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1. The coordinates (X, Y) are determined by using (P') and the 
homography of the reference plane; 
2. The coordinate (Z) is computed by using the scale factor 
along the (Z) axis and the image coordinates of the point and its 
projection (P^. 
Our application gives also the possibility to measure in the 
following planes: 
1. The reference plane; 
2. À plan parallel to the reference plane; 
3. The plane (XZ); 
4. The plane (YZ). 
Measuring the 3D coordinates of four points in one of these 
planes allows computing its homography. Thereafter, the 3D 
digitalization in this plane is possible. 
2.1.2.2. Base line-based modeling 
When applying the previous algorithm, the determination of the 
3D coordinates of a point requires one of its projections in one 
of the three planes of the scene. The manual determination of 
this projection is not always possible on the image. Our 
algorithm consists in determining automatically the projection, 
in the reference plane, of points located in the planes (XZ, YZ) 
or in a free plan which meets the reference plane. This is done 
using the base lines. A base line can be defined as the 
intersection of a given plane with the reference plane. 
2.1.2.3. Distances based modeling 
3D modeling is done by using the algorithm proposed in 
(Criminisi, 1999). Three distances are required to calculate the 
scale factors associated to the axes of a local coordinate system. 
Axes’ vanishing points are used with the resulted scale factors 
to compute the 3D geometry. 
2.2. Topologic and semantic modeling 
Because the topology is an effective way of data structuring, the 
adoption of the topologic modeling in our method facilitates 
data exploitation and avoids graphic redundancy. The topology 
in our approach allows carrying out topologic and geometric 
requests (surface and perimeter of a given face, the normal on 
faces, co-planarity between a given window or door and a given 
wall, etc.). 
The application of the semantic modeling rules to the 3D 
modeling of the indoor scenes, has to take into account the 
following points: 
- The definition of the model to be set up and the semantic 
properties of the entities. This task is based on the 
architectural knowledge and on the geometric 
characteristics of the scene; 
- The extracted data is function of the level of details 
required in the model. The semantic aspects are taken into 
account in the geometric measurement process. 
- The relations between the geometric, topologic and 
semantic levels define the modeling concepts. The 
concepts to be modeled are three-dimensional ones. In our 
approach, the general concept represents the interior part of 
a building. 
The logic phase of modeling consists in translating the 
Conceptual Data Model into a Data Base Management System 
(DBMS). In the relational model, data are organized in 2D 
tables in which lines are recordings and columns are attributes. 
In this system, the basic element is a table, which represents a 
relation between various fields. Every attribute takes its values 
in the corresponding field. To distinguish the various recordings 
in a table, one or several attributes are indicated as keys or 
identifiers. The relational model is easy to implement and the 
addition of new tables, new attributes or new relations between 
existing tables can be carried out easily. Considering these 
advantages, our Conceptual Data Model has been translated into 
a Relational Data Base Management System. 
2.2.1. Algorithm for semantic and topologic data 
extraction 
The surface is the fundamental unit of modeling in our 
approach. For a given surface, the operator extracts the limit 
points and then he specifies the semantic type of this surface. 
We distinguish the following type of surfaces: wall, ceiling, 
ground, window, door, column. The last stage consists in 
clarifying the numbers of the contour points of this surface, 
extracted in the same direction. 
With regard to the surfaces of type window and door, other 
information have to be specified to take into account the co- 
planarity relationships between these surfaces and the 
corresponding WALL. 
At the end of the geometric and semantic restitution, a partial 
database is generated. This one is not complete but it contains 
all data necessary for generating a complete database and 
reconstructing the 3D model. This database contains the 
following tables: 
1. The table T ROOMS that contains the modeled 
component (room, corridor, etc.) identifier and the 
identifiers of faces which constitute this component. 
2. The table T FACES EDGES that contains faces 
identifiers; faces types and edges identifiers. 
3. The table T EDGES that contains edges identifiers and the 
corresponding nodes’ identifiers. 
4. T DOORS and T WINDOWS that contain the numbers of 
doors / windows with the numbers of the walls which 
contain them. 
We notice the absence of the tables that describe the different 
types of faces. These tables are created automatically. 
After completing the database, the generation of the component 
3D model is carried out automatically. 
2.2.2. Algorithm for components merging 
This algorithm allows transforming the components of the 
interior part of a building in the same geometric reference. This 
reference is attached to the component which can be defined as 
the one containing the maximum number of interconnection 
surfaces (doors, windows, etc.). The relations between a 
reference component and a simple one attached to it can be 
described by a 3D conformal transformation. We can use the 
virtual doors to calculate the parameters of this transformation. 
In fact, these doors represent the doors of the simple 
components translated by the value of the corresponding wall 
thickness. These doors have their corresponding in the reference 
component defined in the reference coordinate system. Using 
this idea, the seven parameters of the 3D conformal 
transformation can be calculated. 
3. APPLICATIONS 
3.1. Example of an indoor scene 
Our approach was used to model the first floor of a building at 
ENSAIS (Strasbourg) (figure 4). The 3D reconstruction was 
made by using 3D geometric data and topologic relationships 
recorded in a partial database. 
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