Geological Survey of Denmark and Greenland Bulletin 33, 2015, 73-76 73© 2015 GEUS. Geological Survey of Denmark and Greenland Bulletin 33, 73–76. Open access: www.geus.dk/publications/bull Digital models based on images taken with handheld cameras – examples on land, from the sea and on ice Erik Vest Sørensen, Morten Bjerager and Michele Citterio Geological outcrops can be comfortably modelled in three dimensions in the offi ce using images from a handheld digital camera. Recent developments within the imaging techniques of Structure from Motion (Lowe 2004; Snavely et al. 2008; Fonstad et al. 2013) and photogrammetry (Hirschmüller 2005; James & Robson 2012; Favalli et al. 2012) have made it easier and cheaper to construct so-called digital outcrop models using stereoscopic images from standard digital cam- eras. Th e digital outcrop model (Bellian et al. 2005) is a 3D representation of the outcrop surface and is oft en displayed in the form of a polygon mesh or a point cloud. In this paper we present three examples of such point clouds from images obtained with a handheld digital camera. Th e examples illus- trate how outcrop topography or digital outcrop models can be constructed at diff erent scales, with diff erent accessibility and operational platforms. Two examples illustrate outcrop scales of metres to kilometres, with images obtained by walk- ing along excavated exposures in the Faxe limestone quarry and from a boat sailing past the coastal cliff of Stevns Klint. Th e third example illustrates detailed micro-topography of ice and snow surfaces where the images were obtained from a snowmobile on an ice cap in A.P. Olsen Land, North-East Greenland. Methods Th e images were collected with a 36 megapixel Nikon D800E camera equipped with a fi xed 35 mm f/1.4 Zeiss lens. Th e camera was locked at infi nity in the Faxe quarry and Stevns Klint examples. In the third example from Greenland, the camera was focused and locked so that objects at a distance of c. 2 m were in focus. Th e images were recorded with ste- 55°15´20´´N 55°15´20´´N 12°7´30´´E 200 m 12°7´30´´E Fig. 2A Fig. 1. Overview of the Faxe limestone quarry. Red dots: Images obtained in 2013. Green dots: images obtained in 2014. The inset map shows the location of the Faxe quarry in Denmark. Orthophotograph from Danish Geodata Agency. Fig. 2. A: Perspective view (towards the north-east) of the northern part of the Faxe limestone quarry showing the constructed point cloud gener- ated from oblique images obtained in 2014. The point cloud is coloured according to colour value of matched pixels and can be rotated freely in three-dimensions. For location see Fig. 1. B: Close-up of a bryozoan lime- stone mound with nodular f lint layers. B A Fig. 2B 20 m 5 m 7474 reoscopic overlaps of up to 90%. In this way image acquisi- tion for digital outcrop models diff ers from the traditional approach for 3D stereoscopic work (Dueholm 1992), where a stereoscopic overlap of 60–80% is suffi cient to ensure good precision and continuous stereoscopic overlap. Furthermore, images were acquired from much more varied image posi- tions, for example in the Faxe quarry study (Fig. 1), compared with traditional 3D mapping, where images are typically col- lected along straight parallel lines. Th e construction of the digital outcrop models from the images is based on automatic dense multi-view, stereo- matching routines. Th ese routines attempt to match each pixel across a range of images. Because of the large overlap, the image baseline is quite small, which decreases the preci- sion of matched pixels. Th is is, however, compensated for by the redundancy of determining the same point in multiple images. In practice this approach yields a level of precision which is comparable to that typically obtained with stereo- images with 60% overlap, but with a much better automatic elimination of erroneously matched pixels. Th is leads to the production of dense point clouds, which require little man- ual editing, making them well suited for visualisation. Th e clouds can also be used in morphological analyses. A number of soft ware solutions can generate point clouds from images; in this study we used the professional version of Agisoft Pho- toScan and SURE – Photogrammetric Surface Reconstruc- tion from Imagery. Walking along exposures – the Faxe limestone quarry Danian deep-water bryozoan and coral carbonate mounds are exposed in the Faxe limestone quarry (Fig. 1; 55°15́ 40˝N, 12°07´20˝E), which represents a perfect case study for 3D outcrop modelling. Th e quarry was visited in 2013 and 2014, and a large collection of stereoscopic images documents the changing features of the active quarry. Images of the quarry walls were collected using a handheld digital camera from a distance of 10–20 m, which translates into images with pixel sizes on the ground, also known as the ground sam- pling distance, in the millimetre range. We used a subset of the data from the northern part of the quarry that is being actively quarried. Th e result of the reconstruction is a dense point cloud (Fig. 2), which can be freely rotated in 3D and zoomed in on areas of interest. Th is is a powerful way of vi- sualising geological outcrop data. When combined with a periodic recording of digital images in the active quarry it can provide unique outcrop topographic data sets that make a reconstruction of the 3D mound topography possible in great detail. It also provides a data set that can be used to quantify volumes of specifi c characteristic rock types, such as the amount of black-grey nodular fl int in the greyish white bryozoan limestone mound systems. B A 10 m Fig. 3. A: Perspective view of the point cloud generated from a section with Danien bryozoan limestone mounds in the coastal cliff of Stevns Klint. The point cloud is illustrated with RGB-values of matched pixels. B: Perspective view of the filtered point cloud based on colour and surface roughness calcula- tions. The inset map shows the location of Stevns Klint in Denmark. Fig. 4. Perspective view of the reconstructed snow surface measuring 420 × 160 cm from the ice cap in A.P. Olsen Land, North-East Greenland. Footprint Ruler 50 cm 75 Sailing along exposures – Stevns Klint Stevns Klint (55°15́ 39˝N, 12°24́ 52˝E) was recently included in UNESCO’s world heritage list and is world famous for its excellent exposure of the Cretaceous–Palaeogene boundary. Images were collected along 11 km of the coastal cliff from a boat in June 2014, adding new oblique images to the growing archive from previous studies (Surlyk et al. 2006; Pedersen & Damholt 2012). Th e images were collected from a distance of 10–300 m, which translates to pixel sizes in the millimetre to centimetre range. Th is approach allows for high resolu- tion mapping of the mound structures and mega- and meso- scale bedding. Images from a cliff section at Stevnsfortet in the southern part of the cliff were selected to illustrate how simple manipulation of the generated point cloud data (Fig. 3A) can be used to visualise the overall mound structures. Characteristic black and grey fl int nodules follow the inter- nal bedding of the bryozoan mounds and display a strong colour contrast to the light-coloured limestone that can be used to fi lter away light-coloured points. Th e resulting point cloud can be analysed with calculations of outcrop param- eters such as surface roughness and curvature or, with more sophisticated calculations, used in semi-automatic tracing of discontinuities such as joints, fractures or bedding, devel- oped for terrestrial LiDAR data (Garcia-Sellés et al. 2011). Th e result of the fi ltering is shown in Fig. 3B, which illus- trates the structure of the internal bedding in a diff erent way. With little eff ort this can be extended to include the entire 11 km surveyed part of the coastal cliff . Standing on a snowmobile on an ice cap – North-East Greenland Th e third example is from an ice cap in A.P. Olsen Land (74°37´28˝N, 21°22´30˝W) in North-East Greenland. Th e small-scale topography of snow and ice infl uences the turbu- lent and radiative components of the surface energy balance, as it controls the aerodynamic roughness length and changes the surface albedo (Munro 1989; Warren et al. 1998; Brock et al. 2006). Surface roughness must also be accounted for in remote sensing of the cryosphere (König et al. 2001). Th e spatial scales relevant for such applications span several or- ders of magnitude, with required vertical accuracies in the order of millimetres (Rees & Arnold 2006). Ground-based photogrammetry appears to be a viable technique to map snow and ice micro-topography in the fi eld down to a scale of centimetres (Irvine-Fynn et al. 2014). Our aim is to dem- onstrate the feasibility of millimetre-scale accuracy over an outcrop scale of several square metres, under fi eld conditions. 50 cm A B C D 0.055 0.051 0.048 0.044 0.041 0.038 0.034 0.031 0.027 0.024 0.021 0.017 0.014 0.010 0.007 0.003 0 Roughness Elevation radius = 0.005 m radius = 0.05 m radius = 0.5 m 653.049 653.041 653.034 653.026 653.019 653.011 653.003 652.996 652.988 652.981 652.973 652.966 652.958 652.951 652.943 652.936 652.928 (m above sea level) Fig. 5. Point cloud of the surface shown in Fig. 4, in plane view. A: Coloured according to elevation height. B, C, D: Coloured according to surface rough- ness. The surface roughness is calculated as the vertical deviation of each point from the best fitted plane defined by data within a sphere with a radius of 0.005 m (B), 0.05 m (C) and 0.5 m (D). 7676 For this experiment, a person standing on a snowmobile and pointing the camera obliquely downwards collected 29 im- ages from diff erent positions. Th e distance from the camera to the ground was c. 2 m. Th is approach gives images with a ground sampling distance in the sub-millimetre range. Th e generated data are a very dense point cloud (Fig. 4). Th e height of roughness elements per unit length is shown in Fig. 5 over three diff erent spatial wavelengths of 0.005 m, 0.05 m and 0.5 m. Th is case study shows that it is possible to obtain surface roughness data useful for glaciological and remote sensing applications by relatively simple means. Summary Th is study demonstrates that it is possible to generate high- resolution topographic data at various scales with diff erent accessibility and operational platforms by using a standard digital camera and computer soft ware. Th e method has a high potential for fi eld geologists, who wish to establish ac- curate outcrop topographic models that can be ‘brought to life’ and visualised in 3D surface models. Th ese models can be freely rotated in three dimensions and are well suited for visualisation as well as quantitative purposes in geological mapping. Th is is an important new addition to the way 3D mapping is undertaken in the photogrammetry laboratory at the Geological Survey of Denmark and Greenland. Acknowledgements Data from the Faxe limestone quarry and Stevns Klint were obtained with support from Geocenter Denmark and the European Science Foundation COCAR DE-ER N. References Bellian, J.A., Kerans, C. & Jennette, D.C. 2005: Digital outcrop models: applications of terrestrial scanning lidar technolog y in stratigraphic modeling. Journal of Sedimentary Research 75, 166–176. Brock, B.W., Willis, I.C. & Sharp, M.J. 2006: Measurement and param- eterization of aerodynamic roughness length variations at Haut Glacier d’Arolla, Switzerland. Journal of Glaciolog y 52, 281–297. Dueholm, K.S. 1992: Geologic photogrammetry using standard small- frame cameras. Rapport Grønlands Geologiske Undersøgelse 156, 7–17. Favalli, M., Fornaciai, A., Isola, I., Tarquini, S. & Nannipieri, L. 2012: Multiview 3D reconstruction in geosciences. Computers & Geosci- ences 44, 168–176. Fonstad, M.A., Dietrich, J.T., Courville, B.C., Jensen, J.L. & Carbonneau, P.E. 2013: Topographic structure from motion: a new development in photogrammetric measurement. Earth Surface Processes and Land- forms 38, 421–430. García-Sellés, D., Falivene, O., Arbués, P., Gratacos, O., Tavani, S. & Mu- ñoz, J.A. 2011: Supervised identifi cation and reconstruction of near- planar geological surfaces from terrestrial laser scanning. Computers & Geosciences 37, 1584–1594. Hirschmüller, H. 2005: Accurate and effi cient stereo processing by semi- global matching and mutual information. In: Schmid, C., Soatto, S. & Tomasi, C. (eds): Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), San Diego, CA, USA, 20–26 June 2005, 2, 807–814. Irvine-Fynn, T.D.L., Sanz-Ablanedo, E., Rutter, N., Smith, M.W. & Chandler, J.H. 2014: Instruments and methods. Measuring glacier surface roughness using plot-scale, close-range digital photogrammetry. Journal of Glaciolog y 60, 957–969. James, M.R. & Robson, S. 2012: Straightforward reconstruction of 3D surfaces and topography with a camera: accuracy and geoscience appli- cation. Journal of Geophysical Research 117(F3), F03017. König, M., Winther, J.G. & Isaksson, E. 2001: Measuring snow and glacier ice properties from satellite. Reviews of Geophysics 39, 1–27. Lowe, D.G. 2004: Distinctive image features from scale-invariant key points. International Journal of Computer Vision 60, 91–110. Munro, S. 1989: Surface roughness and bulk heat transfer on a glacier: comparison with eddy correlation. Journal of Glaciolog y 35, 343–348. Pedersen, S.A.S. & Damholt, T. 2012: Cliff collapse at Stevns Klint, south-east Denmark. Geological Survey of Denmark and Greenland Bulletin 26, 33–36. Rees, W.G. & Arnold, N.S. 2006: Scale-dependent roughness of a glacier surface: implications for radar backscatter and aerodynamic roughness modelling. Journal of Glaciolog y 52, 214–222. Snavely, N., Seitz, S. & Szeliski, R. 2008: Modeling the World from in- ternet photo collections. International Journal of Computer Vision 80, 189–210. Surlyk, F., Damholt, T. & Bjerager, M. 2006: Stevns Klint, Denmark: uppermost Maastrichtian chalk, Cretaceous–Tertiary boundary, and lower Danian bryozoan mound complex. Bulletin of the Geological Society of Denmark 54, 1–48. Warren, S.G., Brandt, R.E. & Hinton, O.P. 1998: Eff ect of surface rough- ness on bidirectional refl ectance of Antarctic snow. Journal of Geophys- ical Research 103(E11), 25789–25805. Authors address Geological Survey of Denmark and Greenland, Øster Voldgade 10, DK-1350 Copenhagen K, Denmark. E-mail address: evs@geus.dk