller segments were discarded. The voxel size for space partitioning was 10 cm, which is an apppriate voxel size to have enough precision to identify changes and avoid expensive computations.

**Figure 16.** New spaces with the same rights and ownership obtain the same label and color and form a new physical space that can be linked to the LA\_SpatialUnit.

The running time for surface growing segmentation, identifying the permanent structure, and detecting the changes for the first dataset with 1.7 million points took 2.4 min, 5.6 min, and 7 min, respectively. The space partitioning was computationally more expensive than other processes and it took 10 min for dataset 1 with the voxel size of 10 cm, and it depended on the volume of the building. Larger volumes required more voxels for morphological space partitioning.

In our workflow, the challenge was detecting the permanent changes from the dynamic changes, which were not important for the Cadastre. According to [23], this process can have an average accuracy of 93% for permanent structures and 90% for spaces [57]. Furthermore, the extraction of spaces are really crucial in the process, because the volume and area is calculated from the space subdivision result. Therefore, an expert should check the results of space subdivision and merge or split some of the spaces that are extracted from the point clouds. The interactive corrections are less than 10% of the whole process and, for a building of three floors as large as our case study, it does not take more than 10 min.

The process of linking the spatial units to the 3D Cadastre model was not automated in our approach. This was because of the lack of possibilities for representation and visualization of 3D objects in the 3D Cadastre models. Therefore, our method was limited when it comes to the storage of 3D spatial objects in the Cadastre databases. As future work, linking the 3D objects and 3D Cadastre models, one solution we intend to investigate is using the point clouds as external classes and trying to keep the 3D objects as point clouds for all steps. The extraction of vector boundaries for the Cadastre models can be done with functions from the point clouds.
