Comparison of Valentin Hodnik ’ s Stone Model of Triglav and the Actual Shape of the Mountain

I n Ribčev Laz near Lake Bohinj there is a model of Trig lav, the highest mountain in Slovenia. Made of stones, it is the work of the painter Valentin Hodnik from Bohinj . Although it is a work of art, we wanted to evaluate the correctness of its shape compared to the actual mountain. We photographed it and created a point cloud model using the Structure from Motion process (SfM). By transforming the point cloud to actual size, we were able to compare it with the actual shape of the Triglav mountain range obtained from Laser Scanning of Slovenia (LSS). As expected, the shape of the model varied considerably from the actual shape of the mountain, and the scale of the individual slopes and ridges was not the same. For a qual itative evaluation of the model , we calculated the distances between the transformed model and actual surface. The average absolute distance between the nearest points in both point clouds was 41 .8 m (6 cm at a bui lt-model scale) with a standard deviation of 38.0 m (5.4 cm). The results are represented by a picture of absolute distances. We also produced a smal ler 3D print of the Triglav model and the actual shape of the mountain.


Introduction
Mount Triglav, at 2864 m, is the highest peak in the Julian Alps and in Slovenia.It is particularly prominent and a popular challenge for mountaineers.It has a symbolic significance for Slovenes.Despite its modest height compared to other Alpine peaks, it appeals to the worldwide mountaineering fraternity thanks to its high, magnificent northern face, the remains ofa glacier below the peak, valleys with lakes, and recognizable shape.It has also given its name to the only national park in Slovenia, which covers the wider area ofthe Julian Alps.One of the main entry points to Triglav National Park is Lake Bohinj, the largest permanent natural lake in Slovenia.A stone model of Triglav with its surrounding peaks and huts can be found on its south-eastern shore (Fig. 1).
The model ofMount Triglav and the surrounding area (Fig. 2 left) is about two metres high and 6 metres wide.It is the work ofValentin Hodnik , an artist from Bohinj who studied at the Academy ofFine Arts in Zagreb, Croatia.The Bohinj mountains were one ofhis favourite painting themes.His depictions of the mountains, some realistic, some humorous, are still found on postcards (Sivec 2006).The Triglav stone model Hodnik created between 1931 and 1932 is a unique work ofart.According to the information panel next to the model, he used three tonnes of stones strengthened with cement.In addition to the main peak with the nearby ridges and faces, he also made metal models ofthe mountain huts around Triglav (Triglavski dom na Kredarici, Dom Planika and Dom Valentina Staniča).The model imitates the shape of the mountain, but it was presumably based on the painter's subjective perception, without taking any actual measurements.To confirm this, a comparison ofthe shape ofthe model and the actual shape ofthe mountain (Fig. 2 right) was carried out by the Faculty of Civil and Geodetic Engineering of the University ofLjubljana (Petrovič et al. 2018).

Geodetic measurement of the network and reference points
The stone model is naturally much smaller than Mount Triglav.As a basic step, we carefully planned and implemented the geodetic measurement of the reference point coordinates to determine the exact dimensions ofthe stone model.The measurements were made using a modern Leica Nova MS50 tacheometer and precision prisms, and processed using Leica Infinity software.We allocated seven geodetic network points around the model, labelled from 100 to 700.Nine additional reference points, from 1 to 9 (Fig. 3 right) were marked on the stone model.Network point 100 was defined as the origin of the local coordinate system, where the x-axis was oriented towards the north.
The reference points were distributed to ensure the best possible results of photogrammetric measurement and laser scanning.We marked them with black and white circles with a diameter of 2 cm (Fig. 3 right above).From all network points, observations in three repetitions in both circular positions were done towards the other visible network and reference points.The red lines in Figure 3 (right) show two-sided and yellow one-sided measurements.The accuracy of horizontal direction measurements was 0.40 mgon, of zenith distance, 0.11 mgon, and ofincline lengths, 0.07 mm.The coordinates were calculated separately, with horizontal and vertical adjustment in GEM4 and VimWin software tools.The average three-dimensional position accuracy of the reference points after adjustment was 0.4 mm.

Terrestrial laser scanning of the stone model
The established points of the geodetic network (points 100 -600) were also used as stands for the terrestrial laser scanning (TLS) of the stone model.We used the same instrument, the Leica Nova MS50, which allows scanning speeds ofup to 1000 Hz at a recording distance of up to 50 m (Fig. 4).The intended target scanning density at the maximum distance between the standpoint and model was 4 mm.The result obtained in the Leica Infinity software package was unified and integrated a cloud of scanned points from all six stands.

Photographing and photogrammetric modelling
The model was then photographed using a compact Olympus E-PL7 photo camera with a constant focal length of17 mm (Fig. 5 left).Besides the size ofthe model, the following requirements were taken into consideration: final spatial resolution ofthe photos ofat least 1 mm, the convergence of the recorded photos, at least 80% overlap for adjacent photos, and the visibility ofat least three reference points on each photo taken.Altogether, 125 photos were taken (Fig. 5 right) every ten degrees (0.7-0.9 m) at a distance of 4 to 5 m from the stone model at three heights (squatting -about 0.5 m, standing -about 1.5 m, and from up a ladder -about 2.5 m) Thus, the photos covered the whole stone model evenly.They were processed in PhotoScan software using a process known in computer vision as 'Structure from Motion' (SfM).By identifying a large number of identical points in photos, it is possible to simultaneously determine the geometric parameters ofthe camera (internal orientation) and the relative position of the camera in space (relative orientation) to calculate '3D structures' (Westoby and others 2012).At the same time, a low density point cloud was created, which in our case contained 68,000 points (Fig. 6 left).
Even when a reference point was used as a control point, deviations barely exceeded 0.4 mm.With spatial crosssections of image beams of identical points, the high density point cloud of the stone model with 96 million points was calculated.Each point in the high density point cloud had spatial coordinates and a colour value (Fig. 6

right).
Using two technologies, we acquired two point clouds of the stone model, one from TLS and the other from the photo processing.We analysed their similarity and suitability for further processing.Although both were based on the same geodetic network points and the point clouds were oriented with the same reference points, the clouds differed both geometrically and radiometrically.Some differences were based on the technology and method of establishment: the point cloud from the TLS was not coloured, which made interpretation difficult and due to the smaller number of stands (6 compared to 125) some overhangs, edges and others points hidden from TLS stands were not registered.The adjustment also showed inferior position accuracy due to an apparent shift in the position ofone of the stands during TLS measurements.Therefore, we used a photogrammetric point cloud for further comparison with the actual shape ofthe mountain.
2.4 Data on the actual shape of the mountain For the actual shape of the corresponding Triglav region, we used airborne laser scanning data from the Laser Scanning of Slovenia (LSS) project completed between 2011 and 2015.The main purpose of the project, which was carried out under the auspices of the Ministry ofthe Environment and Spatial Planning ofthe Republic of Slovenia, was to provide relevant height data on the hydrography network and land use (Triglav Čekada and Bric 2015).Aerial laser scanning was done by dividing the territory of Slovenia into 19 blocks, where the resolution of recording in each block depended on the morphology and population density of the area.The Julian Alps highlands area was scanned in 2014 with a resolution of2 points/m2.The LSS resulted in a variety of products: a ground points cloud (OTR), a georeferenced point cloud with ellipsoid altitudes (GOT) and a georeferenced and classified point cloud with orthometric heights (GKOT) -all three in LAS format; a digital relief model with 1 m grid resolution (DMR1) in ASCII format, and an image ofanalytical hill-shading in TIF format.Most ofthese data are freely available on the web portal ofthe Environmental Agency ofthe Republic ofSlovenia (Lidar E-vode 2015).Figure 7 shows the area under consideration on the topographic map and the analytical hill-shading ofthe reliefbased on LSS data.

Comparison of point cloud of stone-built models with LSS data
Based on the distances between the manually identified points from the point cloud of the stone model (peaks, positions of mountain huts) and corresponding actual distances, we calculated the average approximate scale of the stone model point cloud as 1:700.Opensource CloudCompare software was used to process and compare the point clouds.Before comparing the photogrammetric point cloud of the stone model and LSS data, both point clouds needed to be aligned.From the available LSS data, we used ground point cloud data (OTR) which consisted of points classified as ground points only.The OTR was filtered with an octree 1 m in size and reduced to 1 pt/m3.
Before comparing the shapes, alignment ofthe point clouds was performed.We manually identified five points on the stone model point cloud which the programme aligned with identical points on the actual shape point cloud.Figure 8 represents the initial stage and the result ofthe transformation.R0 to R4 are selected points on the actual mountain point cloud, while A0 to A4 are corresponding points on the stone model point cloud.
Due to the large amount of data and huge non-homogeneous deviations between the shape of the stone model and the real mountain at the edges ofthe model, further comparison was performed separately for two areas.In the first, only the central area of the model in the vicinity of Triglav and Mali Triglav peaks was used (Fig. 9 left), while in the second, the entire area of the stone model was included (Fig. 9

right).
Tables in Figure 10 show standard deviations at identical points (column 'Error') for the central part (below) and the whole area (above), which represent the estimated quality ofcloud alignment.
Additional alignment ofthe point clouds was carried out using the ICP (Iterative Closest Point) procedure, which allows alignment of point clouds so that the squares of the distances between identifiable points in both clouds are minimal (Besl and McKay 1992).With ICP, the stone model point cloud was transformed into the actual surface ofthe Triglav mountain range.The final result offine alignment for the central area and the whole area is shown in Fig. 11.RMS at identical points was 16.60 m for the central area and 32.55 m for the whole area.
3 Results of the comparison of the stone model and the actual shape of the mountain The correctness ofthe stone model compared to the actual shape of the mountain was determined by absolute distances between the point clouds in CloudCompare software.We used the default software settings, which computed the distance between two point clouds as 'nearest neighbour distance' (CloudCompare 2018); for each point of the compared cloud (in our case, a photogrammetric point cloud), CloudCompare searched the nearest point in the reference point cloud  (OTR in our case) and computed the (Euclidean) distance.The results are presented separately for the central area and for the entire stone model, with and without the use ofICP additional matching method.Absolute distances are represented by the blue-green-red colour scale with which the stone model point cloud was coloured.Note that at the model scale of approximately 1: 700, 100 m in real life represents 14.3 cm on the stone model.
For the central area without the use of ICP, the calculated mean absolute distance between the point clouds was 45 m (6.4 cm). Figure 12 shows the minimum absolute distances on the ridges, where they reached up to 25 m.On the slopes, they increased up to 125 m.A greater discrepancy between the stone model and the actual mountain was observed on the southern side of the ridge which runs south from Triglav.The greatest absolute distances, over 200 m, appear on the edges (especially the northern one).The western, some central and partly south-eastern slopes in the model were higher than the actual mountain, while other areas, including those with the greatest absolute distances, were lower than the actual mountain shape.
The mean absolute distance between the point clouds on the same (central) area with the additional use of ICP was reduced to 28 m (4 cm) with a standard deviation of36.2 m (5 cm).In Figure 13 we can see that the discrepancy in the central part is significantly smaller, and the areas where the model is lower or higher than the real shape are more dispersed.At the northen edge, the model is still more than 200 m lower, while at the southern edge, the absolute distances from the actual mountain are even larger, comparing the results without ICP.
For the entire stone model range the average absolute distance between the point clouds was 67 m (10 cm). Figure 14 shows the best fits in the area around Triglav, the Planika pod Triglavom hut and all the way to Kredarica Peak, where the distances were up to 40 m, and occasionally up to 100 m.To the east of the Triglav hut at Kredarica, the distances increased to 180 m.In the area around Valentin Stanič hut beneath Triglav, the
Predstavimo još usporedbu izračunanih apsolutnih udaljenosti na užem području (gore) i na cijelom području, obje s dodatnim uspoređivanjem s ICP.Na slici 16. vidi se da se javljaju odstupanja između modela na istim distance was about 110 m.On the southern and eastern edges ofthe stone model, the distances ranged from 30 to 120 m.On the western edge, the distances were between 100 and 260 m.At the northern edge ofthe region, the distances between point clouds rose rapidly, ranging from 100 to more than 300 m.In the central part ofthe area, the stone model was higher than the actual mountain, while the main Triglav ridge, most of the western and entire north-eastern parts of the model were lower than the actual mountain.When we also used the ICP method, the mean absolute distance between the point clouds were again reduced to 41.8 m (6 cm) with a standard deviation of38.0 m (5.4 cm) as shown in Figure 15.The central areas fitted well, while the areas higher and lower than the actual shape were again dispersed.The model was significantly higher at the northernmost part (the western part of Triglav's north face) and in the south-east part (Kredarica Peak).All the major mountain ridges and most of edge areas were lower than the mountain's real shape.
A comparison ofcalculated absolute distances in the central area only (above) and in the entire area (both aligned with the additional use of ICP) is presented in Figure 16.There are noticeable divergences between point clouds, mostly in the same areas, while the deviation values for the central area are smaller.
The results of comparing the stone model point cloud and actual mountain point cloud show that Valentin Hodnik captured the actual shape of Triglav and its surroundings fairly well.The average deviation is less than 50 m compared with real shape, which is only 7.1 cm in the model.The differences are more distinct along the ridges; they are generally lower on the model and less sharp than the actual ones, but this may be due to a physical damage to the model caused by the weather or visitors climbing on it.The differences are least in the area between Kredarica hut and the summit ofTriglav, which is the central, most interesting part of the model to many visitors.As the distance from Triglav Peak increases, deviations increase.This is especially obvious at the edges ofthe stone model, where the deviations exceed 200 m.We assume that the author had to adapt the model to the ground configuration ofthe site.Perhaps he needed to finish the edges smoothly to avoid crumbling.
We also discovered that mountain huts on the stone model were only roughly located, while their actual positions are rather different.We realised this while calculating the approximate model scale, when noticed very different relations between the mountain huts and Aljaž Tower. Figure 17 shows the actual positions of the mountain huts and Aljaž Tower and their positions on stone model.

3D printing of shapes
In order to enable visual comparison and evaluation, we produced 3D prints of both shapes.Of course, we   reduced them for this purpose to 14 cm in length.The stone model ofTriglav near Lake Bohinj was printed in the approximate scale of1:53 and the model ofthe actual shape of the Triglav mountain range in the scale 1:18,570.To facilitate comparison, we also printed a geometrically adjusted reduced stone model (transformed point cloud).Figure 18 shows all three models; in the left column are the shaded and hypsometric tints images of digital data, and on the right are the illuminated 3D prints.Figure 19 additionally shows the comparison between the outlines ofthe actual mountain shape and the geometrically adjusted stone model in an oblique view from four different directions.This visual comparison shows good matching of shapes in the central part and larger deviations at the edges.Above all, it is obvious that the shape ofthe stone model is rougher, which was surprising at first, as we always thought that the limestone mountains were extremely rough with few smooth slopes.However, with the scale reduction, all apparent recesses and bulges are concealed by the size ofthe mountain.

Conclusions
The stone model of Triglav and its surroundings at Bohinj Lake in Ribčev Laz is a good approximation ofthe actual shape of the mountain.Visitors and observers dijelovima, ali su iznosi odstupanja na užem području manji.
Ustanovili smo dalje, da su planinarske kuće postavljene samo za grubu orijentaciju jer njihovi položaji na maketi prilično odstupaju od njihovog stvarnog položaja.To smo primijetili već kod određivanja približnog mjerila makete dobivši dosta različite razmjere između planinarskih domova i Aljaževog stupa na vrhu Triglava.Na slici 17 vide se stvarni položaji planinarskih  can easily recognize individual peaks, mountain huts, ridges and faces.The exactness of the shape was estimated using a precise geodetic survey.Traditional geodetic measurement methods were suitable for accurate measurements of individual selected points to assess their correctness, but not for the complex shapes ofthe surfaces as a whole.Using photogrammetric methods, we created a dense point cloud ofthe stone model from photographs and compared it to the point cloud of the actual Triglav mountain range, acquired from Laser Scanning of Slovenia data.The average absolute distance between the point clouds was 41.8 m (6 cm at a built-model scale) with a standard deviation of 38.0 m (5.4 cm) for the entire area with the additional use ofICP method, while for the central part ofthe model it was 28 m (4 cm) with a standard deviation of36.2 m (5 cm).The results ofthe comparison showed that the stone Triglav model matched the actual mountain shape well close to Triglav Peak, Mali Triglav peak and Kredarica hut, while differences arose at the edges ofstone model.Peaks and ridges were lower than their real counterparts, but this might be explained by natural erosion and human interference.The model is rougher, since the author was limited by the shapes ofthe stones he used.We also performed terrestrial laser scanning of the stone model, but the point cloud made from it was less useful for interpretation, less accurate and less complete, so we decided not to use it in later steps.
The Triglav model is a work of art which also has cultural, historical and tourist significance.From the cultural heritage conservation perspective, the data obtained through this project could be used in any future reconstruction ofthe stone model.For a more accurate presentation of the area around Triglav, a new model based on LSS data could be created and perhaps printed with a large-scale 3D printer, showing mountain paths and the proper positions of the mountain lodges.To summarise, the stone model ofTriglav shows the shape of the relief well for orientation and presentation purposes only.domova i Aljaževog stupa te njihovi položaji na kamenoj maketi.

Fig. 7
Fig. 7 Area under consideration on topographic map DTK 50 (Surveying and Mapping Authority of the Republic of Slovenia) and the shaded relief of the area based on LSS data (Environmental Agency of the Republic of Slovenia).Slika 7. Područje rada na topografskoj karti DTK 25 (Geodetska uprava Republike Slovenije) i sjenčani prikaz reljefa područja izrađen na osnovu podataka LSS (Agencija Republike Slovenije za okoliš).

Fig. 1 6
Fig.16 Deviations between the point clouds of the stone model and the actual mountain calculated for the central and entire area, both using the ICP method.Slika 1 6.Odstupanja između oblaka točaka kamene makete i stvarnog oblika planine za uže i cijelo područje, oboje s upotrebom metode ICP.