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Paola Podest` a, Barbara Catania, and Alberto Belussi
8.7.3 Consistency Checking
In order to present an application example of the proposed notions to consistency checking, we evaluate the topological consistency of two maps ML1
R
roads and
ML1
L
roads , containing the streets of a municipality of Lombardy (Italy) represented
as regions in ML1
R
roads and as lines in ML1
L
roads .
6 Figure 8.10 presents two snapshots
from corresponding areas of ML1
R
roads and ML1
L
roads .
By performing a consistency check on such data sets, we find that they are neither
eq-based nor dist-based consistent. For example, we discovered that roads 72 and 160
are not dist-based consistent (see Fig. 8.10). Their relation is T ouch in Fig. 8.10(a)
and Dis joint in Fig. 8.10(b). According to the table presented in [2], this pair violates
both dist-based and eq-based consistency. On the other hand, the pair of roads 70
and 160 are eq-based consistent since their relation is T ouch in both Fig. 8.10(a) and
Figure 8.10(b).
8.8 Conclusions
In this chapter, we have identified some new approaches for processing multiresolution maps in an integrated environment by using qualitative information represented by topological and cardinal relations. In the multiresolution model considered, the same object can be represented with geometries of different dimensions
(points, lines, and polygons) in different maps. The proposed approaches refer to
three distinct scenarios: (i) similarity-based query processing; (ii) GIS mediation architectures; (iii) map consistency checking. In order to support the contexts presented
above, two main issues have been addressed. First of all, starting from some wellknown models, distance functions for topological and cardinal directional relationships have been defined. Then, such functions have been used to define two distinct
consistency notions, pointing out their properties with respect to the chosen set of
relationships. Finally, for each scenario considered, examples of the applications of
the proposed notions have been provided. Future work includes the extension of the
proposed approaches to deal with other types of spatial relations and the refinement
of the proposed distance functions to cope with quantitative measures.
References
1. Belussi A, Catania B, Podest` a P (2005) Towards Topological Consistency and Similarity
of Multi-resolution Geographical Maps. In: Shahabi C, Boucelma O (eds) Proc. of the
13th Int. Symp. on Advances in GIS. Bremen, Germany, 220–229
2. Belussi A, Catania B, Podest` a P (2006) Using Qualitative Information in Query Processing over Multi-resolution Maps Technical Report DISI-TR-06-18, Dipartimento di
Informatica e Scienze dell’Informazione, University of Genova, Italy
6 These data sets were provided by COGEME Spa (Rovato BS, Italy) in the context of the
research project SpadaGIS funded by MIUR.
Paola Podest` a, Barbara Catania, and Alberto Belussi
8.7.3 Consistency Checking
In order to present an application example of the proposed notions to consistency checking, we evaluate the topological consistency of two maps ML1
R
roads and
ML1
L
roads , containing the streets of a municipality of Lombardy (Italy) represented
as regions in ML1
R
roads and as lines in ML1
L
roads .
6 Figure 8.10 presents two snapshots
from corresponding areas of ML1
R
roads and ML1
L
roads .
By performing a consistency check on such data sets, we find that they are neither
eq-based nor dist-based consistent. For example, we discovered that roads 72 and 160
are not dist-based consistent (see Fig. 8.10). Their relation is T ouch in Fig. 8.10(a)
and Dis joint in Fig. 8.10(b). According to the table presented in [2], this pair violates
both dist-based and eq-based consistency. On the other hand, the pair of roads 70
and 160 are eq-based consistent since their relation is T ouch in both Fig. 8.10(a) and
Figure 8.10(b).
8.8 Conclusions
In this chapter, we have identified some new approaches for processing multiresolution maps in an integrated environment by using qualitative information represented by topological and cardinal relations. In the multiresolution model considered, the same object can be represented with geometries of different dimensions
(points, lines, and polygons) in different maps. The proposed approaches refer to
three distinct scenarios: (i) similarity-based query processing; (ii) GIS mediation architectures; (iii) map consistency checking. In order to support the contexts presented
above, two main issues have been addressed. First of all, starting from some wellknown models, distance functions for topological and cardinal directional relationships have been defined. Then, such functions have been used to define two distinct
consistency notions, pointing out their properties with respect to the chosen set of
relationships. Finally, for each scenario considered, examples of the applications of
the proposed notions have been provided. Future work includes the extension of the
proposed approaches to deal with other types of spatial relations and the refinement
of the proposed distance functions to cope with quantitative measures.
References
1. Belussi A, Catania B, Podest` a P (2005) Towards Topological Consistency and Similarity
of Multi-resolution Geographical Maps. In: Shahabi C, Boucelma O (eds) Proc. of the
13th Int. Symp. on Advances in GIS. Bremen, Germany, 220–229
2. Belussi A, Catania B, Podest` a P (2006) Using Qualitative Information in Query Processing over Multi-resolution Maps Technical Report DISI-TR-06-18, Dipartimento di
Informatica e Scienze dell’Informazione, University of Genova, Italy
6 These data sets were provided by COGEME Spa (Rovato BS, Italy) in the context of the
research project SpadaGIS funded by MIUR.