International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W15 
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5th International 3D Geolnfo Conference, November 3-4, 2010, Berlin, Germany 
between 3D objects (Clementini et al., 1993; van Oosterom et 
al., 1994; Zlatanova, 2000; Billen et al., 2002) and projective 
relations between 3D objects (Billen and Clementini, 2006). 
Another big issue which should be faced is the need of structur 
ing a semantic model for objects in 3D space in a “multi-level” 
ontology. We distinguish the entity level from the geometric 
level: each level must hold its own description of objects, rela 
tions, and integrity constraints. Let us exemplify the latter con 
cept. Most conceptual approaches for spatial data modeling 
consider geographic entities (e.g., roads, building) and geomet 
ric relations that can apply to them. For example, a typical con 
ceptual model of a road network would state that the admissible 
topological relations between two roads are “touch”, “cross”, 
and “disjoint” (excluding “inside”, “contains”, or “overlap”). 
This mixed view relates the entities by using the topological 
relations that apply to their geometric representations. In the 
view that we push forward in this paper, at the entity-level of 
the ontology, spatial relations among entities are expressed in 
context-based terms, e.g., by saying that roads can “have a junc 
tion” or “intersect” or whatever term is better suited to express 
the spatial relation between two roads in a given context. 
We keep separate the geometric level of the ontology, which 
can be put into correspondence with the upper-level (entity 
level) via a mapping. At the geometric level, the topological 
relations can describe the interaction between geometric fea 
tures. The geometric level can actually be thought of as to be 
based on multi-representations. The road entities can be mapped 
to a 2-D geometric representation where they are represented by 
polylines and the topological relations by existing models, or 
they can be mapped to a given 3-D geometric representation 
where they are represented by surfaces and volumes and the 
topological relations are taken from a 3D set of relations. 
On this distinction between spatial relations at the conceptual 
level and spatial relations at the geometric level, another exam 
ple follows. Let us consider buildings and the following spatial 
relations between them: 
1. Building A is inside building B: A is a part of B or A is a 
smaller building that is located inside an area surrounded 
by B; 
2. Building A and building B are connected: buildings are 
close to each other (not necessarily touching) and it is 
possible to walk from A to B without going back to the 
street; 
3. Building A and building B are bordering: buildings have a 
wall or other part in common but it is not possible to go 
directly from A to B; 
4. Building A and building B are neighboring: buildings are 
located in adjacent areas but don’t have a physical con 
nection; 
5. Building A and building B are close: they are at walking 
distance; 
6. Building A and building B are distant: an effort is needed 
to move from A to B (in a given context). 
The above entity-level ontology of binary spatial relations be 
tween buildings could find many corresponding spatial relations 
at the geometric level, where multiple representations of the 
same scenario exist. The spatial relations that translate the entity 
level concept to a given geometric representation could be not 
so obvious to define. For example, the first spatial relation 
(“building A is located inside building B”) could be translated 
to various embedding spaces: e.g., for a 2D space, the geometric 
level relation could correspond to “region A’ is contained in 
region B’ or region A’ is contained in the convex hull of region 
B”\ Regions A’ and B’ are the 2D representations of buildings 
A and B, respectively. 
Other examples of semantic relations (e.g., from a traffic net 
work (Métrai et al., 2009)) could be “Bus line 14 crosses the 
Northern part of Milan” or “There is a bus stop near the cross 
ing of roads A and B”. The following class relations could be 
extracted from those relations: “BusLine cross CityPart” and 
“BusStop near CrossRoad”. These new semantic relations must 
be coherent with the geometric model as well. Class relations 
can be used also as semantic constraints that are able to define 
subclasses (Tarquini and Clementini, 2008). For example, from 
a class River, a class Tributary River can be defined as the set of 
rivers that have the ending point inside another river. 
Spatio-semantic coherence is an important issue that needs to be 
enforced between the semantic hierarchy of classes and the 
geometric hierarchy (Stadler and Kolbe, 2007). The relations at 
the semantic level can be used for data validation purposes. In 
(Stadler and Kolbe, 2007), authors suggest that the introduction 
of spatial integrity constraints can be useful to test the correct 
ness of geometrical representations, e.g. the fact that faces must 
be connected in the boundaries to form a volume, and, if they 
are thought at the semantic model, constraints can validate do 
main-specific aspects, e.g., a window must be inside a wall sur 
face. Semantic relations now present in CityGML (Kolbe, 2010) 
are the generalization (is_a relation), e.g., SecondaryRoad is_a 
Road, the aggregation (is_ part of relation), e.g., Wall 
is_part_of Building, and the semantic/geometric link (relation 
has_type), e.g., RoofSurface has_type Polygon. 
Modeling semantic relations goes a step forward the overcom 
ing of ontological impedance, by ensuring independence from 
the specific geometric relations’ model that is used in the geo 
metric part. For example, the semantic relation “Building con 
nected Road” could be translated with the topological relation 
“meets” of the 9-intersection model (Egenhofer and Herring, 
1990) or the relation “touch” of the CBM (Clementini, Di Felice 
et al., 1993). Multiple representations are dealt with in 
CityGML (named Level Of Detail (LOD)), where more geomet 
ric models can correspond to a single semantic model. The spa 
tio-semantic relations among concepts have to be coherently 
represented in various geometric models corresponding to 
LODs. For example, if two roads have a junction, the corre 
sponding spatial relation at the geometric level depends on the 
spatial data type representing roads, which could be a polyline, 
a region, or a volume. 
Another important group of spatial relations are directional and 
visibility relations (Tarquini et al., 2007). Especially in 3D ap 
plications for wayfinding, it is important to describe the direc 
tional relations between city objects in various frames of refer 
ence (Retz-Schmidt, 1988): absolute frames of reference (e.g., 
an object to the North of a city), intrinsic frames of reference 
(e.g., an object in front of a church), and relative frames of ref 
erence (e.g., an object which is met by a driver to the left of his 
path) (Tarquini and Clementini, 2007). 
The last issue on semantic enrichment that we mention is the 
modeling of spatial data uncertainty and approximate spatial 
relations. The majority of models for representing uncertain