ADAPTIVE TRANSFORMATION OF CARTOGRAPHIC BASES BY MEANS OF 
MULTIRESOLUTION SPLINE INTERPOLA TION 
Maria Antonia Brovelli, Giorgio Zamboni 
Politecnico di Milano — Polo Regionale di Como, Via Valleggio 11 — 22100 Como 
390313327517, fax 4390313327519, e-mail maria.brovelli@polimi.it 
390313327528, fax 4390313327519, e-mail giorgio.zamboni(polimi.it 
KEYWORDS: cartography, GIS, integration, algorithms, multiresolution, vector 
ABSTRACT: 
GIS databases often need to include maps from diverse sources. These can differ one another by many characteristics: different 
projections or reference systems, (slightly) different scales, etc. Theoretical and/or empirical transformations are available in 
literature to obtain maps in a unique system with a fixed tolerance. These transformations are nevertheless insufficient to completely 
remove differences and deformations: the outcome is that the geographic features on the maps do not fit in a perfect way. To reduce 
the deformation several transformations (affine, polynomial, rubber-shecting) exist. The paper presents a new approach to the 
problem based on an interpolation by means of multiresolution spline functions and least squares adjustment. One map is taken as 
reference and the others are warped to comply with it. The interpolation is made by comparison of coordinates of a set of 
homologous points identified on the maps. The use of spline functions, compared to affine or polynomial interpolation, allows to 
have a greater number of coefficients to make more adaptive and localized the transformation. The multiresolution approach 
removes the rank deficiency problem that ordinary spline approach suffers for. Moreover the resolution of the spline functions 
depends areawise on the spatial density of homologous points: the denser are the points in the area, the better adapted to them can be 
the interpolating surface. A statistical test has been built to automatically choose the maximum exploitable resolution. The paper 
presents the method and one application in the example. 
1. INTRODUCTION 
1.1 Interoperability in Geographic Information Systems 
The increase of application fields of GIS (local administration, 
tourism, archaeology, geology, etc.) has made of new interest 
the study of the sharing of information from different 
geographic — databases, also known as “GIS data 
interoperability". 
In general, with the technical term interoperability we define a 
user's or a device's ability to access a variety of heterogeneous 
resources by means of a single, unchanging operational 
interface. In the GIS domain, interoperability is defined as the 
ability to access multiple, heterogeneous maps and 
corresponding geo-referenced data (either local or remote) by 
means of a single, unchanging software interface. 
Interoperability engages at several levels: network protocol, 
hardware & OS, data files, DBMS, data model and application 
semantics. Nowadays greater automation is already evident, 
especially at the first four levels of interoperability; however at 
the most fundamental levels (data model and semantics) there 
remains further room for improvement. 
Usually geographic information is formed by geometric and 
thematic attributes. For this reason the research on 
interoperability is focused on topological compatibility (at the 
level of data structure) and on semantic compatibility (at the 
level of identifiers) of the data. 
To guarantee the interoperability there is another very 
important problem often not mentioned: the geometrical 
compatibility (at the level of coordinates) of the maps. 
GIS databases often include maps coming from diverse 
sources. These can differ one another by many characteristics: 
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different projections or reference systems, (slightly) different 
scales, different kinds of representations, etc., with the result of 
geometric incompatibility of the different maps. 
1.2 The “Conflation Maps” problem 
Map conflation was first addressed in the mid-1980s in a 
project to consolidate the digital vector maps of two different 
organizations (Saalfeld, 1988). The problem was split into two 
parts: the detecting of homologous elements between the two 
maps, and the transformation of one map compared with the 
other (Gillman 1985: Gabay and Doytsher, 1994). Point 
elements within one map were selected as the group of features 
whose counterpart points on the other map enable the conflation 
process (Rosen and Saalfeld, 1985). 
Since then, many conflation algorithms have been developed 
and improved. Recently, the main concern has been focused on 
data integration. Several geodata sets which cover the same 
area but are from different data providers, may have different 
representation of information and may be of different accuracy 
and forms. 
Conflation can be used to solve different practical problems like 
spatial discrepancy elimination (such as sliver polygons, shifts 
of features, etc.), spatial feature transfer (new features can be 
added into the old map, or old coordinates can be update). 
attribute transfer (i.e. the attributes in the old maps can be 
transferred into the new maps). 
The conflation algorithms can be classified into three kinds: 
geometric, topological and attribute method. 
Geometric methods are mostly used because we are dealing 
with spatial objects. They scan geometric objects from both 
data sets and compare them by geometrical criteria: distance, 
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