16TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS ©2014 ISGG4–8 AUGUST, 2014, INNSBRUCK, AUSTRIA

Paper #072

THE GEOMETRY OF THE “PROSPECT GEOMETRIQUE”BY MICHELI DU CREST (1754)

A QUANTITATIVE ANALYSIS WITHIN A HYBRID LEAST-SQUARESADJUSTMENT FRAMEWORK

Helmut KAGER1, Martin RICKENBACHER2, and Andreas RONCAT11Research Groups Photogrammetry and Remote Sensing,

Department of Geodesy and Geoinformation, Vienna University of Technology, Austria2Swiss Federal Office of Topography swisstopo, Wabern, Switzerland

ABSTRACT: The “Prospect Geometrique” by Jacques-Barthelemy Micheli du Crest (1690–1766) isthe oldest panorama visualization of the Alps with a scientific background. Its creator was a remarkablefigure in Swiss history: He studied physics, astronomy, geodesy, and cartography in France andinvented a temperature scale which was in use until the 19th century. On the other side, his politicalactivities led to a sentence to death in absence, later transformed into a life sentence which he spentmostly in Aarburg castle (canton of Aargau, Switzerland). During his imprisonment, he developeda concept of land survey and realized the most possible in his situation with primitive instruments:the Prospect Geometrique, i.e. a central perspective surveying of his field of view mapped onto acircular cylinder with vertical axis. This technique was once considered as photogrammetry withoutphotographs by the renowned Swiss cartographer E. Imhof.The term Prospect used by Micheli means the correct geometric representation of the landscape fromthe observer’s viewpoint. A first numerical investigation of its “correctness” was conducted in 1995[10] and later refined in 2012 [11]. While the referenced publications have a more cartographic scope,this paper is intended as a sequel to the latter, focusing on the geometry and stochastics for analysingthe Prospect thoroughly in a hybrid adjustment approach by least squares. Several input categories forthe adjustment have been considered: (a) the upper and lower scale bars for azimuth and (b) left andright scale bars for elevation given on the outlines of the Prospect (see facsimile in Figure 4) and (c)control points identifiable in contemporary official geodetic maps. The core issue of this study was todetermine how exact Micheli could construct the Prospect, based upon the determination of the actualprojection centre, the calibration of the radius and orientation of the projection cylinder and further apotential exaggeration of the elevation scale.

Keywords: Photogrammetry, Central Perspective, Map Projection, Adjustment by Least Squares

1. INTRODUCTION

Panoramas are considered as map-related repre-sentations in the field of cartography so that geo-metric aspects are inherent to this kind of repre-sentation. This study is dedicated to the “ProspectGeometrique” by Jacques-Barthelemy Micheli duCrest (1690–1766). It is the oldest panorama ofthe alps with a scientific background.

By choosing the term “Prospect Geometrique”,its result is supposed to reflect correctly the actualgeometric situation of the landscape from theobserver’s viewpoint in a central projection. Theoutdated french term “Prospect” has its roots inthe latin term “prospectus” (for view) and meansthe view of a distanced landscape. In our case, theobserver’s viewpoint was a very special location:

Micheli Du Crest was imprisoned in Aarburgcastle when he worked on his Prospect.

The aim of this paper is to assess the geometricquality of and the accuracy of its representationin the Prospect. In contrast to a previous study[10], a purely digital data flow is used in this anal-ysis by means of GIS (Geographic InformationSystems) software and a photogrammetric bundleblock adjustment tool.

Section 2 presents the Prospect and its creator.In Section 3, the workflow and analysis strategyare presented. Results are given in Section 4,whereas the last section is dedicated to discussionand outlook.

2. THE PROSPECTJacques-Barthelemy Micheli du Crest (1690–1766), the creator of the Prospect, was an out-standing personality with a tragic faith, which hasbeen portrayed a lot in literature and describedin great detail in a historiographic novel by theSwiss writer P. Meier [8]. Born in Geneva intoa noble family originating from Lucca in Tus-cany, the young Micheli was at first a sociallyapproved person. However, he started discussionabout Geneva’s fortresses and came more andmore deeply into trouble with the authorities inhis town. As a consequence, he was even sen-tenced to death in absence. The execution wasconducted symbolically on behalf of an image(in effigie) because Micheli had fled to France.There, he was in a circle with renowned scientistsof the day and kept up with newest developmentsin physics (thermo- and barometry), astronomy,geodesy and cartography.

Homesick, he returned close to his home re-gion, but not directly to Geneva where it was stilldangerous for him to stay. In 1746, on initiativeof the authorities of Geneva, Zurich and Bern hewas arrested in Neuenburg and brought to Aar-burg castle for the first time. After some monthsin home arrest in Bern, he was sued to life sen-tence in Aarburg castle. There, he wrote an essayof several pages on June 26, 1754, containing aconcept of land survey. This concept comprises

a two-step approach with a land survey on theone side (base measurements, triangulation nets,topographic maps in smaller scales) and detailedsurveys with fine-scaled maps [3, pp. 97–101].Despite his small operating range, Micheli real-ized the most possible in his situation with prim-itive instruments: From autumn 1754 to spring1755, he made a central perspective projection ofhis field of view, in fact the projection of a por-tion of the surrounding landscape onto a handypiece of paper, in a well-defined coordinate sys-tem of azimuths and height measurements forthe determination of the elevations above sealevel of 40 alpine summits which limited the dis-tanced field of view. This was the creation ofthe Prospect. Originally, Micheli entitled it as“Prospect Geometrique des Montagnes neigees,dittes Gletscher, telles qu’on les decouvre en temsfavorable, depuis le Chateau d’Arbourg, dans lesterritoires des Grisons, du Canton d’Ury, et del’Oberland du Canton Berne” (geometric view ofthe snow-covered mountains, called glaciers, asthey are visible in good weather conditions fromthe Aarburg castle, in the regions of Graubunden,of the canton Uri, and of the oberland in the can-ton Bern, see Figure 4).

Micheli documented his procedures with asmall “Avertissement” (legend) directly on theProspect, and had a separate “Memoire” of fourprinted pages [9]. By means of the latter, the maincharacteristics of his work may be explained, con-sisting mainly of the measurements of azimuthsand elevations.

Following his description, Micheli constructedthe landscape drawing using simple aids in theprinciple of the measuring table. He drew aquarter circle using a compass and partitionedit “relatively precise”. However, he did not tellanything about this partitioning in detail. More-over, the quarter circle has not been discoveredyet, thus there are only assumptions about thistask. Micheli may have partitioned the quarter cir-cle further with the compass, using Archimedes’pragmatic method.

In order to orientate the quarter circle, Micheli

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determined the position of the South direction,the meridian, twice by observing the polar starusing a plummet. He calculated the timestampof its upper and lower meridian transitions usingthe “Connaissance des Tems”, the first astronom-ical almanach which had been published since1679. He marked the mean direction in field us-ing a wooden “meridian pole” (French “Poteaudu Meridien”).

In this way, Micheli determined the South az-imuths of the summits in a sector of 44◦ East(equal to a North azimuth of 136◦) and 11◦ West(equal to an azimuth of 191◦), w.r.t. the meridianthrough Aarburg. The field of view fits thereforewell into a quarter circle.

With the azimuths of the Prospect given inregular intervals, the mapping corresponds to acylindrical projection: In the front view, the land-scape is projected onto a vertical cylinder whichis developed in the image plane (Figure 1).

Figure 1: The projection model of the Prospectas a projection of the landscape onto a circularcylinder with vertical axis. Micheli’s observedvalues are the azimuth α w.r.t. the South meridianS and the reading h on the rod w.r.t. the local levelN defined by the water level. The elevation H canbe determined from the distance D (taken fromthe map), h and radius c. From [11].

The core element of the whole campaign wasthe determination of the elevation differences.For this purpose, an extremely simple measuringdevice was used: A wooden roof gutter of 24feet (around 7.8m) length, was closed thoroughlyon both sides, filled up with water and served

in this way as a giant level, directed in azimuthtowards the summits whose elevations were tobe determined. The observer placed himself be-hind this level opposite to the mountains. Onthe other end of the level, a helper moved a rodof one foot length upwards, perpendicularly tothe water surface, until the top of the rod wascollinear with the observer’s eye and the respec-tive summit. Micheli reports that he usually hadthe observations done by two very clear-sightedpeople, each observation was performed severaltimes from far and next to the level. He estimatedthe measurement error to be less than half a line,corresponding to approximately half an arc sec-ond. The “Hauteurs sur le Niveau” determined inthis way are given in “Pouces” and “Lignes” inthe Prospect.

The elevation differences of the summits couldin this way easily be calculated using the rule ofproportion: the height of the rod above the watersurface of the level gives the opposite leg in anrectangular triangle, the length of the level givesthe adjacent leg; together with the distance to thesummit, their elevation relative to the observer’sposition can now be determined.

Micheli knew that the distances to the sum-mits were the main problem in his task. He tookthe distances out of Scheuchzer’s map, publishedin 1712 in four map sheets as “Nova Helvetiaetabula geographica”. He determined its scaleby setting the length of one degree in the locallatitude in relation to the value published by J.Picard in his book “La Mesure de la Terre”. Inthis way, he calculated the distance from Basel toGeneva and compared it with a newer map fromthe “Connaissance de Tems”. He recognized thathe had to reduce the distances in Scheuchzer’smap by more than a sixth in order to make themcompatible with newest findings. The “Distancessur la carte de Scheuchzer” are given in “Pouces”and “Lignes” above the readings of the verticalrod below the upper scale bar in azimuth (Fig-ure 4). However, Micheli could not eliminate thebig interior distortions of Scheuchzer’s map withthis scale correction.

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The influence of Earth curvature correspondingto the respective distance of the summit was de-termined by means of a table which was based onthe principles published in the book “La Mesurede la Terre” by J. Picard in 1671. Micheli did notaccount for the influence of refraction.

He determined the elevation of his “Niveau”using a long series of observations on a self-constructed barometre. This year-long series re-sulted in a value of 237 Toises (461.9m). Micheliadded the elevation difference to the local ele-vation of Aarburg and also the amount of Earthcurvature. In this way, he determined the eleva-tion above sea level of the summits which arelisted in a table in the lower part of the Prospect.

In accordance with his modern way of thinking,Micheli wanted to have his Prospect reproducedand to have his work discussed among prominentscientists. He originally thought about engravingthe Prospect in Paris, the copperplate engravingwas though made by Tobias Conrad Lotter (1717–1777) in Augsburg.

From top to bottom, the Prospect contains thefollowing main elements:

• Upper scale bar in azimuth

• distance to the respective summit inScheuchzer’s map (in inches/lines)

• reading on the vertical rod with respect tothe local level of Aarburg (in inches/lines)

• horizontal line at the height of 12 inches asupper limit of the landscape image

• landscape image with letters, numbers andsymbols for identifying the summits

• local horizon line as lower limit of the land-scape image

• lower scale bar following the same principleas the upper one

• four text fields with names of the summits,their elevations and a field with the “Aver-tissement” (short description).

All elements but the last are visible in Figure 4.The Prospect represents a complete central per-spective in a cylindrical coordinate system. Itsdatum is given by the origin, being the perspec-tive centre, the local meridian, and the local leveldetermining both main axes.

Micheli’s measurements are defined in theFrench system, based on the “toise de Perou”determined in a meridian arc measurement inPeru [7, p. 478]. A toise (fathom) correspondsto a length of 1.949m and is subdivided into6 pieds (feet; 1 pied = 324.84mm), their fur-ther subdivided into 12 pouces (inches; 1 pouce= 27.07mm) and each pouce finally subdividedinto 12 lignes (lines; 1 ligne = 2.26mm). In thisway, 1 toise equals 864 lignes.

3. METHOD OF ANALYSISThe geometric aspects of the Prospect had beeninvestigated for the first time in 1995 [10]. Asdigital analysis methods have offered increasingpossibilities since then, the analysis was refinedin 2011 [11]. It is the basis of the herein presentedstudy, relying in the determination of both imagecoordinates within a Geographic Information Sys-tem (GIS) and subsequent evaluation within thephotogrammetric bundle block adjustment soft-ware ORIENT1. Thus, Micheli’s work is anal-ysed with the software probably fitting best to themapping strategy he used at that time. The mostimportant prerequsite for this procedure was thescanning of the Prospect in high resolution in or-der to retrieve the image coordinates of selectedpoints for evaluation in ORIENT.

The current evaluation has been based on ascan done with 600dpi resolution approximatelyfour years after the first mentioned publication[10]. In comparison to the scan used in [10],distortions of up to 0.2% appeared; they can beexplained by paper deformation.

The image coordinates of the following point

1http://www.ipf.tuwien.ac.at/products/produktinfo/orient/html_hjk/orient.html, last accessed: June 12, 2014

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groups were measured in ArcMap2:

• 1 – 39: Points labelled with letters in theProspect

• 91 – 96: Churches located close to the pro-jection centre, most of them reference pointsof the Swiss cadastre triangulation

• 101 – 134: further identifiable points inthe landscape which were not labelled byMicheli

• 1136 – 1191: lower scale bar in azimuth(geographic North direction = 0◦ (degrees);the number corresponds to 1000 plus theNorth azimuth in degrees)

• 2136 – 2191: upper scale bar in azimuth (thenumber corresponds to 2000 plus the Northazimuth in degrees)

• 3001 – 3039: directions to the points 1 – 39

• 4000 – 4012: left scale bar in elevation (thenumber corresponds to 4000 plus the lineindex)

• 4100 – 4112: right scale bar in elevation(the number corresponds to 4100 plus theline index)

The coordinates of the points in the first threegroups were determined by means of the currentofficial map in scale 1 : 25000; their standarddeviation a priori was set to 5m in x and y coor-dinates and 1m in elevation. Most points of thesecond group are reference points of the Swisscadastre triangulation so that their coordinatesare given in high accuracy; their standard devi-ation a priori was assumed to be ±0.1m in thesingle coordinates. The heights above ground ofthese points were further determined photogram-metrically at swisstopo.

A already stated, the numerical analysis wasperformed in ORIENT. It is a universal software

2http://www.esri.com/software/arcgis,last accessed: June 12, 2014

package for photogrammetric point determina-tion, in which several forms of observations andparameters can be analysed simultaneously [4, 5]:

• Image points from perspective images (x,y)and line scanners (x = t,y),

• 3D model points (x,y,z),

• polar points (horizontal direction, zenith an-gle, distance),

• reference points (X ,Y,Z) and

• fictitious observations (planes and lines,surfaces and curves (polynomials), splinecurves)

as observations and

• transformation parameters (calibration, ori-entation),

• additional parameters for image deformationand shape of objects and

• parameters of scanner trajectories (polyno-mials and splines)

as parameters to be determined or known a priori.The current special case of a perspective cylin-

drical projection can be seen as a vertical sen-sor line rotating around the vertical cylinder axis.The sensor line is a generatrix of the cylinder;the South meridian gives the reference for thegeneratrices.

The quantitative image analysis using ORI-ENT is aimed at the reconstruction of the map-ping geometry of the prospect. Moreover, theaccuracy of this mapping is to be assessed. Forthis purpose, it is necessary to determine the pa-rameters of the exterior and interior orientationof the Prospect. The first group of the parametersconsists of the planar coordinates and the eleva-tion of the draftsman’s position, the orientationof the cylinder axis in space and the azimuth ofthe South direction in the Prospect.

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The interior orientation describes the positionof the projection centre (i.e. the eye of the drafts-man) w.r.t. the imaging plane of the sensor linein the image coordinate system. In our case, onlythe distance of the projection centre to the imageplane is of interest. For a narrow viewing angle,this would be referred to as principal distance (cf.the focal length of a camera) [6].

The representation of single elements of theProspect in ORIENT is as follows:

Geodetic reference frame: The calibrationswere performed in the Swiss geodeticreference frame LV03. The azimuths ofMicheli in the Prospect and the ones inLV03 differ by the meridian convergence. Itamounts to 0.3382◦ in Aarburg.

Scale bars in azimuth and elevation: As theProspect does not allow to assign anelevation angle to the points on the upperand lower scale bar (azimuth), the definitionof the points 1136 – 1191 and 2126 – 2196in object space is just given via their imagecoordinates (with drawing accuracy). Thiscorresponds to an angular measurementwith a theodolite in two horizontal planes.The relative position of this two “theodo-lites” on a vertical line is formulated as a“GESTALT” constraint in ORIENT withan a-priori accuracy of ±1mm. Theirvertical offset is an unknown parameter tobe determined in the adjustment. The scalebars in elevation “Pouces de Nivellement”(inches) are represented as a sequence ofCartesian 3D points, in analogy to the markson a vertical (±1mgon) measuring rod. Theexaggeration in elevation can be determinedby setting the distance of these rods to theprojection centre to 24 feet (length of thelevelling instrument).

Vertical axis of the cylinder: According to thereadings on the measuring rod orthogonallyto the water surface, the cylinder axis can beset to be vertical up to the reading accuracy

of the rod. Micheli reported the readings toaccurate up to ±0.5′′.

Selection of reference points for reconstruction:As the reference point groups exhibit differ-ent accuracy levels, three selection variantswere considered. The first was based on39 points actually measured by Micheliwith high accuracy; the second group addi-tionally consisted of 6 points representingchurches and castles in close distances,and the third included 34 additional pointswhich were presumably not measured byMicheli but just drawn in the Prospect.

Stochastic model and quality control: The ac-curacy of the coordinates of the referencepoints was set to the values given above;the image coordinate accuracy was set to±0.1mm for both coordinates in case ofwell-defined points and to ±0.3mm for flatsummits orthogonal to the viewing direc-tion.

4. RESULTSVariance component analysis allows for compar-ing these a-priori values with the ones retrieveda posteriori. The a-priori accuracies turned outto be too optimistic. As the official maps are ofhigh quality, practically only the accuracies of theimage coordinates are left to be altered [6]. As-sumed that Micheli could read the azimuths up to±0.2mm accuracy at his quarter circle, this cor-responds to a mean planar accuracy of ±0.3mmin the Prospect. How precise the copperplateengraving fits to the original drawing has notbeen investigated yet. Assumed this precisionamounted to another ±0.3mm the mean planaraccuracy would resulted to ±0.4−0.5mm.

The influence of single gross errors on the ad-justment results was analysed using data snoop-ing [2]. In this technique, the most “suspicious”observation is eliminated and the adjustment isrepeated without this observation, resulting in asequence of solutions for the projection centreswhich can be visualized (Figure 3). For the dif-

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ferent reconstruction variants different paths areretrieved which may not correspond to the errorellipses describing the planar accuracy.

The low accuracy of the first selection of refer-ence points may be due to their geometric config-uration close to the dangerous circle of resection.Also the freedom of artistic expression, resultinge.g. in oversized drawings of important buildingsor slight misplacements of such, may bias theresults if not properly analysed in quality control.

On the other hand, knowledge about the topog-raphy of the mapped scene ought to be introducedas additional input to data snooping rather thanjust relying on stochastics.

Figure 2: Visibility map containing the summitsvisible in the Prospect, calculated using SCOP [1]on basis of the digital elevation model DHM25.Visible parts are overlaid in red over the hillshade.From [11].

A simple break of the iteration when a normaldistribution of the remaining residuals has beenreached may give implausible results—just be-cause the assumed normal distribution need notreflect reality. Let us take the selection variant

2http://www.swisstopo.admin.ch/internet/swisstopo/en/home/products/height/dhm25.html, last accessed: June 12, 2014

Figure 3: Influence of the selection of referencepoints on the reconstruction of the projection cen-tre. The two points marked with “1994 . . . ” rep-resent the two variants calculated in 1994. Back-ground: Data from the local surveying authorityin the canton of Aargau (Ubersichtsplan Blatt 94).Numerical values for the error ellipses are givenin Table 1. From [11].

“LF3CH” in Figure 3 as an example: eliminationof the reference points in the foreground leadsto a big jump in the resulting projection centreso that “LF3” corresponds to “LF1” while in-cluding more summits. The error of unit weightσ0 has already been reduced from ±0.59mm to±0.33mm, meeting the expectations. With thejump in the projection centre, the cylinder ra-dius is enlarged by 0.5mm; however, its standarddeviation increases by 20% (from ±0.16mm to±0.19mm). I.e., essential information has beenlost.

5. DISCUSSION AND CONCLUSIONThe repeated intensive analysis of Micheli’s map-ping strategy confirmed the results of the years1994/95 to a large part. The Prospect, stemmingfrom the age of enlightenment, resolved a mainscientific question of that time in an inventivebut still effective manner—well adjusted to thedifficult situation of its creator— and reached asurprisingly high accuracy.

Data snooping in the “LF1” reference point se-lection resulted in a standard deviation in the im-

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Table 1: Change in size of the semi-axes of errorellipses (A, B [m]) w.r.t. elimination of referencepoints. Left: before elimination, right: after elim-ination of the point given in the rightmost column.The σ0 [mm] is the error of unit weight in the im-age a posteriori. “Variant‘” refers to the solutionsshown in Figure 3.

variant A B σ0 A B σ0 elim.LF1UB 75 30 .284 59 19 .209 11LF2UB 23 2.6 .256 18 1.8 .229 15LF3UB 34 3.9 .537 18 2.1 .298 26

age of ±0.2mm after 15 coordinate eliminationsout of 39 reference points (originally ±0.3mm atthe start). This gives clear evidence that Michelireached his goal of a “geometrique” representa-tion. In the “LF2” selection variant, this standarddeviation decreased from ±0.4mm to ±0.25mm,and in “LF3” from±0.59mm to±0.4mm. Thesevalues result from a combination of influences,e.g. the original measurement, the copperplateengraving, random paper distortion, digitizationwith different scanners.

In addition to the results already given in [10],new findings were made during the enhancedanalysis in ORIENT. First, Micheli may havebuilt a model of his measuring device in thescale 1 : 12. As the radius R resulted to 657.4±0.12mm, 657.2±0.13mm and 656.8±0.18mmin the selection variants LF1, LF2 and LF3,resp., this corresponds up to 1.1% to 24 inches= 649.7mm. The length of the level was 24 feet.Given that Micheli wanted to map 1 inch of thereading to 1 line in the Prospect (factor 1 : 12),for one calculation variant the scale bar in ele-vation on the left would have been exaggeratedby a factor of 1.073±0.016 and the right one by1.057± 0.016. The principal distance c variesfrom 660mm to 710mm in the different variantsof selected and eliminated reference points.

Another aspect is the meridian deviation: itis the direction to Micheli’s South direction,corrected by the meridian convergence. Re-projected to the projection plane, values from

−0.3 to −0.7mm in LF2 and −0.6 to −0.9mmin LF3 were retrieved. The common negative signindicates a slight bias towards the South directionin the mapping frame. A deviation of 0.03◦ corre-sponds to 0.03mm in the Prospect. The Studentt-factor resulted to values from 0.5 to 1.5; thus, asignificant deviation from Micheli’s Polaris mea-surement could not be proved.

Summarizing the above findings, Micheli’sProspect Geometrique can be considered asone of the first remarkable geodetic-topographicworks, even in its central-perspective conception.It belongs to the initial works fostering the devel-opment of the proverbial Swiss precision in thisfield and of the international reputation of Swisscartography.

ACKNOWLEDGMENTSThe authors want to express their thanks for thegraphical design and image overlays to MichaelPfanner (Figure1), Nicolai Lanz (Figure 2) andAdrian Bohlen (Figures 5 and 6) from swisstopo.

REFERENCES[1] SCOP++ product information.

http://photo.geo.tuwien.ac.at/software/scop/, 2014. Depart-ment of Geodesy and Geoinformation,Research Group Photogrammetry. Lastaccessed on June 12, 2014.

[2] W. Forstner. The reliability of block trian-gulation. In Proceedings of the 38th Pho-togrammetric Week, Schriftenreihe des In-stituts fur Photogrammetrie der UniversitatStuttgart, pages 225–242. Stuttgart, Ger-many, 1982.

[3] J. H. Graf. Das Leben und Wirken desPhysikers und Geodaten Jaques BarthelemyMicheli du Crest aus Genf, Staatsgefan-gener des alten Bern von 1746 bis 1766.Wyss, Bern, 1890.

[4] H. Kager. Orient: A universal photogram-metric adjustment system. In A. Grun and

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H. Kahmen, editors, Optical 3-D Measure-ment Techniques. Applications in inspection,quality control and robotics, pages 447–455.Wichmann Verlag, 1989.

[5] H. Kager. Orient User Manual. Instituteof Photogrammetry and Remote Sensing,Vienna University of Technology, Austria,2000.

[6] K. Kraus. Photogrammetry – Geometryfrom Images and Laser Scans. De Gruyter,Berlin – New York, 2 edition, 2007.

[7] I. Kretschmer, J. Dorflinger, and F. Wawrik.Lexikon zur Geschichte der Kartographie.Von den Anfangen bis zum Ersten Weltkrieg,volume C/1 and C/2. Deuticke, Vienna, Aus-tria, 1986.

[8] P. Meier. Die Einsamkeit des Staatsgefan-genen Micheli du Crest. Eine Geschichtevon Freiheit, Physik und Demokratie.Pendo, Zurich – Munich, 1999.

[9] J.-B. Micheli du Crest. Memoirepour l’explication du Prospect des Mon-tagnes neigees que l’on voit du chateaud’Aarbourg. 4 pages.

[10] M. Rickenbacher. Das Alpenpanoramavon Micheli du Crest – Frucht eines Ver-suches zur Vermessung der Schweiz imJahre 1754. Cartographica Helvetica, (Son-derheft 8): 24, 1995. With facsimile of theProspect Geometrique and reconstructionof the panorama by means of the DHM 25.

[11] M. Rickenbacher and H. Kager. Ge-ometrische Bildanalysen am Beispiel des

”Prospect Geometrique“ von Micheli duCrest von 1754. In Festschrift fur Univ.-Prof. Dr.-Ing. Kurt Brunner anlasslich desAusscheidens aus dem aktiven Dienst, num-ber 87 in Schriftenreihe des Instituts furGeodasie der Universitat der BundeswehrMunchen, pages 197–212. 2012.

ABOUT THE AUTHORS1. Helmut Kager: born in 1950. Studies in

geodesy at Vienna University of Technology.Dipl.-Ing. (MSc) 1974, Dr.techn. (PhD)1980. Since 1974 with the Institute of Pho-togrammetry and Remote Sensing (since2012 within the Department of Geodesy andGeoinformation) at Vienna University ofTechnology. Contact: helmut.kager@geo.tuwien.ac.at.

2. Martin Rickenbacher: born in 1954. Stud-ies in geodesy at ETH Zurich and his-tory at Basel University; Dipl.-Ing. ETH.Dr.phil. (PhD) in history 2009. Scien-tist at the Swiss Federal Office of Topog-raphy swisstopo and leader of the WorkingGroup on the History of Cartography in theSwiss Society of Cartography (SSC). Er-atosthenes Award 2011. Contact: martin.rickenbacher@swisstopo.ch.

3. Andreas Roncat: born in 1981, studies ingeodesy, geometry and computer science atVienna University of Technology and Uni-versity of Vienna. Dipl.-Ing. (MSc) 2006.Currently Research Associate and PhD Stu-dent at the Research Groups Photogram-metry and Remote Sensing, Department ofGeodesy and Geoinformation, Vienna Uni-versity of Technology. Contact: andreas.roncat@geo.tuwien.ac.at.

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Figure 4: Upper part of the Prospect (facsimile).

Figure 5: Visualization of the deformation analysis. Grid width: 30′ for vertical lines and 2 pouces(inches) for horizontal lines. Residual vectors are given in scale 1 : 1. Top: left part, bottom: rightpart of the Prospect. From [11].

Figure 6: Graphical comparison by overlaying the Prospect with silhouttes generated with SCOP[1] and the digital elevation model DHM25. The vertical exaggeration of the Prospect wasconsidered. Top: left part, bottom: right part of the Prospect. From [11].

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