Historic cartography and early maps has been, for long time, a
privileged domain of study almost exclusively for historians and not so much
for cartographers and specialists in modern mapping sciences and technologies.
Therefore, the early map has been considered as a typical archive document, a
testimony of the past, of territories and cities in diverse historical periods.
In the last years due to the advancements of new computational technologies the
study of the metric properties of early maps, the numerical approach to the
issue has gained terrain. Old maps are no longer considered as passive graphic
documents offering the grounds for historic, artistic, sociological or literary
studies but become representations containing a lot of spatially referenced
information affined to geometry, in general, and to geometry-related entities,
in particular (Fuse, Shimizu and Morichi, 1998). This modern possibility,
thanks to modern technologies, offers new tools in the study of early
cartography and maps opening new possibilities in cartographic heritage (Guerra
et al, 1999). In this paper the geometric analysis of early maps is based on an
approach, which is common in current cartography according to which the extraction
of territorial information is spatially referenced, or georeferenced (see, e.g., Balletti, Guerra and Monti 2000, Balletti
2000a).
But how is it possible to
georeference early maps? Especially when this map-family presents, in the vast
majority of cases, some common characteristics related to the uncertain
metrical map properties, as it is the undefined system of reference, the
non-constant or even unknown scale of representation, the unknown units of
measure, the veiled, non-existing or approximate projection system, the
scarcity of reference surface definition, the semantic content which is
difficult to interpret.
These entire shortcomings
which are all or partially emerging when one tries to introduce early maps into
a GIS environment, lead to the necessity of adopting special strategies which
could be diverse in each particular case. An early map presents different
levels of point and relational accuracy in planimety and topography. Geometric
proportions, conventions and hierarchies are varying from map to map even by
the same mapmaker. All these should be identified and distinguished by the
modern user who has, in addition, the task to classify them and evaluate
according to the early map typology, i.e. in a sea chart, distances, coastlines
and bearings are much more accurate than in some other map with different
function. Harbours and river mouths are positioned with care and, often, magnified
regarding the general map scale of the chart. On the other hand the coasts are
represented in a conventional way as well as the topography of the hinterland
(such as mountains or representative architectures of a place).
Two types of
historic cartographic material are considered here: In the first, maps and
plans are of pure cartographic interest made for technical and public purposes
as they represent geographic outlines, respecting the proportional relations.
In this case, the geographical configuration is in orthogonal projection, while
topographical characteristics are depicted in perspective or in front views,
according to a schematic conventional look. In the second type belong maps and
plans for didactic purposes, mainly for providing illustrations rather than for
offering geographical information. But in any case, even such, they are spatial
representations of the territory and therefore are contain geoinformation.
In any case, the
important issue is that, in general, assigning a proper metric support to all
these cartographic documents of the past is very important for the analysis of
the geometric content and modern cartographic use. This is important not only
to assist the old map as a document for the archives, having a qualitative
value, but also to make it useful and valuable for modern cartographic
implementations for the extraction of quantitative information.
The
idea, which governs the whole concept and supports the research in this
direction is that these old map-work has been created in order to serve as an
operative and practical tool and that it was used as such. This means that
geometry was always present in different ways and in various implementations.
Only the metric definitions and properties
have changed over the periods of mapmaking and, of course, the level of the
accuracy threshold, which means the level of the technology of measurements
involved in mapping practice and the precision achieved each time.
Georeference
The georeference is applied
here as the process, which assigns to non-metrical maps (usually the early
maps) a ‘metric reference’ from the actual geospace or its mappings. When the
metric reference is related to the system of earth coordinates or their
map-projection counterparts, it is called georeference.
This assignment is done with
the use of geometric transformations
applied to points of the non-metrical map with known or given coordinates.
These points are called control points.
The result of the transformation is that all the other points of the
non-metrical map are then getting coordinates which are ‘predicted’ (through
proper interpolation functions) from the known or given coordinates of the
control points. It is called global
the transformation due to which the best possible metric reference is assigned
to the un-georeferenced map, without keeping unaltered, after the
transformation, the coordinates of the control points. On the other hand, it
is called local the transformation,
which keeps unchanged the coordinates of the control points after the
transformation. The main characteristics of global
transformations can be summarized in the next few steps: The transformation is
based on parameters which are calculated before the transformation, with the
aid of the known coordinates of the control points; the parameters are valid for any point of the
map, in other words they concern the map globally; the larger is the
number of the control points used for the computation of the parameters the
better statistical solution is achieved; a statistical estimate of the
transformation results is among the output of the process in terms of regular
statistical quantities.
Global transformation
The
global transformations are derived from the well-known full polynomial system
of equations
, 
where the
summation convention in i,j is
applied up to the order of the polynomial m,n.
This system relates the coordinates of the control points Xk and Yk
in the geospace (or its mappings) with their coordinates xk and yk
on the map to be georeferenced, where k (k=1,2,3,…) is the control point involved
in the transformation. For each point k
a set of two equations are taken and the required value of k for the solution of the system, depends on the order of the
polynomial used. Today these coordinates xk
and yk are obtained
digitally form the map to be georeferenced. The quantities aij and bij,
are the unknown parameters which are obtained by the transformation process
and are valid all over the area. In a computational process the number of the
control points should be always more that the unknown parameters. In the case
in which only linear terms are taken into consideration, the above system is
providing the linear transformations commonly used in mapping disciplines,
known as conformal, affine and projective. The
use of non-linear terms provides the higher order polynomial transformations with most used that of the second order.
Local transformations
The local transformations are
those in which the unknown parameters of the transformation are calculated for
a small area close to the control point or for each single control point having
thus, a local validity. In the first case belongs the finite element transformation in which the whole area to be
transformed is divided in a mesh of triangles with the control points as the
vertices of the triangles (here the Delaunay triangulation is followed, because
of the proper configuration of the resulting triangles). Then, for each
triangular area defined by the vertices of the corresponding three control
points, an affine transformation is applied, and the parameters obtained are
valid within the specific triangular area. The smaller the triangular areas of
the mesh the better are the results. This, requires and great enough number of
control points.
In the second type of local
transformations belong the ones based on conditions, which force the points (or
features) on the surface to be transformed to fit exactly to the corresponding
control points (or control features). Such transformations are usually known as
point based warping and feature based warping.
Some applications
In
order to illustrate the methods mentioned above, three examples are used from
the early map-typologies of the Venetian cartographic heritage. The first comes
from the isolarii tradition, the second concerns a portolan nautical map and
the third the perspective city map of Venice by Jacoppo de’ Barbari.
Bordone’s Crete
The
first example, from the domain of the isolarii, shows how the simplest possible
transformation can be applied in studying the rotation of a map without
changing at all its shape. In Fig. 1, Bordone’s depiction of Crete, from his
Isolario from the early 16th century, is georeferenced and
transformed to fit optimally to a modern map, keeping unaltered its shape. The
transformation used here is a conformal transformation of the global type.
In
this case no deformation analysis can be done since the transformation regards
only a single orientation issue with respect to the actual North, which here is
tilted 6 degrees clockwise. If the interest is focused on the deformational
pattern of this Bordone depiction of Crete, then a point wise warping
transformation is applied of the local type. In Fig. 2 the original shape of
the island is alterated in order to fit in the best possible way the actual
coastline.
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Figure 1.
Bordone’s Crete is rotated to fit optimally (conformal georeference) the actual
orientation of the island, without deforming the shape as depicted in the
original map.
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Figure 2.
Bordone’s Crete is deformed to fit optimally the actual coastline
(point-wise exact georeference).
Sideri’s East
Mediterranean
The
second application concerns the study of portolan nautical maps. The 16th
century Sideri’s representation of East Mediterranean, from the post-Mercator
period, has taken as a pilot study to investigate, first (Balletti 2000b) the
conformal fitting of the coastline to the actual counterpart (Fig. 3) and second
the compliance of the ‘rose of the wind’ radial pattern, dominant in this type
of maps, with the actual alignment of the meridians and parallels (Fig.4). Even if portolan maps were
thought as maps without a projection reference, the lack of clear and visible
geographic framing in terms of geographic coordinates, do not necessarily imply
the lack of, or the non-relation with, a projective system. The results given
in a previous research (Boutoura, 2000), on the relation between the ‘rays’ of the wind roses
and the geographic graticule in portolan maps, is confirmed here as it is shown
in Fig. 4.
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Figure 3. Left:
The Sideri’s portolan map after the conformal fitting to a modern map in Mercator’s
projection is rotated 9 degrees clockwise. Right: The residuals of the control
points, after the conformal fitting, are illustrated. The areas with best
fitting (less residuals) are in the area of the Ionian Islands, Peloponnese and
Crete.
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Figure 4. Left:
The central ‘rose of the winds’ dominant in Sideri’s portolan map. The map
obeys a 9 degrees clockwise rotation after the conformal fitting to a modern
map in Mercator’s projection. Right: The modern map in Mercator’s projection,
where the ‘rose of the winds’ is conformally projected from Sideri’s map. The
relation between the roses on the perimetre of the central rose and the actual
parallels and meridians, is evident.
de’ Barbari’s Venice
The third example is applied
to de’ Barbari’s perspective map of Venice (1500). This celebrated
representation among the first of this type in the map history represents is a
most exciting example of the new method of urban representation of the city
based on perspective. For the georeference of the perspective map, a modern
photomap of Venice is used to test a number of transformations. In Fig. 5
(centre) the photomap of Venice has been auto-transformed according to a
perspective projection and this image is compared to the original map, Fig. 5
(top). Fig. 5 (bottom) shows the difference in perspective induced by de’
Barbari’s representation.
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Figure
5. Top: The perspective view of Venice by de’ Barbari’s. Centre: A modern city
photomap in a ‘correct’ perspective projection. Bottom: The perspective view by
de’ Barbari’s (in grey shaded tone) with respect to the ‘correct’ perspective
photomap.
The
perspective alterations in the original city map can be shown also when
transforming the perspective photomap into the original following the finite
element transformation. In Fig. 6 the alterations in the alignment of the
perspective lines are evident. This confirms the theory that the de’ Barbari’s
map does not preserves full projectivity.
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Figure 6. Finite elements transformation: applying
this transformation, the new image of the photomap obtained has the same
geometry of the de’ Barbari one, but the irregular deformation of the grid underlines
that the view is not a correct perspective.
References
Balletti C.,
F. Guerra, C.Monti (2000). Analitical methods and new technologies for geometrical
analysis and georeferenced visualisation of historical maps. In International Archives of Photogrammetry
and Remote Sensing, Vol.XXXII, Part 6W8/1, ISPRS WG VI/3 e WG IV/3, Ljubliana.
Balletti C.
(2000a). Analytical and quantitative methods for the analysis of the geometrical
content of historical cartography. In International
Archives of Photogrammetry and Remote Sensing, Vol. XXXIII, ISPRS WG V/5,
Amsterdam.
Balletti C. (2000b). Metodi analitici
e quantitative per lo studio del contenuto geometrico delle carte storiche.
Tesi di dottorato di ricerca in scienze geodetiche e topografiche, XII ciclo,
Politecnico di Milano.
Boutoura C.
(2000). Scoperta di un il reticolato
geografico in una carta nautica dell'Egeo del XVI secolo. In E. Livieratos (ed.)
Raggi di vento sul mare. Thessaloniki: Hellenic National
Centre for Maps and Cartographic Heritage.
Fuse T., E.
Shimizu, S. Morichi (1998). A study on geometric correction of historical maps.
In International Archives of Photogrammetry
and Remote Sensing, Vol XXXII, Part 5, Hakodate.
Guerra, F., C. Balletti,
C.Monti, E. Livieratos, C.Boutoura (1999).
Studi ed elaborazioni informatiche e ‘infografiche’ sulla veduta
prospettica di de’Barbari. In G. Romanelli, S. Biadene, C. Tonini (eds.) A volo d’uccello, Jacopo de’Barbari e le
rappresentazioni di città nell’Europa del Rinascimento. Venezia:
Arsenale editrice.