creating the virtual eiger north face

Creating the virtual Eiger North Face

Manfred Buchroithner*

Institute for Cartography, Dresden University of Technology, Mommsenstr. 13, D-01062 Dresden, Germany

Received 15 January 2002; accepted 23 August 2002

Abstract

The described activities aim at combining the potentials of photogrammetry, remote sensing, digital cartography and virtual

reality/photorealism with the needs of modern spatial information systems for tourism and for alpinism in particular (the latter

aspect is, however, not covered in the paper). Since for slopes steeper than 45j, a digital relief model in nadir projection cannot

adequately depict the terrain even in low-angle views, digital Steep Slope Models (SSMs) with a rather vertical reference plane

are desirable. This condition very much applies to the Eiger North Face which has been chosen as a testbed for the realisation of

a virtual rock face and which shall later be embedded into a lower resolution synthetic landscape of the Eiger–Moench–

Jungfrau Region generated from a DTM and satellite imagery. Our ‘‘SSM approach’’ seems justified by the fact that except for

the visualisation, commercial software was used which is very limited both in DTM modelling and texture mapping. For the

creation of the actual SSM, a pair of oblique coloured air photos has been used, resulting in both a digital face model of 3.7 m grid

size and an orthophoto with a resolution of 0.25 m. To demonstrate the alpinistic potential of the product, climbing routes have

been inserted into the face model, thus enabling even non-experienced individuals to enjoy the ‘‘virtual reality conquest’’ of the

Eiger North Face and potential climbing candidates to prepare themselves for the actual ‘‘real world’’ enterprise.

D 2002 Elsevier Science B.V. All rights reserved.

Keywords: mountain cartography; tourism cartography; virtual reality; 3D landscape models; steep slope models; alpinism

1. Motivation

Modern photogrammetric image processing and

3D visualisation software tools enable us to generate

synthetic landscapes of high accuracy and a high

degree of immersivity. Beyond the production of

fancy digital playgrounds, these 3D scenes may also

serve to satisfy the needs for concrete geo-information

and for planning purposes (cf. Sections 6 and 7).

1.1. General

High-resolution image data of slopes steeper than

45j may represent input to touristic/alpinistic virtual

reality models of prominent mountains. Thus, they

provide the possibility to generate realistic synthetic

views from different viewing points and varying

distances. In the presented project, we used the

Eiger North Face as a testbed. This rockface has

an average steepness of 60j and is amongst alpi-

nists known as the most famous climbing wall

worldwide. The Eiger (3970 m) is situated to the

south of the tourist village of Grindelwald in the

Swiss Canton Berner Oberland (see Fig. 1).

0924-2716/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.

PII: S0924-2716 (02 )00109 -0

* Tel.: +49-351-4633-48-09; fax: +49-351-4633-70-28.

E-mail address: [email protected]

(M. Buchroithner).

www.elsevier.com/locate/isprsjprs

ISPRS Journal of Photogrammetry & Remote Sensing 57 (2002) 114–125

Fig. 1. Location of the Eiger, scale 1:50000.

M. Buchroithner / ISPRS Journal of Photogrammetry & Remote Sensing 57 (2002) 114–125 115

The first successful ascent of the north face took

place in 1938. On July 24, 1938, the crew consisting

of the two Austrians Fritz Kasparek and Heinrich

Harrer and the two Germans Andreas Heckmair and

Ludwig Vorg stood at the top of the Eiger after a 4-

day struggle with the wall (Heckmair et al., 1943). In

the past 65 years, lots of mountaineers have tried to

conquer the Eiger taking a route through its north

face. But several of them paid a high price due to the

face’s own weather conditions, rockfall, ice and debris

avalanches or just adventurous carelessness. Between

1935 and 1991 the Eiger North Face demanded 51

casualties (Hausmann, 1997; Eiger, 2002).

1.2. Geometry

It is a well-known basic geometric fact that in real

high-alpine terrain, the areal amount of slopes steeper

than 45j—and thus in vertical projection diminished

by a factor of 2 and more in relation to the true

surface—is significantly high. This is why for steep

rock faces which are of touristic and in particular of

alpinistic interest, specific landscape models in obli-

que or transverse projection are superior to the nadir-

projected digital terrain and surface models, even if

they are of considerably high resolution (The prob-

lem, though, is not the nadir projection per se but the

2.5D modelling).

According to Kostka and Buchroithner (unpub-

lished internal reports) these ‘‘non-nadir’’ data sets

are called Steep Slope Models (SSMs). Naturally, in

the case of the Eiger North Face, the projective area is

much better presented on the oblique reference plane

of a SSM than on the horizontal one of the DTM (see

Fig. 2); no doubt, a truly three-dimensional concept

would not require such consideration).

2. Input data

All necessary input data were kindly supplied by

the Chair of Photogrammetry and Remote Sensing,

ETH Zurich, Prof. Dr. Armin Grun.

2.1. Airborne imagery

ETH Zurich supplied an oblique pair of coloured

air photos (No. 2934 and 2928) which has been taken

at an angle of 65 gon (corresponding to 58.5j) fromvertical. Despite the time of the data take during

summer (August 1977) the wall displays a compara-

tively intensive cover of snow and ice. This and the

intensive light and shadow effects (most of all the cast

shadows) significantly influence the image quality.

This also hampered the generation of the DTM.

Fortunately, however, the stereo model is not deterio-

rated by other climatic aspects like clouds, cloud

shadows or haze (cf. Buchroithner and Kostka, 1997).

All data for the inner orientation have been taken

from the Camera Calibration Certificate (CCC) of the

camera used, a WILD RC 10.

2.2. Ground control points (GCPs)

For the realisation of the exterior orientation the

coordinates of the national Swiss Geodesic System,

eight ground control points were used. One of the

geodetic GCPs, which were also used for the gener-

ation of the first Eiger orthophoto (Spiess, 1986, p.

436), is situated next to the summit of Eiger, another

one in the North Face, close to the Tunnel Outlet. This

Tunnel Outlet (‘‘Stollenloch’’) can be reached from

the Jungfraubahn via a special tunnel. It plays an

important role for all rescue operations (as for Kurz in

1936). In 1961, the first winter conquest started from

this point (cf. Fig. 8 and Section 5.3).

The remaining six other GPCs are all at the base of

the wall. Apart from the GCP at the summit, whichFig. 2. Conventional DTM vs. SSM: applicability.

M. Buchroithner / ISPRS Journal of Photogrammetry & Remote Sensing 57 (2002) 114–125116

appears in the aerial photographs as a black spot, all

other GCPs have been marked in the field by orange

target sheets. According to Mr. Buhrer (Chair of

Photogrammetry and Remote Sensing of the ETH

Zurich) one can assume a GCP accurracy of 10–15

cm.

Since the display of the eight GCPs used in this

project in aerial image or in a map would not be

overly instructive due to their narrowness, a numerical

presentation seems more adequate, despite its redun-

dancy (cf. Table 1).

3. Model system—Steep Slope Model (SSM)

There existed several problems which made a

transformation into a model system inevitable:

(1) The x,y-plane is not parallel to the image plane.

The digital photogrammetric software system

PHODIS (cf. Section 4.1) is only suitable for the

evaluation of aerial photographs taken in nadir direc-

tion or close to nadir with a maximum deviation of 5

gon. This means that the nadir texture had to be quasi-

‘‘simulated’’.

(2) Due to the overhangs, many x,y-coordinate

pairs have two or more z-coordinates.

Also in Steep Slope Models, hidden surfaces may

occur. For this particular rock face, however, there

exists no single plane which fulfills the requirement

that each x,y-coordinate pair only possesses one single

z-coordinate.

The Swiss National Coordinates of the GCPs have

been transformed into the Model 2000 System via a

spatial 3D transformation. The x,y-plane of this model

is nearly parallel to the image plane.

The superimposition system of the analytical plot-

ter cannot cope with negative values. Therefore, to

each transformed coordinate, 2000 m have been

added, resulting in exclusively positive coordinates.

The model system which has thus been created was

called Model 2000 (see Fig. 3).

The matrix R(x,u,j) with a certain scale factor is

orthogonal, i.e. R� 1 =RT and det R= + 1. Thus, the

transformations from one to the other system are

significantly simplified. The transformation parame-

ters were taken from Elberink (1998, p. 15).

Scale factor : 1:01467986

Spatial rotation angles : x ¼ �55:00140501j

u ¼ �25:62614604j

j ¼ �163:9782123j

Translation :

DX

DY

DZ

266664

377775¼

44140:911 m

�40290:074 m

2703:271 m

266664

377775

Table 1

GCPs of the Swiss National Coordinate System (in m)

Number of GCP X Y Z

349 42664.87 � 40320.99 2052.04

501 42232.53 � 40426.22 2060.50

502 42043.68 � 40109.57 1928.71

503 43205.53 � 39883.13 2007.01

504 43679.31 � 39665.91 2018.92

505 43825.15 � 39950.77 2206.52

510 42786.77 � 41191.30 2740.73

520 43448.83 � 41358.01 3968.77

Fig. 3. Smearing of ortho-image texture due to geocoding based on

DTM. Retaining of pixel structure in SSM.


4. Data processing

4.1. Digital photogrammetric workstation PHODIS

With increasing improvements in hard- and soft-

ware, more and more digital software systems are used

for air photo stereo restitution. With the PHODIS

system, CARL ZEISS Oberkochen brought a nowa-

days already ‘‘classical’’ workstation onto the market

(Braun, 1997), which was available for the present

project at the Dresden University of Technology.

Extremely time-consuming processes like disparity

measurements, point transformations, aerotriangula-

tion or DTM generation can now be accomplished

by digital photogrammetric image processing in an

automated way (Wolf, 1999, p. 1). Within the present

project, the majority of the PHODIS software modules

were used (cf. Sections 4.2–4.5).

4.2. Generation of the stereo model

The generation of the stereo model was accom-

plished using PHODIS ST (Version 3.1.0), a stereo

module of PHODIS for the production and metric

restitution of digital stereo models. The version used

in this project, ST 30, works with fixed images and

moving cursor.

The aerophotographs have been scanned with the

precision scanner SCAI selecting a resolution of 1200

dpi (21 Am). The output data existed automatically in

the ZEISS-internal TLD format.

For the generation of the stereo model the follow-

ing steps had to be performed:

1. Generation of the image pyramids with six pyramid

levels for a fast zooming-out and -in, the resolution

from one to the next zoom level always being half

or double.

2. Inner orientation (data from the Camera Calibration

Certificate).

3. Outer orientation (relative and absolute orientation):

3.1. Relative orientation: by means of a feature-

based matching (FBM) and intensity-based

least-square matching (LSM) a sufficient

number of homologue point pairs could be

determined. Difficulties mainly occurred in the

upper part of the air photos, since at the

horizon, no homologue points could be found.

3.2. Outer orientation: for this, the GCP coordinates

transformed intoModel 2000 (SSM) were used.

4. By eliminating the vertical disparities in the stereo

image pair, the elements of the relative orientation

then served the computation of the epipolar images

(normalised images). Through automatic matching

of the homologue image elements, these images

equal human spatial vision (Kraus, 1997, p. 358).

For the subsequent processing of the data in

PHODIS TS, normalised epipolar images have to

be calculated.

4.3. Measurement and integration of breaklines

It would have meant an enormous effort and time

consumption to measure the whole DTM manually. In

order to find a feasible solution which guaranteed both

the required accurracy and an agreeable amount of

work and, therefore, reduced working time, it has been

decided to introduce manually measured breaklines in-

to the DTM computation by means of autostereo

correlation.

A total of 799 breaklines with approximately

8500 individual points were measured. The points

were stored in an ASCII file in the PHOCUS

format and could therefore be directly imported into

PHODIS TS.

4.4. Generation of the digital relief model

PHODIS TS is a very comprehensive software sys-

tem for the automatic generation of digital terrain

models. TopoSURF, the core of this system, generates

a great number of height points on the basis of feature-

based matching (FBM), which then serve for the

generation of the raster DTM. According to the

official ZEISS product information, the height accurr-

acy lies between 0.1x and 0.3xof the flying

height. Considering an average distance of roughly

2600 m between Eiger North Face and the airplane,

this corresponds to a ‘‘height’’ accuracy between 0.26

and 0.78 m (see Fig. 4).

4.4.1. Workflow

In each of the previously mentioned pyramid levels,

the DTM generation is performed in three steps:

� preliminary matching


http:\\www.zeiss.de

� computation of ray intersection� robust bilinear finite-element interpolation

Amongst others, the following used parameters are

of importance:

� terrain type: mountainous

� smoothing degree: low� sigma: 1.40 m (representing the theoretical a priori

accuracy of the measured height points)

These parameters yielded the best results. In all

other cases, the structures of the rock face were either

too much smoothed or a higher sigma value had to be

Fig. 5. Flowchart of data processing.

Fig. 4. Flowchart of PHODIS TopoSURF (http://www.zeiss.de, modified).


http:\\www.zeiss.de

used. This, together with the original scale of the

analogue air photos and the dpi applied led to a final

raster size of 3.7 m.

4.5. Generation of the orthophoto image

For the computational geometric rectification/geo-

coding of the digital image (no. 2934), which is the

eastern air photo and the derivation of the orthophoto

product on a digital basis was accomplished by the

software module PHODIS OP. It makes use of the

indirect method of numerical rectification. Based on

the raster image matrix of the input image, a collinear-

ity condition calculates the pixel centres of the output

image.

The generated orthophoto product shows a spatial

resolution of 25 cm corresponding to a hardcopy scale

of approximately 1:10000. The scale differences in

the air photos might lead to noticeable local geometric

distortions (height errors), which can be roughly

assessed by the formula of Kraus (1990, p. 309):

Dr ¼ DZr

cmb

r = distance between the nadir point and the respective

radially displaced points; Dr = radial displacement;

DZ = height difference; mb = image scale factor.

Due to the previously mentioned errors generated

during the rectification process, the orthophoto had

Fig. 6. Anaglyph representation of Eiger North Face in horizontal view.


then to be adjusted to the wall relief. This implies that

the orthoprojection cannot be called totally ‘‘clean’’.

The objective of this final work, however, was to

generate a well-adjusted image texture. Since the

measured breaklines perfectly fit the relief geometry,

the points of these breaklines were used as reference

points for the geometric ‘‘fine-tuning’’ of the ortho-

photo. Since the remaining errors were almost negli-

gible, a simple rubber sheeting approach for the

precise transformation of the respective image points

by means of Erdas Imagine 8.3 software seemed to be

justified, even more so as no accurate measurements

will be made in this product, but its main purpose is

the photorealistic visualisation.

See Fig. 5 for the flowchart of data processing.

5. Results and applications

5.1. Anaglyph imagery

Based on the existing DTM and the geocoded

image texture, an axonomic anaglyph image pair

could be calculated using in-house software of the

Institute for Cartography of the Dresden University

of Technology (cf. Fig. 6).

5.2. VirtualGISk representation

Using the existing DTM and geocoded image

texture of the same areal extent and pixel size, the

Erdas Image tool VirtualGISk allows to generate a

virtual model. Within in this ‘‘virtual world,’’ one can

navigate freely (see Fig. 7).

5.3. Visualisation of climbing routes and their profiles

Since 1938, not only the classical Heckmair

Route through the Eiger North Face has been

climbed, but alpinists found many other possibilities

to conquer the face. The adventure ‘‘Eiger North

Face’’ inspired alpinists to complete routes of

increasingly higher difficulties. In 1961, for the first

time, the Eiger North Face has been climbed during

winter, using the so-called ‘‘Stollenloch’’ (Tunnel

Outlet) of the Eiger Railway as a base (cf. Fig. 8

and Section 2.2). The ascent from the bottom of the

wall to the Stollenloch was also carried out at a

Fig. 7. Virtual Eiger Model (performed by means of Erdas Imagine Modul VirtualGISk) seen at a vertical elevation angle of 45j (original

image in colour). Note the distortion in comparison to Fig. 6.


certain time of this expedition, however, not in the

‘‘correct’’ sequence. In 1966, an American–British–

German party conquered the face for the first time

on a direct route, the so-called John Harlin Route

(Winter Direttissima); the route got its name in

memory of the famous American climber John

Harlin who was killed during that attempt in March

1966. Another route which leads through the western

parts of the face gained significant importance. It

was opened by six Japanese climbers in 1969 and is

since then called the Japanese Direttissima.

These three most important or at least most well-

known routes were, together with prominent spots of

the Eiger North Face, inserted (cf. Fig. 8). Further-

more, the cross-sections and the real three-dimen-

sional distances of the routes were calculated (cf.

Fig. 9). More detailed information on the climbing

routes can be found in Hausmann (1997), Heckmair et

al. (1943) and Hiebeler (1973, 1985).

It seemed to be a rewarding task to generate a sort

of combined image-line map (CIL map) of the Eiger

North Face showing the abovementioned routes. In

fact, such a representation, displayed in ‘‘real’’ 3D

(McAllister, 1993) in the form of anaglyphs, was

highly appreciated by professional mountain guides

who were exposed to this product.

6. Further activities

6.1. De-shading

Natural shadings in terrestrial or aerial photographs

are useful to enhance the 3D effect of the image,

Fig. 8. Enlargement of a CIL map representation of the Eiger North Face showing the most important routes and some characteristic spots.

Route colour assignment like in Fig. 9.


especially for small morphological features. However,

the preservation of the shadows caused by small

features (not included in the geometric model),

together with a simultaneous reduction of the large

shadows in the imagery, leads to optimised draped

images for the Eiger VR model.

In this project, one of the major tasks will be the

elimination of the abundant large cast shadow areas in

the western part of the Eiger North Face. For this, the

natural illumination conditions at the time of the data

take have to be reconstructed, a task which nowadays

can be achieved by commercial software. Based on

the high-precision geometric face model, a raytracing

has to be applied, and, in combination with surface

material properties as well as global image statistics,

an equalisation of illuminated and shadow areas will

be performed.

6.2. 3D VR model

The merging process between the high-resolution

Steep Slope Model (SSM) and a medium-resolution

Digital Elevation Model (DEM) of the surrounding

area will be tried to be achieved in a (semi-) auto-

mated manner. There the compensation of 3D network

stress caused by inhomogeneous accuracies and

actualities in both models, especially in overlapping

areas, is the central problem.

Fig. 9. Route profiles including the real 3D distances. Note the equal vertical and horizontal scales.


Furthermore, algorithms for data reduction have

to be applied to the resulting 3D surface. The

inhomogenous resolution and different terrain types

provide numerous possibilities for optimising the

network structure and surface description. A re-

interpolation of the entire surface by means of

spline patches (NURBS) will be tested on account

to morphologic and absolute accuracy.

Once the spline patches are completely deter-

mined, for every patch or group of patches textures

will be processed from (de-shaded) terrestrial and

aerial photographs. A prerequisite for such future

activities is an additional survey by means of

terrestrial photogrammetry. The equalisation of

radiometry and particularly the mapping and trans-

formation algorithms for spline texture patches are

still ongoing research tasks in this project.

The integration of 3D objects like houses or the

Eiger Tunnel will complete the virtual world, whereas

the level of detail depends on the availability of

external data.

6.3. Applications planned

Further activities comprehend the study of carto-

graphic visualisation possibilities for the Eiger data

set.

First, additional thematic information will be added

to the Eiger North Face CIL-Map using a GIS database.

The graphic design and the calculation of 3D profiles as

additional map information (route profiles) have to be

improved.

Based on the VR model, an overflight animation

will be generated, and, at a later stage, an inter-

active user interface for the autostereoscopic Dres-

den 3D Display (‘‘D4D’’) will be accomplished.

The interface will permit the database access as

well as the free selection of the viewing points and

the fields of view. The system can be used for

route and rescue planning and, with additional

features, for tourist information.

The final VR model will be used as a basis for

cartographic 3D hardcopy products (Buchroithner,

1999; Schenkel, 2000). Thereby, the technological

gap towards high-quality products has to be reduced,

and, on the other hand, cartographic design recommen-

dations and deliberations in cartographic theory

(Schenkel, 2000) should be considered.

7. Conclusion

The generated ‘‘digital wall model’’ of the Eiger

North Face has a raster width of 3.7 m. This corre-

sponds to the best grid size achievable on the basis of

the available input data, and is by far sufficient for

visualisation purposes. An even higher spatial reso-

lution would only be achievable if the analogue air

photos would have been scanned with a resolution

better than 21 Am. However, due to the enormous

amount of data, this does not seem to be unjustified.

The present geometric and image data set repre-

sents just one step towards a widespread application

of Steep Slope Models (SSMs) for touristic and, in

particular, alpinistic purposes. For the realisation of

the envisaged further activities (cf. Section 6), still

many detailed problems have to be overcome. How-

ever, the potential of such products could already be

demonstrated.

Acknowledgements

Apart from Prof. Dr. Armin Grun, Chair for

Photogrammetry and Remote Sensing of the ETH

Zurich, who provided the air photos (cf. Section 2), I

would like to thank the following individuals and

institutions for their kind support. Without their help

the accomplishment of the ‘‘Eiger North Face

Project’’ would not have been possible: Dr. Rolf-

Peter Mark of the Institute for Photogrammetry and

Remote Sensing of the TU Dresden, Dipl.-Ing.,

Bettina Bruschke, HTW Dresden, (both provision of

software and workstations) as well as Robert Schenkel

(anaglyph calculation) and Michael Winkler of the

Institute for Cartography of the TU Dresden.

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creating the virtual eiger north face

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