**3. The reasons of the choice and the previous studies**

76 Cartography – A Tool for Spatial Analysis

can be performed through GIS applications.

technical considerations about the map-making procedures.

heritage.

**2. Materials** 

few years later (1599).

to an alteration in the analogue support; other errors can be recorded in the cartographic document, for instance errors that were made by the cartographer during survey or draft steps, or errors inherent to the surveying instruments at that time. In order to compare an ancient cartographic document to a modern one (usually a modern map used as reference), a georeferencing process is performed in a digital environment, assigning cartographic coordinates to a number of still existing and recognizable Ground Control Points (GCPs). This way, the native metric content of the map can be reproduced in the digital image, and furthermore an analysis of the existing map deformations is allowed. Thus, it becomes possible to understand the characteristics of metric precision of the original product (e.g. the projection type) in respect to the present reference cartographic base, as well as to evaluate and represent the degree of deformation recorded in the ancient document. The historical map, now in digital form, can be easily exploited and compared with other cartographic databases, thanks also to current web services; change analysis and analytical procedures

This way, regeneration of ancient maps in digital form appears to be useful for many users: not only the public and institutions who collect them, but also experts who exploit this kind of documents to derive information for their studies, ranging from urban development to geomorphological or environmental topics. Many institutions today are digitalizing their cartographic heritage, in order to preserve and catalogue it and give online access to it (Adcock et al., 2004). On the evidence of growing interest in the argument, the International Cartographic Association (ICA) instituted in 2007 the "Commission on Digital Technologies in Cartographic Heritage", whose aim is to encourage digital approaches to cartographic

The present research would demonstrate the usefulness of the digital regeneration of ancient cartography; it provides an example of studies that can be performed after digital regeneration of ancient cartography, with a non-conventional approach mainly focused on

In this study, a set of three maps, depicting the northern coast of the Adriatic Sea along the Po river delta (South of Venice, Italy) at the end of the 16th century, is analysed (Figure 1). The first two maps were both drafted in the year 1592, whereas the third one was drafted

The maps represent a rare case where the authors of documents are known. The same cartographer, Ottavio Fabri, was author of the first map (hereinafter "F map") and co-author in the other two (hereinafter "P map" and "L map"), in which the main authors were Gerolamo Pontara and Bonaiuto Lorini, respectively. All of them were very famous landsurveyors in Renaissance Venice (*Savi ed Esecutori delle Acque della Serenissima Repubblica*).

The dimensions of these documents are very large, and their average scales range between about 1:12,000 and 1:13,000, not being constant throughout the entire maps. The original Even if the above mentioned existence of a textbook probably related to the chosen maps would not be taken into account, other strong motivations appear to exist to focus our analysis on those cartographic samples.

As these maps were made during the very short period between the years 1592 and 1599, i.e. the lapse of time immediately forerunning a series of very important works aiming at the Po river channel diversion, they stimulate a compelling geomorphological analysis (Cremonini 2007a; Cremonini & Samonati 2009) focused on the easternmost peripheral areas that today no longer exist, due to erosional dynamics of seashore evolution developed during the last four centuries (Cremonini 2007b; Cremonini 2010). A further problem arises, due to the fact that the maps depict in a quite different manner the same landforms, although they appear to have been drawn in the same years by the same author or co-author (Ottavio Fabri). For these reasons the maps have already been studied from various viewpoints and metrically analysed in a digital environment (Bitelli et al. 2009, 2010), to try to overcome the merely qualitative comparison between the available maps.

Although the modern digital techniques, in particular georeferencing of the cartographic samples coupled with a study of the map deformations, help in metric analysis of ancient cartography, in pre-geodetic cartography studies specific analytical tools need to be used, e.g. in the step-by-step solution here proposed.

Analysis of Pre-Geodetic Maps in Search of Construction Steps Details 79

**Figure 2.** Images derived from O. Fabri, *L'uso della squadra mobile* (1673 edition, kept in the Engineering Faculty Library of the University of Bologna): (a) a picture of the *squadra mobile*; (b) measurement of

Georeferencing is the technique of inserting a map into a reference system, usually a modern cartographic one. The process is performed by selecting in the ancient map a proper number (usually as large as possible) of peculiar points (GCPs, Ground Control Points), still existing today, and deriving their cartographic coordinates from the present cartography or a specifically designed survey. In the peculiar case of ancient cartography, the task can be very difficult or also impossible, because of the remarkable landscape evolution over time

When a sufficient number of points is available, a *one-to-one* correspondence between the two set of control points lying on two different plane surfaces (i.e. points on the digital image of the ancient map, expressed in image coordinates, and reference points, expressed in cartographic coordinates) is established through a "best-fit" process, that finishes with the calculation of the transformation parameters. The number of involved parameters can varies

river widths; (c) an exercise of forward intersection.

**3.1. The quantitative approach** 

*3.1.1. Georeferencing* 

(Benavides & Koster, 2006).

**Figure 1.** The three analyzed maps proportionally scaled (red bar = 1 m): a) *Delta del fiume Po*, by Ottavio Fabri, 1592. *Savi ed esecutori delle acque, serie Po,* dis. 9bis. Size: about 3.5 x 2.5 m; b) *Delta del fiume Po*, by Gerolamo Pontara, Ottavio Fabri, 1592. *Savi ed esecutori delle acque, serie Po,* dis. 8. Size: about 2.9 x 1.6 m; c) *Delta del fiume Po*, by Bonaiuto Lorini, Ottavio Fabri, Gerolamo Pontara, Alessandro Betinzuoli, Bartolomeo Montini, 1599. *Savi ed esecutori delle acque, serie Po,* dis. 10*.* Size: about 2.3x1.4 m.

Analysis of Pre-Geodetic Maps in Search of Construction Steps Details 79

**Figure 2.** Images derived from O. Fabri, *L'uso della squadra mobile* (1673 edition, kept in the Engineering Faculty Library of the University of Bologna): (a) a picture of the *squadra mobile*; (b) measurement of river widths; (c) an exercise of forward intersection.

### **3.1. The quantitative approach**

#### *3.1.1. Georeferencing*

78 Cartography – A Tool for Spatial Analysis

**Figure 1.** The three analyzed maps proportionally scaled (red bar = 1 m): a) *Delta del fiume Po*, by Ottavio Fabri, 1592. *Savi ed esecutori delle acque, serie Po,* dis. 9bis. Size: about 3.5 x 2.5 m; b) *Delta del fiume Po*, by Gerolamo Pontara, Ottavio Fabri, 1592. *Savi ed esecutori delle acque, serie Po,* dis. 8. Size: about 2.9 x 1.6 m; c) *Delta del fiume Po*, by Bonaiuto Lorini, Ottavio Fabri, Gerolamo Pontara, Alessandro Betinzuoli,

Bartolomeo Montini, 1599. *Savi ed esecutori delle acque, serie Po,* dis. 10*.* Size: about 2.3x1.4 m.

Georeferencing is the technique of inserting a map into a reference system, usually a modern cartographic one. The process is performed by selecting in the ancient map a proper number (usually as large as possible) of peculiar points (GCPs, Ground Control Points), still existing today, and deriving their cartographic coordinates from the present cartography or a specifically designed survey. In the peculiar case of ancient cartography, the task can be very difficult or also impossible, because of the remarkable landscape evolution over time (Benavides & Koster, 2006).

When a sufficient number of points is available, a *one-to-one* correspondence between the two set of control points lying on two different plane surfaces (i.e. points on the digital image of the ancient map, expressed in image coordinates, and reference points, expressed in cartographic coordinates) is established through a "best-fit" process, that finishes with the calculation of the transformation parameters. The number of involved parameters can varies with the transformations, each transformation requiring a different number of control points.

Analysis of Pre-Geodetic Maps in Search of Construction Steps Details 81

Squared error) was about 588 m in F and P maps, ranging between 18 and 1,320 m in F map and between 85 and 1,650 in P map; it was more constrained in L map (mean: 452 m; range: 29 ÷ 1,068 m). The residuals appear to be lower in the map centre, whereas they increase in size in the peripheral areas. This is the classical border effect due to the polynomial transformation associated to the lack of reference points in the area. But in this specific case it can be supposed that the effect can be due also to other reasons, such as the survey

**Figure 3.** Overlay of the three ancient maps, georeferenced by means of a second order polynomial

Comparing an ancient map with a present one allows evaluation and representation of the deformation degree of the former. Map deformations can be induced by physical alteration of the analogical support (a very frequent case for ancient maps) or by the old type of cartographic transformation (that frequently is unknown to us, and usually quite different from that used today and inducing less constrained deformations), or finally by surveying and drafting errors. Map deformations can be very high for ancient cartography; therefore, their assessment is essential in order to use the old samples for further studies (Livieratos, 2006). The assessment of map deformations consists in calculating some parameters from a comparison of the ancient map with a modern one as a reference (usually a present cartography to an appropriate scale, i.e. comparable with

transformation, on present high resolution satellite images (in *Bing Maps*TM environment).

*3.1.2. Study of map deformation* 

technique locally adopted, accidental or intentional drawing errors, etc.

In fact, many kinds of georeferencing methods exist, and they produce results that can be qualitatively and quantitatively different. In particular, the georeferencing algorithms can be grouped in two different classes: global and local transformations (Balletti 2006; Boutoura & Livieratos, 2006). In a global transformation (conformal, affine, projective, generic order polynomial) the unknown parameters are calculated for the whole area. On the other hand, in a local transformation (finite elements, morphing) the unknown parameters are calculated for a small area, defined by a small number of control points or close to each control point. The *best* georeferencing method probably do not exist, because the choice of a specific georeferencing method depends on the specific case (map characteristics, number of available GCPs, etc.) and on the purpose which the georeferenced images will be used for.

By means of a georeferencing process, the native metric content of the map being reproduced in the digital image, the historical map can be compared with the present cartography or other cartographies (also coeval ancient maps) in the same reference system. The process generates a new aspect of the ancient map, showing the typical deformation induced by its cartographic characteristics (and partly by the applied algorithm): in this way it is possible to understand the metric quality of the map representation (e.g. by means of the residuals errors associated to each single point, output by the geroreferencing process) and the projection features of the historical map, but also to perform many other kinds of analysis, e.g. studies related to change of the landscape.

In this specific case, after careful analysis of the three cartographic samples, a set of about 80 common GCPs, clearly identifiable also on the IGM (Italian Military Geographic Institute) topographic sheet, was recognized on the three ancient maps. It has to be stressed that in this phase a great deal of problems arose, concerning the basic characters of the points themselves (e.g. their planimetric precision, their graphic representation on the ancient maps, etc.), in addition to the difficulty in finding points that are still existing. North and East coordinates were attributed to each selected point according to the UTM-ED50 (fuse 33) grid. Different georeferencing methods were tested on the three map samples, and the most useful in order to compare them with the present landscape resulted polynomial transformations. In particular, the second order polynomial transformation resulted a good compromise between adaptation of the ancient maps to inland area details of the present landscape, on one hand, and constraint of deformations (indicated by the mean residual errors) throughout the maps, on the other (Bitelli et al. 2009).

Polynomial transformations coincide with a linear transformation (6-parameter affine) in the first order, and a non-linear one at higher degrees. A linear transformation corrects for scale, offset, rotation and reflection effects, whereas a non-linear transformation (for example, the 2nd order polynomial transformation) corrects for non-linear distortions: the final result depends very much on the number of control points and their spatial distribution in the image plane.

In Figure 3 an overlay of the three maps on present high resolution satellite images (in *Bing Maps*TM environment) is reported. The mean residual error (expressed as RMS, Root Mean Squared error) was about 588 m in F and P maps, ranging between 18 and 1,320 m in F map and between 85 and 1,650 in P map; it was more constrained in L map (mean: 452 m; range: 29 ÷ 1,068 m). The residuals appear to be lower in the map centre, whereas they increase in size in the peripheral areas. This is the classical border effect due to the polynomial transformation associated to the lack of reference points in the area. But in this specific case it can be supposed that the effect can be due also to other reasons, such as the survey technique locally adopted, accidental or intentional drawing errors, etc.

**Figure 3.** Overlay of the three ancient maps, georeferenced by means of a second order polynomial transformation, on present high resolution satellite images (in *Bing Maps*TM environment).

### *3.1.2. Study of map deformation*

80 Cartography – A Tool for Spatial Analysis

points.

with the transformations, each transformation requiring a different number of control

In fact, many kinds of georeferencing methods exist, and they produce results that can be qualitatively and quantitatively different. In particular, the georeferencing algorithms can be grouped in two different classes: global and local transformations (Balletti 2006; Boutoura & Livieratos, 2006). In a global transformation (conformal, affine, projective, generic order polynomial) the unknown parameters are calculated for the whole area. On the other hand, in a local transformation (finite elements, morphing) the unknown parameters are calculated for a small area, defined by a small number of control points or close to each control point. The *best* georeferencing method probably do not exist, because the choice of a specific georeferencing method depends on the specific case (map characteristics, number of available GCPs, etc.) and on the purpose which the georeferenced images will be used for.

By means of a georeferencing process, the native metric content of the map being reproduced in the digital image, the historical map can be compared with the present cartography or other cartographies (also coeval ancient maps) in the same reference system. The process generates a new aspect of the ancient map, showing the typical deformation induced by its cartographic characteristics (and partly by the applied algorithm): in this way it is possible to understand the metric quality of the map representation (e.g. by means of the residuals errors associated to each single point, output by the geroreferencing process) and the projection features of the historical map, but also to perform many other kinds of

In this specific case, after careful analysis of the three cartographic samples, a set of about 80 common GCPs, clearly identifiable also on the IGM (Italian Military Geographic Institute) topographic sheet, was recognized on the three ancient maps. It has to be stressed that in this phase a great deal of problems arose, concerning the basic characters of the points themselves (e.g. their planimetric precision, their graphic representation on the ancient maps, etc.), in addition to the difficulty in finding points that are still existing. North and East coordinates were attributed to each selected point according to the UTM-ED50 (fuse 33) grid. Different georeferencing methods were tested on the three map samples, and the most useful in order to compare them with the present landscape resulted polynomial transformations. In particular, the second order polynomial transformation resulted a good compromise between adaptation of the ancient maps to inland area details of the present landscape, on one hand, and constraint of deformations (indicated by the mean residual

Polynomial transformations coincide with a linear transformation (6-parameter affine) in the first order, and a non-linear one at higher degrees. A linear transformation corrects for scale, offset, rotation and reflection effects, whereas a non-linear transformation (for example, the 2nd order polynomial transformation) corrects for non-linear distortions: the final result depends very much on the number of control points and their spatial distribution in the image plane.

In Figure 3 an overlay of the three maps on present high resolution satellite images (in *Bing Maps*TM environment) is reported. The mean residual error (expressed as RMS, Root Mean

analysis, e.g. studies related to change of the landscape.

errors) throughout the maps, on the other (Bitelli et al. 2009).

Comparing an ancient map with a present one allows evaluation and representation of the deformation degree of the former. Map deformations can be induced by physical alteration of the analogical support (a very frequent case for ancient maps) or by the old type of cartographic transformation (that frequently is unknown to us, and usually quite different from that used today and inducing less constrained deformations), or finally by surveying and drafting errors. Map deformations can be very high for ancient cartography; therefore, their assessment is essential in order to use the old samples for further studies (Livieratos, 2006). The assessment of map deformations consists in calculating some parameters from a comparison of the ancient map with a modern one as a reference (usually a present cartography to an appropriate scale, i.e. comparable with

the scale of the ancient map), such as the rotation angle with respect to the present cartographic North, the scale variation throughout the map and the distortion of the present cartographic grid as resulting after its adaption onto the old map. The process is performed recognizing in the ancient map a proper number of still existing points, whose cartographic coordinates can be derived from the present cartography. A specifically designed software tool can result very useful for analysis of map deformations, allowing the calculation of all the aforementioned parameters and their subsequent drafting in an intuitive way (Jenny & Hurny, 2011).

Analysis of Pre-Geodetic Maps in Search of Construction Steps Details 83

**Figure 4.** Graphical results from a deformation analysis performed on the three maps (see Jenny & Hurny 2011 for software description): in blue the UTM-ED50 grid (mesh size = 2 km), in red the residual vectors on the GCPs, in yellow the scale isolines, in orange some values of the calculated map scale.

The study of map deformation characterising the cartographic samples here analysed showed scale factors quite variable throughout the maps, being slightly more homogenous in F map than in P map. The average scale resulting from the calculation was 1:12,300 (1:14,300 ÷ 1:10,300) and 1:13,400 (1:16,600 ÷ 1:10,200) in F and P maps, respectively. Notwithstanding this, the former map showed two severe anomalous variation areas near the northern and southern delta lobe corners (Bitelli et al. 2009). In particular, the northern gross deformation affecting F map is supposed to derive from a shift of the drawing, intentionally made by the author for unclear reasons. L map presented a bit more constrained scale factor (mean 1:11,200, range 1:13,200 ÷ 1:11,200) and a smaller deformation than the other two, but it has to be taken into account that L map depicts a smaller area in respect to F and P maps (Figure 4). Moreover, the calculated rotation angles were 15.7°, 8.9° and 3.6° for F, P and L maps, respectively: they indicate an angular displacement of about 7° between the first and the second map, and 12° between the first and the third map.

In this specific case, where large areas, depicted in the maps, correspond to disappeared coastal (i.e. peripheral) belts, points suitable to be used as GCPs cannot be found in the present landscape, and the insertion of GCPs all around the deltaic area becomes obviously impossible. The metric analysis that was possible to perform on the set of maps highlighted gross deformations in all maps (especially in F and P maps). Notwithstanding some differences in the results showed by the maps, this analysis alone resulted insufficient to state which map has to be considered as the most faithful to the real asset of the ancient landscape.

Thus, a question still remains open: why does exist a family of so severe deformations?
