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Arabian Journal for Science and Engineering

Open Access 18.05.2024 | Research Article-Earth Sciences

Landmark Base Point Approach to Positional and Coastal Accuracy Analysis for Historical Map Before WWI: A Case Study 1836 Moltke and 1914 German Blue about in Historical Peninsula of İstanbul

verfasst von: Cumhur Sahin, Bahadir Ergun, Furkan Bilucan

Erschienen in: Arabian Journal for Science and Engineering

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Abstract

Cartography, unquestionably one of the world’s oldest disciplines of scientific study, is among the fields that have been most influenced by technological improvements. These improvements have enhanced interest in historical maps while also paving the way for modern mapping. All of this process has created new topics of study for cartographers. It is possible to examine old maps using software such as MapAnalyst which can enable the investigation of time-dependent changes. In this study, two historical maps, namely, Moltke and German Blue, were analyzed in the study area including the Historical Peninsula, Golden Horn, some part of Bosphorus, and the Marmara Sea in İstanbul, Türkiye, employing Helmert, Affine, and Huber loss robust estimation methods. It was revealed that the region with the highest deterioration on both maps is between Beşiktaş and Üsküdar. The coastline change analysis was also performed. According to the results, it was observed that the regions with the most coastal change are located on the southern and eastern coasts of the Historical Peninsula.

1 Introduction

Cartography is the discipline dealing with drafting, editing, proofing of map content, production, and study of maps. According to the International Cartographic Association (ICA) [1], a map is “a symbolised representation of a geographical reality, representing selected features and characteristics, resulting from the creative effort of its author’s execution of choices, that is designed for use when spatial relationships are of primary relevance.” Maps provide irreplaceable information about the location. Historical maps represent an important part of our cultural heritage. Additionally, they are becoming increasingly popular as a source of data for historical research, particularly with the rapid advancement of geographic information system (GIS) software and applications [2].

When referencing historical maps geographically, it is important to evaluate the precision and dependability of geometric and semantic data to gather information for historical research [3]. Moreover, the bi-dimensional regression approach is one of the key mathematical techniques used in cartometric analysis [4, 5]. This technique enables evaluating the similarity of any planar point arrangement. The basic idea behind it is that pairs of related points on two maps are written as vectors and regressed, and the least squares approach is used to determine how similar the two maps are. All the calculations required for this method can be drastically simplified with modern softwares (e.g., ArcGIS, etc.), and the graphical depiction of the findings can be improved. Adjustment is a process that employs one of the following transformations to achieve the best fit between pairs of related locations on a historical and contemporary map: Euclidean (also known as Helmert in MapAnalyst; with a translation, a scale adjustment, and a rotation), affine (a translation, a rotation for each coordinate axis, and different scale adjustments concerning the x and y directions), and robust Helmert transformation methods that available in MapAnalyst (too many outliers are expected in this transformation). All of these transformations are global (they apply uniformly to the whole space of the map) and linear (straight lines are always rendered as straight lines). The nonlinear interpolation used in the second step, allows one to see localized space-warping fluctuations on the historical map. At this stage, the two control point samples are made to coincide exactly, and isolines are then produced using a regular grid of interpolated coordinate values for the area between the two samples [6].

The studies of assessing the accuracy of historical maps are a fundamental goal of cartographic discipline, and these studies enable scholars in other historical disciplines to use cartographic inventories with confidence [7]. When the literature is reviewed, it is observed that some case studies carried out on old maps and examined the accuracies of those maps. The accuracy of historical maps planimetry can be analyzed and visualized using digital methods explained by Jenny and Hurni [3]. The planimetric accuracy of historical maps can be calculated using cartometric methods like Helmert transformations. San-Antonio-Gómez et al. [8] applied the methodology of georectification to compare historical maps with current orthophotos from 2005. A base map was obtained for further analysis and graphical reconstruction.

The purpose of Korodi et al. [9] is to provide a brief overview of the historical cartography of the maps with a focus on the mid-nineteenth century geological mapping activities in the Anina (Steierdorf) coal mining district in Banat Mountains (Romania). In contrast, the paper provides a summary of the cartographic analysis of the maps, which was conducted using the MapAnalyst software program to assess their accuracy in terms of cartography and to create (or facilitate) the georeferencing process. The long-term dynamics of the landscape can be better understood by the application of the methods that are used in this particular case study. In the wake of its 250th anniversary, Aguilar-Camacho et al. [10] reevaluated the accuracy of the so-called Map of Olavide, which bears the name of the person who spearheaded the project, using a new methodological technique that examines each of its four pages separately.

Through the use of the MapAnalyst open-source map software [11], several comparisons are made between digital reproductions of Saxton’s maps and a contemporary map, the 1:1,000,000 Ordnance Survey transport map. The scales of the two Saxton maps can be established from these comparisons. To address distortions, [12] turned to a novel method known as differential distortion analysis, which was motivated by the treatment of distortions in map projection theory. This technique determines local distortion metrics, including the area scale factor and the maximum angular distortion, by examining the behaviors of the partial derivatives of a thin plate spline interpolation function. The Czech Lands between 1526 and 1720 are depicted on this map, which is among important cartographic works. The process for determining the accuracy is based on geometric and cartometric assessments of groups of identical locations on the old map and a reference map using the multi-quadratic interpolation method [13].

In general, coastline analyses are performed using aerial photographs or satellite images from different times [14, 15]. There are also coastline analysis studies in the literature where historical maps are used [16]. Potential errors associated with historical coastal maps and charts include scale errors; distortions from uneven shrinkage, stretching, creases, tears, and folds; different surveying standards; different publication standards; projection errors; and partial revision. However, their advantage is being able to provide a historic record that is not available from other data sources [17].

In this study, the Moltke map produced in 1836 and the German Blue map produced in 1914 were analyzed with 29 common tie points. There is a time difference of about a century between the production of the two maps. Considering the speed of development of İstanbul during this period, only 29 absolute common tie points were determined on the Moltke and German Blue maps. The convenience of using the MapAnalyst software and the calculation techniques offered are investigated in detail. In this context, Helmert, five and six parameters Affine transformation linear methods were used to calculate the positional displacements. Huber loss, which is one of the most popular loss functions widely used in regression problems, was also used as a robust estimation method in the study. In addition, the coastline change was also analyzed. Some significant findings about displacements, orientations, and coastal fillings were observed with the using ArcMap 10.8 software.

2 Cartography

It is suggested that “among the three means of communication established by mankind, (language, music, and the map), the map, which is the product of the science of cartography, is the oldest one” [18]. Besides the importance of understanding our current geography, maps have a progressive character, and this progression can be found anywhere throughout history. The history of a thorough examination of the world and our environment is recorded on the map. The Latin words "carta, charta," which mean hard paper, and "graphia," which means to represent by drawing, are combined to form the English word "cartography," which refers to a painting on paper. Cartography, used for many centuries but defined as a science in 1921 by Max Eckert, forms its own methodology for detailed data, information, and mainly knowledge about space. In addition, classical cartography is a recursive science following thousands of years of cartographic output based on a flat representation of spatial relationships [19]. Additionally, it is one of the fine arts that appeal to the eye since the map is made to be examined. Thus, a cartographer means a person who draws or produces maps.

2.1 History of Cartography

Humans began to hunt after making the shift to settled life, and they felt the urge to make rudimentary sketches in and around their homes. Also, the Çatalhöyük Map, on display at the Museum of Anatolian Civilizations in Ankara and dated to 6600 BC at Çatalhöyük, is thought to be the oldest piece of art that can be acknowledged as the oldest map that has survived to the current day [20]. This map does not contain any written text because it was created before the invention of writing.

In 1300 BC, Egypt made the first land measurements to collect taxes based on land ownership. Anaximander (610–546 BC), a student of Thales of Miletus, is credited as being the inventor of cartography. Also, Eratosthenes (276–195 BC), a philosopher, poet, and geometrician, who was in charge of the Library of Alexandria, made significant contributions to the field of cartography and accurately calculated the circumference of the earth [21]. Additionally, Ptolemy (85–165 AD) laid the first foundations of scientific cartography in 150 AD, and he wrote an eight-volume book called the Cartography Guide. He created the groundwork for the still in use conical projection and coordinate system [22]. In the few centuries after the Ptolemaic maps, there was not much development in the field of cartography. In Medieval Europe, maps commonly called Terrarum Orbis were produced [23]. The angle-measuring instrument (the astrolabe), which was first invented by the Greek astronomer Hipparchus in 200 BC, was rearranged by the Arabs, and this instrument had been used for a thousand years in Europe [24]. Al-Khwarizmi conducted research from which his global map derived the latitude and longitude for 2402 regions. He was influenced by Ptolemy but he produced a more precise work from him. Moreover, Al-Biruni authored a book about global angles [25].

Due to the impact of religion rather than scientific maps of the Middle Ages, Christian Europe was submerged in some dogmatic ideas, and portolan charts, which were a different form of map used by sailors, began to be developed. Portolan charts are maps containing maritime information showing islands, harbors, coasts, estuaries, cliffs, and shallow places. These maps made it easier for sailors and navigators to travel to the high seas. In the sixteenth century, Gerardus Mercator was the world’s leading expert in maps (1512–1594). He found the useful cylindrical projection, which had many applications, and discovered the cylindrical projection, which was widely used in nautical and land maps [26]. The invention of binoculars in 1608 and their development for geodetic applications by Johannes Kepler made it possible to relate and measure the entirety of a country and its areas. Additionally, the first time the measure-based cadastre was put into practice was during the 1st Napoleonic Era (1808). At the start of the nineteenth century, the pressures of growing industry raised the demand for cartography, and cartography had a period of rapid development from the eighteenth to the nineteenth centuries. In the years following the First World War (1914–1918), photogrammetry advanced dramatically [27]. The aerial photogrammetry method, which emerged during the Cold War following the Second World War, became a significant and useful method that accelerated the creation of maps. In addition, remote sensing and satellite photography are two of the most significant advancements in mapping in the twentieth century.

2.2 Cartography in the Ottoman Empire

As the first map produced by Turkish scholars, the spherical globe in Kaşgarlı Mahmud’s Divan-ı Lugati’t Türk which was written between 1072 and 1074 is acknowledged. Moreover, the sea (portolan) map created by Süleyman et-Tancî in 1413 is the first Turkish map created during the Ottoman era. It is well known that Mehmed the Conqueror translated many books found in Byzantine libraries, including Ptolemy’s works after he conquered İstanbul in 1453. On the other hand, Piri Reis provided information about currents, shallow areas, and hazardous rocky shipping locations on maps of various locations in his work Kitab-i Bahriye about the waters dominated by the Ottoman Navy [28]. In addition, Piri Reis is most known for creating a world map in 1513 that includes the Atlantic Ocean and was colored on gazelle skin.

The second documented source of information after Kitab-i Bahriye, which provides information about the New World, is the 10-volume work titled Muhit, written in 1554 by Seydi Ali Reis (1498–1563). An Ottoman historian and painter named Matrakçı Nasuh (1480–1564) depicted his architectural creations and city plans during the growth period of the Ottoman Empire. Cihannüma, the pivotal work written by Katip Çelebi (1609–1657), marks the change from an eastern to a western perspective on geography. Although Katip Çelebi wrote Cihannüma, Ibrahim Müteferrika published it in 1732 together with certain texts, figures, and annexes.

Thanks to the increasing usage of maps throughout the eighteenth and nineteenth centuries, institutional effort, as opposed to individual cartographers’ works, has risen, and more organized institutions carried out the production and activities associated with mapping. Before Erkan-ı Harbiye (General Staff) took on the task of creating maps, the Ottoman Empire relied on foreigners to fulfill its requirement for maps. Heinrich Kiepert’s 1:1,000,000 scale Map of Western Anatolia in 1845 is among these maps. During the reign of Mahmud II, Helmuth von Moltke (1800–1891), who was brought to give training to the Ottoman army between 1835 and 1839 and was given the title of Pasha, made a map of İstanbul with a scale of 1:25,000 between 1836 and 1837 and a map of the Dardanelles with a scale (plane table) of 1:20,000 in 1837. Another example of the maps made before World War I is the maps called German Blue map that formed the basis of İstanbul’s urban planning.

3 Study Area and Historical Maps Used

İstanbul, which is connecting Asia to Europe by Bosphorus, is one of the world’s major cities. The western side of Bosphorus is the European continent, and the eastern side is the Asian continent (Fig. 1). The Black Sea is located in the north of the Bosphorus while the Marmara Sea is located in the south. One of the first settlement areas of İstanbul is the Historical Peninsula. There is the Golden Horn which is a long bay in the north of the Historical Peninsula, the Bosphorus in the east, and the Marmara Sea in the south. The west of the Historical Peninsula is surrounded by city walls built to defend the city and protect it from external factors. There are many historical monuments in the Historical Peninsula, which is known to have hosted different civilizations and cultures throughout its approximately 8500-year history. Hagia Sophia, Topkapı Palace, Grand Bazaar, Sultanahmet Square, and Süleymaniye Mosque are the historical artifacts located in the Historical Peninsula. Galata Tower built by the Genoese is located on the opposite coast of the Historical Peninsula. Maiden’s Tower, which dates back to before Christ, is situated in the east of the Historical Peninsula and on the coast of Üsküdar (Asian continent).

The Moltke map produced by Helmuth von Moltke and the German Blue map produced by a company were used in the study (Fig. 2). Helmuth von Moltke was commissioned by Mahmud II who was the 30th sultan of the Ottoman Empire, to make a detailed map of İstanbul and to come up with a plan to correct the street view [29]. Helmuth von Moltke, an officer in the Ottoman army, made a 1:25,000 scale map in Bonne projection of İstanbul between 1836 and 1837. The sheet size of the Moltke map is 94 × 104 cm. The map shows the water facilities in the embankments, the Rumeli and Anatolian lighthouses at the entrance of the Bosphorus, and the residential areas. The scanned Moltke map pixel resolution employed in the study is 3920 × 3544.

The German Blue map was prepared by German surveyors before World War I for İstanbul Bosphorus and received this name since the edges of its sheets were blue (Fig. 3). Also, the French Topography Society devised the triangulation system based on the Galata Tower, and its measurements were finished in 1911. In 1914, the task of acquiring maps was awarded to a German company, and drawings were produced by providing materials [30]. Individual colored 66 × 100 cm sheets in 1:1000 and 1:500 scales were manufactured using Bonne projection. Furthermore, the German Blue map was utilized as a starting point for the cadastral maps of İstanbul when the General Directorate of Maps and Cadaster was established in 1925. The German Blue map used in this study consists of a combination of 208 sheets, and it was scanned with 25,116 × 20,360 pixels resolution.

4 Methodology

4.1 Coordination Systems and Transformation

A coordinate system describes a point’s location on the planet. The three-dimensional cartesian coordinate system refers to the middle segment of the three parallel planes. The system in which the position of a point on the earth is defined according to the reference ellipsoid with the magnitudes of latitude and longitude is the geographical coordinate system. It is directly related to the cartesian coordinate system. The position of point P on an ellipsoid is determined by latitudes and longitudes. The angle formed by the surface normal with the ellipsoid point P to the equator is geographical latitude (fi: φ). The angle formed between the planes of the initial meridian and the passing through meridian point P is called the geographical longitude (lambda: λ), and the geographic network on the reference surface is composed of the meridian and parallel circles (Fig. 4).

Coordinate transformation is the determination of the coordinates of points whose coordinates are known in only one coordinate system in the second coordinate system by using the transformation parameters calculated with the help of common points. In the literature, various coordinate transformations are available depending on the intended purposes and the number of parameters used.

Two-dimensional linear transformations are based on linear relations between the local coordinates on the old map and global coordinates in a defined coordinate system. The relations between the local and global coordinates consist of a set of simple geometric operations, resulting in a corresponding transformation. Moreover, similarity, 5-parameter affine, 6-parameter affine, and projective methods are generally used in transformation studies [31]. Affine transformation is widely used because the shrinkage of the paper could be eliminated, and the map image is not badly distorted [32].

4.2 Two-dimensional Similarity (Helmert) Transformation

The similarity transform looks for a condition of steepness between the systems used, and the same magnitude scale factor is used along the X- and Y-axis. Thus, the angles and shapes in the system are preserved after the transformation. Also, there are four transformation parameters in the direction of the X- and Y-axis: sliding, rotation, and scale.

$$\left[\begin{array}{c}X\\ Y\end{array}\right]=\uplambda {R}_{\alpha }\left[\begin{array}{c}x\\ y\end{array}\right]+\left[\begin{array}{c}{T}_{x}\\ {T}_{y}\end{array}\right]$$

(1)

In the equation, ${T}_{x}$ and ${T}_{y}$ represent the shift in the direction of the X- and Y-axis, ${R}_{\alpha }$ refers to rotation on the X- and Y-axis, and λ refers to the scale factor. If equality 1 is explicitly written, the following equation is obtained:

$$X=ax-by+c$$

(2)

$$Y=bx-ay+d$$

(3)

where x and y are the first system coordinates, X and Y are the second system coordinates, and a, b, c, and d are the similarity transformation parameters [33].

4.3 Two-dimensional Affine Transformation

There is no requirement for perpendicularity between various coordinate systems in the affine coordinate transformation; however, the geometric distribution becomes distorted following the modification. These distortions are not distributed uniformly throughout the various axes. Additionally, an affine transformation is a suitable coordinate transformation technique for photogrammetric and cartographic studies.

$$\left[\begin{array}{c}X\\ Y\end{array}\right]= \left[\begin{array}{c}\begin{array}{cc}0&\upvarepsilon \end{array}\\ \begin{array}{cc}0& 1\end{array}\end{array}\right]{R}_{\alpha }\left[\begin{array}{c}{\lambda }_{x}\\ {\lambda }_{y}\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right] +\left[\begin{array}{c}{T}_{x}\\ {T}_{y}\end{array}\right]$$

(4)

${\lambda }_{x}$ and ${\lambda }_{y}$ are scales in the direction of the X- and Y-axis, ${T}_{x}$ and ${T}_{y}$ are shifts in the direction of the X- and Y-axis, and ${R}_{\alpha }$ is rotation in the direction of the X- and Y-axis. When equality is written in three explicit ways, the following equation is obtained:

$$X={a}_{0}+{a}_{1}x+{a}_{2}x$$

(5)

$$Y={b}_{0}+{b}_{1}x+{b}_{2}y$$

(6)

where x and y are the first system coordinates, X and Y are the second system coordinates, and ${a}_{0}$, ${a}_{1}$, ${a}_{2}$, ${b}_{0}$, ${b}_{1}$, and ${b}_{2}$ are the affine transformation parameters [34].

4.4 Huber Loss Function

The traditional least squares paradigms may not be efficient methods for contaminated data due to sensitivity to outliers. Therefore, alternative robust methods to the least squares are required [35]. In line with this context, the Huber loss which is a robust function can be used for a wide range of regression problems [36]. To employ the Huber loss, a parameter that controls the transitions from a quadratic function to an absolute value function is selected [37]. For each element ${Y}_{j}$ of the input, the equation of the Huber loss algorithm can be expressed by the following equation.

$${{\text{loss}}}_{j}\left\{\begin{array}{cc}\frac{1}{2}{({Y}_{j}-{T}_{j})}^{2}& \mathrm{if }\;\left|{Y}_{j}-{T}_{j}\right|\le \delta \\ \delta \left|{Y}_{j}-{T}_{j}\right|-\frac{1}{2}{\delta }^{2}& {\text{otherwise}}\end{array}\right\}$$

(7)

where ${T}_{j}$ is the corresponding target value to the prediction, ${Y}_{j}$ and δ are the transition point where the loss transitions from a quadratic function to a linear function. If the transition point is 1, it is also known as smooth L₁ loss. To reduce the loss values to a scalar, it reduces the element-wise loss using the following equation.

$${{\text{loss}}}_{j}=\frac{1}{N} \sum_{j}{m}_{j}{w}_{j}{{\text{loss}}}_{j}$$

(8)

where N represents the normalization factor, ${m}_{j}$ is the mask value for element j, and ${w}_{j}$ is the weight value for element $j$.

4.5 Used Software in Analysis

In the application, two mapping software (MapAnalyst and ArcMap) were used to analysis the Moltke and German Blue maps. The MapAnalyst open-source software, developed by Monash University faculty member Bernard Jenny, allows us to make many analyses and generate ideas on old maps. The main purpose of MapAnalyst is to calculate the distortion grids that show the geometric accuracy, scale, rotation, and distortion of the old map [11]. Checkpoint pairs on an old reference map and a new reference map are used by MapAnalyst. MapAnalyst’s primary window is split vertically into two parts. The right side of the window displays a new reference map, and the left side of the window displays the old map that needs to be evaluated. Also, there is a point on the new map for each point on the previous map, and the window’s bottom side offers customization options for the analysis parameters.

ArcMap, a crucial part of Esri’s ArcGIS geospatial processing software, performs the functions of viewing, updating, querying, analyzing, and reporting the results of graphical and non-graphic data by providing cartographic presentations to the user. A dataset’s data can be explored using ArcMap, and maps can be made by symbolizing characteristics appropriately.

The Moltke and German Blue historical maps from two separate eras are reviewed in this study. The accuracy analysis is carried out in the MapAnalyst application by using OpenStreetMap (OSM). OSM maps are rendered using the Web Mercator projection. The coordinates collected from OSM in degrees–minutes–seconds are transformed into the ITRF system with the aid of transformations in the ArcMap 10.8 application, and these data are then used for analysis. Given the rapid change of the city and the dates when the maps were produced, the locations and names of the 29 points determined are shown in Fig. 5.

5 Results

5.1 Analysis of the Moltke Map

In application, the German Blue map is evaluated first, and the points are marked on the map. After the points are linked sequentially, the deformation network is generated using 29 identical points (Fig. 6).

The 2 × 1 matrices used for the X- and Y-axis to fit the 6-parameter affine results to the Huber loss function in the Moltke map are given in Eq. 10. The map coordinates and robust-fit graphs obtained for the X- and Y-axis using this equation are shown in Fig. 7. The threshold was chosen c_.95 = 1.345 for a real-valued case. The calculated results after the transformation process for the Moltke map are given in Table 1. The amount of the X and Y displacement of 29 identical points according to the transformations methods are also displayed in Fig. 8.

Table 1

Post-transformation displacements for the Moltke map

Landmark base point	Helmert-4 (m)		Affine-5 (m)		Affine-6 (m)		Huber loss (m)
Landmark base point	V_x	V_y	V_x	V_y	V_x	V_y	V_x	V_y
1	− 10.245	46.178	− 30.351	58.985	− 49.11	26.212	43,097	− 52,561
2	162.976	26.211	154.801	35.57	141.181	19.987	22,740	137,959
3	28.895	11.365	29.214	19.085	18.076	15.735	7,983	14,935
4	30.067	− 27.135	32.181	− 20.394	22.481	− 21.155	− 30,782	19,420
5	25.5	31.071	26.379	33.25	23.246	30.756	25,255	20,656
6	18.56	29.353	16.929	31.511	13.792	25.408	23,284	11,229
7	− 0.828	− 137.634	− 0.346	− 150.402	18.089	− 153.329	− 150,201	17,007
8	− 46.844	− 57.557	− 46.14	− 75.029	− 20.911	− 77.594	− 72,214	− 21,522
9	− 19.415	25.138	− 17.236	11.4	2.622	10.923	12,300	1,621
10	− 0.622	− 38.573	2.638	− 45.058	12.042	− 44.048	− 48,048	10,300
11	36.084	− 23.438	51.703	− 33.28	66.121	− 14.463	− 33,220	64,594
12	− 90.878	49.764	− 79.057	51.402	− 81.259	64.65	44,768	− 83,902
13	− 19.745	60.781	− 9.547	69.669	− 22.238	80.516	58,883	− 25,595
14	− 106.837	29.729	− 98.374	43.605	− 118.287	51.911	29,903	− 122,129
15	58.836	− 235.527	65.318	− 214.899	35.633	− 209.505	− 232,513	31,132
16	30.062	18.773	34.27	15.941	38.415	18.282	11,030	36,296
17	− 82.329	145.25	− 91.108	144.098	− 89.564	127.744	137,000	− 91,723
18	− 14.686	− 51.604	− 26.478	− 47.375	− 32.742	− 68.112	− 57,730	− 35,412
19	48.645	58.665	45.638	63.768	38.231	55.659	53,785	35,386
20	19.41	− 10.269	14.939	− 10.775	15.608	− 20.939	− 17,810	13,341
21	− 5.523	31.205	− 7.334	26.423	− 0.457	20.124	22,002	− 2,320
22	49.249	− 1.522	39.802	4.75	30.62	− 12.632	− 6,503	27,721
23	− 52.125	65.13	− 56.014	43.56	− 24.933	34.428	48,186	− 25,086
24	− 0.191	30.739	− 5.819	36.101	− 13.634	24.218	25,720	− 16,480
25	9.856	2.01	2.179	6.904	− 4.99	− 7.922	− 3,418	− 7,768
26	39.372	− 42.431	24.287	− 34.667	12.876	− 60.172	− 47,290	9,882
27	− 6.066	5.12	9.61	− 7.404	27.899	11.52	− 5,861	26,642
28	− 8.01	24.967	4.179	15.998	17.29	29.873	15,244	15,710
29	− 93.169	− 65.758	− 86.261	− 72.736	− 76.095	− 66.473	− 75.100	− 77.823

$$X=\left[\begin{array}{c}-69029\\ 20.4838\end{array}\right]\quad Y=\left[\begin{array}{c}708140\\ -165.4523\end{array}\right]$$

(9)

5.2 Analysis of the German Blue Map

The same points were used in the analysis of the German Blue map to obtain comparative results. The grid range is entered as 1000 m. Also, with the "compute" command, visualizations such as the deformation network, displacement vectors, etc., can be performed. The MapAnalyst application provides information about the scale and orientation of an old map. The analysis is made from the German Blue (old map) to OSM (new map). After the points are connected and the network is produced, it can be deduced that the rate of deterioration between Beşiktaş (represented by the numbers 11 and 28) and Üsküdar (represented by the numbers 12 and 13) regions is high (Fig. 9).

In the transformation processes, four parameters for the Helmert method (Helmert-4), five parameters for the affine method (Affine-5), and six parameters for the affine method (Affine-6) were employed. The lowest standard deviation values were calculated on both maps by the Affine-6 transformation method. Therefore, the calculated Affine-6 displacements were fitted by employing the Huber loss function, which is one of the most popular loss functions commonly used in regression problems, considering the Affine-6 parameters. The 2 × 1 matrices used for the X- and Y-axis to fit the 6-parameter affine results to the Huber loss function in the German Blue map are given in Eq. 9. The map coordinates and robust-fit graphs obtained for the Xand Y-axis using this equation are shown in Fig. 10. Additionally, the threshold was chosen c_0.95 = 1.345 for a real-valued case.

$$X=\left[\begin{array}{c}-69482.2\\ 2.06103\end{array}\right] \quad Y=\left[\begin{array}{c}-127730\\ 29.9873\end{array}\right]$$

(10)

The calculated results after the transformation process for the German Blue map are given in Table 2. In addition, Fig. 11 shows the X and Y displacement of 29 identical points according to the transformations methods.

Table 2

Post-transformation displacements for the German Blue map

Landmark base point	Helmert-4 (m)		Affine-5 (m)		Affine-6 (m)		Huber loss (m)
Landmark base point	V_x	V_y	V_x	V_y	V_x	V_y	V_x	V_y
1	− 191.045	23.977	− 156.501	− 35.898	− 34.166	36.191	− 15,494	− 41,163
2	− 19.866	− 17.915	− 10.309	− 54.527	65.398	− 35.358	− 19,043	60,312
3	− 26.088	− 119.535	− 36.557	− 142.862	12.969	− 166.314	− 95,201	8,891
4	− 16.456	− 128.42	− 30.156	− 146.368	8.39	− 176.57	− 96,797	4,791
5	− 14.826	− 94.548	− 19.509	− 101.85	− 3.897	− 112.219	− 58,045	− 6,327
6	− 15.345	− 81.158	− 13.842	− 91.1	6.8	− 88.248	− 51,080	4,201
7	56.117	− 5.999	71.239	32.177	− 9.657	66.221	62,944	− 7,364
8	75.296	5.309	95.488	55.568	− 11.035	101.001	82,990	− 7,490
9	62.811	− 19.952	74.787	19.757	− 9.065	47.085	52,446	− 6,668
10	43.908	− 77.852	43.985	− 56.77	− 0.043	− 55.79	− 16,395	0,366
11	122.158	− 177.169	95.676	− 134.156	7.922	− 189.532	− 77,705	10,089
12	73.187	395.059	40.261	411.187	9.148	340.892	472,086	8,598
13	35.28	374.52	− 2.204	367.994	14.346	287.005	432,101	11,519
14	15.331	360.467	− 25.033	338.605	23.763	250.82	404,756	19,398
15	− 122.232	175.56	− 163.873	133.636	− 73.083	42.325	200,918	− 79,424
16	29.315	− 103.129	22.635	− 92.55	1.065	− 106.529	− 47,812	0,351
17	− 44.783	10.605	− 21.848	0.974	− 3.523	49.999	27,714	− 5,783
18	− 78.112	7.977	− 53.909	− 16.714	− 4.239	34.459	9,498	− 7,950
19	− 42.665	− 69.799	− 41.121	− 89.914	0.76	− 87.365	− 49,748	− 2,831
20	− 17.531	− 33.1	− 5.456	− 37.51	2.812	− 11.675	− 4,132	0,905
21	5.697	− 30.882	16.39	− 20.99	− 5.1	2.421	13,000	− 5,630
22	− 75.523	− 22.928	− 59.27	− 52.039	0.251	− 18.159	− 20,829	− 4,006
23	81.486	98.139	118.355	153.688	− 0.512	235.243	170,692	3,789
24	− 52.344	− 53.361	− 44.998	− 76.42	2.581	− 61.489	− 39,797	− 1,214
25	− 59.39	− 25.214	− 46.2	− 48.427	1.246	− 20.917	− 15,421	− 2,480
26	− 93.553	45.536	− 65.232	7.587	11.803	67.119	31,473	6,857
27	129.236	− 161.105	105.706	− 110.779	2.452	− 159.514	− 56,280	5,375
28	95.99	− 149.565	76.694	− 113.369	2.617	− 153.532	− 61,253	4,221
29	43.945	− 125.518	34.802	− 98.93	− 20.003	− 117.595	− 52.939	− 19.190

The results pointed out that the Affine-6 transformation method for the Moltke and German Blue maps has the lowest standard deviation values (Table 3). The calculated transformation and standard deviation values according to the Huber loss function for the Moltke and German Blue maps are also shown in Table 4. In addition, the displacement vectors for the maps according to Affine-6 transformation results are displayed in Fig. 12. The displacement vectors of the Huber loss function according to the Affine-6 parameters for both maps are given in Fig. 13.

Table 3

Summary table of the study for Affine-6

Map	Moltke	German Blue
Pixel resolution	0.264 mm	0.626 mm
Scale	1:25,000	1:1000
Affine-6 transformation parameters
X₀	4247.542 m	4251.233 m
Y₀	3196.669 m	− 1536.384 m
a₁	4247.542	4251.233
a₂	0.000038	0.001
a₃	0.000007	0.000002
b₁	3196.669	− 1536.384
b₂	− 0.0000077	0.000058
b₃	0.000038	0.00108
Standard deviation at pixel (1:1 scale)	13	225
Sheet size	94 × 104 cm	66 × 106 cm

Table 4

Summary table of the study for Huber loss function

Map	Moltke	German Blue
Pixel resolution	0.264 mm	0.626 mm
Scale	1:21,436	1:808
Affine-6 transformation parameters
X₀	4247.542 m	4251.233 m
Y₀	3196.669 m	− 1536.384 m
a₁	4247.542	4251.233
a₂	0.000038	0.001
a₃	0.000007	0.000002
b₁	3196.669	− 1536.384
b₂	− 0.0000077	0.000058
b₃	0.000038	0.00108
Standard deviation at pixel (1:1 scale)	2	32
Sheet size	94 × 104 cm	66 × 106 cm

5.3 Coastline Analysis

The ArcMap software was also used to analyze the maps. It is possible to determine the displacements, size, digitization, and orientation of the shoreline using the identical regions. Geographical coordination is performed using a georeferencing tool, and the satellite-based imagery is provided by the Bing satellite. The Moltke and German Blue maps are coordinated using the same reference points first. The coastline of the Moltke map was digitized in ArcMap 10.8 software which is shown in Fig. 14. The red line represents the current coastline obtained from the relevant ministry, and the blue line represents the digitized Moltke map (Fig. 14.) As can be seen, coastal fills and coastline changes made over time on some coastlines can be observed.

The German Blue map’s coastline was also digitized in the ArcMap 10.8 software as illustrated in Fig. 15. When interpreting Fig. 15, the red line represents the current coastline obtained from the relevant ministry, and the blue shade represents the digitized German Blue map. When the historical maps are analyzed, some significant findings can be easily deduced from the maps even after a visual interpretation. On the other hand, there is a positioning in which topological relations are preserved in general for both maps.

Five different zones were determined for coastline change analysis in the study area as shown in Fig. 16. The shores of the Golden Horn are considered as a zone. Other regions are as follows: the coastline from the Galata Bridge to the end of the Historical Peninsula (Western Marmara Sea), the European side of the Bosphorus from the Galata Bridge (Western Bosphorus), and the coastline from the east coast of the Bosphorus to the Maiden’s Tower (Eastern Bosphorus), from the Maiden’s Tower to the Marmara Sea (Eastern Marmara) coastline.

As shown in Table 5, the regions with the highest coastline change are the coasts of the Marmara Sea. In the area where the change in coast length is highest, the differences between today’s coastline and the Moltke map and German Blue coastlines are 6.77 km and 6.731 km, respectively. In the area with the second highest change, the differences are 5.993 km and 4.613 km for the Moltke and German Blue maps, respectively (Fig. 16).

Table 5

Coastline length measurements for Moltke map, German Blue map, and current (m.)

Zone	Moltke	German Blue	Current
Western Marmara	12.394	12.433	19.164
Golden Horn	19.826	20.946	22.947
Western Bosphorus	8.268	8.315	9.917
Eastern Bosphorus	5.362	5.249	6.174
Eastern Marmara	7.942	9.322	13.935

Given the Moltke map and today’s coastlines, the filling areas are calculated as 2.5367 km² for the south of the Historical Peninsula and 2.1719 km² for the Harem-Kadıköy coast. Considering the German Blue and today’s coastlines, the filling areas are calculated for the south of the Historical Peninsula and the coast of Harem-Kadıköy, 2.4412 km² and 1.9353 km², respectively. Coastal fillings are generally used as coastal roads, car parks, and recreation areas. On the other hand, as shown in Fig. 17, large-scale filling areas have also been added to the coasts, which significantly change the form and boundaries of the coasts.

In particular, the Yenikapı Meeting and Recreation Area, which transforms the original coastline of the Historical Peninsula into a new form, and the intercity bus garage on the shores of Harem-Kadıköy are located on the filling areas. There are also ferry and passenger terminals in both areas.

6 Discussion

Given all processes, some important findings were revealed result of the analysis and evaluation of two historical maps, which are not found very much in the literature. The fact that the displacement errors on the German Blue map are larger than on the Moltke map is thought to be since the scale difference between the Moltke map and the German Blue map. In addition, it should be noted that the sheets used as map materials in the cartographic analysis process have been deformed over the years. Therefore, the analyses were performed according to the Affine-6 transformation method, which provides the best results for two maps, to minimize the cartographic impact of deformations on aged sheets. It is also worth mentioning that the German Blue map consists of a combination of 208 different sheets, while the Moltke map consists of a single-piece map; thus, lower standard deviation values (higher cartographic accuracy) of the Moltke map can be considered normal.

The control points used in the Moltke map provided the closest result to the location of the present maps, according to the analysis of the error and scale differences in the x and y directions achieved by the transformation methods utilized. When the Galata Tower was considered as a reference point, it was observed that the smallest deformation was in the Historical Peninsula region. The smallest deformation is 32 m in the X direction and 37 m in the Y direction, and the angular deformation was calculated as 3.7884 degrees. According to the Galata Tower reference, the biggest deformation was found to be on the Anatolian Side of İstanbul with 301 m in the X direction and 416 m in the Y direction. In addition, the angular deformation was calculated as 7.2593 degrees, and this value was checked by overlapping the sheets on top of each other. These deformations represent the amount of deformation between two sheets independent of the current coordinates (without OSM).

The topological relations on both maps have been studied in ArcMap 10.8 software. When the maps are examined, it is observed that the topological relations are generally preserved. Coastal filling areas are clearly visible when compared with the present situation of coastline borders provided by the Ministry of Environment, Urbanization, and Climate Change. According to the results, it was observed that significant changes in the coastal areas because of rapid urbanization and industrialization as well as political reasons starting in the 1950s [41]. Human activities such as coastal filling carried out on the coastlines of İstanbul since the second half of the twentieth century affect the geomorphology and cause changes in the natural structure of the coastlines. The characteristics and silhouette of the city change with the coastal fillings.

7 Conclusion

The present study attempts to fill the lack of studies on positional and coastal accuracy analysis for historical maps is rare in the literature. The lack of studies on historical maps and their comparative analysis is rare in the literature. The current study attempts to partly fill this gap. In the study, the analyses of old maps, which are, namely, Moltke and German Blue maps, were performed. The different transformation methods, Helmert-4, Affine-5, and Affine-6 transformations, were used to calculate the positional displacements that resulted from the transformations made with the chosen points separately for the chosen historical maps. In addition; the Huber loss function was used as a robust estimation method.

After the transformations performed in the MapAnalyst software, the transformation scale from the German Blue for transformation to OSM is determined as 1:1000 and for the Moltke map as 1:25,000. The standard deviation values for the Moltke and German Blue maps were calculated during three different transformation procedures and a robust estimation function. It can be interpreted that the accuracy results are sufficient accuracy if the technical conditions at the time the maps were produced are taken into account.

Planimetric data of historical maps were obtained with this application. It can be observed that although the Moltke and German Blue maps were created on various dates, there were comparable displacements at the same spots in terms of position when compared to the 29 points utilized in practice. This is a vital output in terms of showing the accuracy of the topographical neighborhood relations of the maps. According to position, the area between Beşiktaş (represented by the numbers 11 and 28) and Üsküdar (represented by the numbers 12, 13, and 14) have a bigger difference.

Both historical maps were produced using classical methods before mapmaking by satellite technologies and aerial photogrammetry. It has been observed that topological relationships are preserved despite the time differences in the production of the two maps. This result shows that the knowledge accumulated over time in map production is old, consistent, and valuable. Historical maps also provide unique data since they can show people’s interventions in natural areas, especially coasts, over time. In a nutshell, it is considered that this research will serve as a guide for digitizing, repositioning, comparing, coastal change analyzing, and interpreting for the historical maps.

Acknowledgements

We would like to thank Prof. Dr. Manfred Buchroithner from the Technical University of Dresden for his contributions regarding the projection information of the historical maps.

Declarations

Competing interests

The authors declare no competing interests.

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Titel: Landmark Base Point Approach to Positional and Coastal Accuracy Analysis for Historical Map Before WWI: A Case Study 1836 Moltke and 1914 German Blue about in Historical Peninsula of İstanbul
verfasst von: Cumhur Sahin
Bahadir Ergun
Furkan Bilucan
Publikationsdatum: 18.05.2024
Verlag: Springer Berlin Heidelberg
Erschienen in: Arabian Journal for Science and Engineering
Print ISSN: 2193-567X
Elektronische ISSN: 2191-4281
DOI: https://doi.org/10.1007/s13369-024-09074-7

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