Comparison of techniques for generating digital

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Comparison of techniques for generating digital terrain models from contour lines ALBERTO CARRARA , GABRIELE BITELLI & ROBERTO CARLA Published online: 06 Aug 2010.

To cite this article: ALBERTO CARRARA , GABRIELE BITELLI & ROBERTO CARLA (1997): Comparison of techniques for generating digital terrain models from contour lines, International Journal of Geographical Information Science, 11:5, 451-473 To link to this article: http://dx.doi.org/10.1080/136588197242257

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int. j. geographical information science, 1997 , vol. 11 , no. 5 , 451± 473

Research Article Comparison of techniques for generating digital terrain models from contour lines ALBERTO CARRARA


CNR-CSITE, Viale Risorgimento 2, 40136 Bologna, Italy

GABRIELE BITELLI DISTART, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

and ROBERTO CARLA’ CNR-IROE, Via Panciatichi 64, 50127 Firenze, Italy ( Received 20 September 1995; accepted 4 December 1996 ) Simple but objective criteria for evaluating the quality of DTMs, derived from digital contour lines, are de® ned. Such criteria are then applied to terrain models, obtained by means of four di erent procedures, which refer to three sample areas characterized by complex morphological settings. The results of the comparison shows that each DTM is a ected by one or more types of error or pitfall; however, one TIN generator and one grid interpolator proved to be capable of e ectively producing terrain models which largely re¯ ect the ground morphology as expressed by the input contour lines. Abstract.

1. Introduction

The potential of digital terrain models ( DTMs) for solving a wide spectrum of theoretical and applied problems has long been known ( Evans 1972). However, only since the early 1980s has computer technology made it possible to acquire, process and display elevation data e ciently and cost-e ectively, through the application of sophisticated hardware and software modules capable of readily manipulating large volumes of spatial data. At present, DTMs and their derivatives are routinely exploited for a wide range of planning and engineering applications, such as land reclamation, calculation of cut-and-® ll requirements for earth works, optimization of the location of radiotransmission stations by intervisibility analysis, and, more recently, the determination of ¯ ooded area potential or other relevant geomorphological parameters of the landscape ( Burrough 1986, Arono 1989, Weibel and Heller 1991). Hence, nowadays they constitute a fundamental element of many two or three-dimensional geographical databases. The methods used to capture and store elevation data over intermediate or large areas can be grouped into four basic approaches: contour lines, pro® les, regular grids (raster), and triangulated irregular networks ( TIN ). Each one exhibits advantages and pitfalls and their respective applicability is largely dependent on the way source data are collected and stored. Contours, which have most often been used by 1365 ± 8816/97 $12´00

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1997 Taylo r & Francis Ltd.


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cartographers to portray relief, and pro® les, are best derived from photogrammetric analysis of stereo aerial photographs. Owing to their crude topological structure, both are not particularly suitable for automated spatial analysis of ground morphology. Even the derivation of slope or shaded relief maps from contours is a rather cumbersome operation. Grid formats, which are still the most common approach to store and analyse elevation data within a GIS, are usually derived from digitized contour lines of existing topographic sheets or, more recently, directly from automated processing of stereo aerial/satellite data through digital image correlation techniques ( Krzystek and Ackermann 1995, Kolbl 1996 ). Most recently, the poor e ciency in terms of memory requirements and accuracy of raster DTMs has been argued as an advantage of TIN structures, which are generally obtained by digitized contour lines or irregularly distributed elevation points ( Lee 1991, Falcidieno and Spagnuolo 1991). Regardless of the approach selected to capture elevation data, raster and TIN are the two basic structures used today for electronically storing, manipulating and analysing DTMs. In the literature, the advantages and drawbacks of each structure have been thoroughly discussed ( Burrough 1986, Arono 1989 ); likewise, the accuracy of numerical terrain models generated by traditional photogrammetric techniques has long been investigated (Ackermann 1978, Li 1994). Conversely, a few authors have attempted to evaluate the reliability of a terrain model by image processing or statistical techniques ( Wood and Fisher 1993, Bitelli et al . 1993), or compare a contour-derived DTM with its source data, using formalized criteria (Carrara et al . 1996 ). This paper is part of an investigation on DTM generation and application (Carrara 1988, Carrara et al . 1995, 1996, Bitelli et al . 1996). First the criteria for evaluating the quality of DTMs, derived from digitized contour lines covering wide regions or entire countries, are presented. Then through their application, DTMs obtained by two grid-based contour interpolators and two TIN generators are compared for three sample areas characterized by complex morphological settings. Lastly, the advantages and limitations of the techniques for creating large DTMs from contour lines are examined in the light of current technological advancements. 2. Evaluation of DTM quality

Various methods have been applied to assess DTM quality where the term indicates how faithfully the elevation model re¯ ects ground morphology as expressed by the input information (contour lines, height spots, etc.). Some attempt to statistically compare calculated or interpolated elevation values with the actual ground surface relief obtained by detailed photogrammetric analysis or ® eld surveys ( Li 1994 ). Others estimate the quality of a DTM by visually inspecting the spatial pattern of the calculated elevation surface or its derivatives by means of a variety of rendering tools, such as shaded-relief maps, isopleth maps or similar powerful display techniques ( Wood and Fisher 1993). Nowadays, most DTMs of large regions are still derived from scanned/vectorized contour lines of existing topographic sheets. To accomplish this task, no other input information, such as breaklines and height spots, is generally exploited either to improve the accuracy, or to test the reliability of the terrain model obtained. Such supplementary data, which would improve the performance of TIN generators and,


Evaluating the quality of D T Ms

453

to a lesser extent, of grid-based interpolators, are costly or di cult to acquire over wide regions. Hence, public or private institutions involved in the DTM production are not eager to invest extra funds for capturing them. Consequently, in the present work this type of ancillary data was not used as input for generating the DTMs. Additionally, DTM accuracy was evaluated in comparison with the data source, namely, the original contour lines from which they were derived through di erent interpolation algorithms or TIN generators. To what extent contours re¯ ect the actual morphology of the region displayed on a topographic sheet is generally di cult or costly to evaluate. Contour accuracy is mainly dependent on the quality and scale of the aerial photographs, on the characteristics of the photogrammetric device and on the skill of the operator. These three factors may signi® cantly vary from one topographic map to another and even within the same map sheet. As part of a recent study on the potential of the new digital photogrammetric techniques ( Bitelli et al . 1996 ), contour accuracy of a topographic sheet at 1 : 25 000 (with contour interval of 25 m) was tested against actual ground relief, for the ® rst sample area, located in Calabria (southern Italy, ® gure 1 ). Ground truth was derived from traditional analytical photogrammetry. Results showed that contour errors vary signi® cantly throughout the map from less than 1 m up to 30 m with a RMS error close to 6 m. Since the aim of the present investigation is to compare methods, no attempt is made to evaluate contour reliability of the second and third sample areas. Actually, for the scope of this work input contours could be treated as error-f ree or even obtained by a simulation algorithm. Having outlined the aims and limitations of the present investigation, the criteria de® ned for assessing the quality of a DTM are summarized as follows: (a) DTM heights falling near the original contour lines (i.e., at a distance equal or close to the grid sampling space) must have values equal or almost equal to the contour labels (i.e., they should di er by less than 5 per cent of the contour interval ). ( b) In each area bounded by a contour pair, DTM heights must assume values within the elevation range de® ned by the two contour labels. (c) Within such an area, DTM heights should vary almost linearly between the elevations of the two bounding contours. (d ) In areas characterized by low relief information, namely wide valley bottoms or ¯ at hill tops, DTM height patterns must re¯ ect a reasonable or realistic morphology. (e) Distributions of DTM heights which de® ne unrealistic morphological features (artefacts ) should be limited to a small (say less than 0´1 or 0´2 per cent) proportion of the whole data set. The ® rst three criteria are founded upon the simple assumption that, as contour lines are the basic source of information, DTMs which are obtained either by interpolating such contours or from TIN-raster conversion, should be able to reproduce them with an accuracy that will be mainly dependent on the resolution (spacing) of the grid-cell. The choice of a disagreement threshold value (about 5 per cent, ® rst criterion) dependent on the input map contour interval, derives from the fact that contour interval generally re¯ ects map relief accuracy better than any other map feature, such as scale.


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Figure 1. Location of the southern (Calabria) and northern (Trentino) sample areas. For each area (in grey) and its neighbourhood, input contour lines used in the analysis are displayed.

As far as linearity between each contour pair is concerned, the criterion does not hold true in all circumstances. In natural slopes concave or convex pro® les are likely to be more frequent than rectilinear pro® les; however, any slope shape can be adequately approximated by a set of straight segments bounded by each contour pair. Without extra information, this approximation is the most reasonable even for gently sloping, valley bottoms or ridge tops which are generally concave and convex surfaces, respectively. The fourth criterion is the most di cult to assess. It relies on the subjective comparison of DTM heights with respect to a ground morphology which is generally inferred from the spatial pattern of the input contours which may well be a ected by various errors. The ® fth criterion may appear the simplest to verify. Rendering techniques may well allow easy detection of major artefacts, where other methods would require much more careful inspection of the statistical parameters of the height frequency distribution, or the analysis of the height derivatives (slope and aspect) which are


455

very sensitive to unrealistic elevation patterns. Clearly, the threshold value for artefacts (close to 0´1± 0´2 per cent) ® nd better application for large data sets. Most importantly, there are two conditions where artefacts are more likely to occur: areas with high and low contour density. In the ® rst case, they can be detected using criteria (a ), (b ) and (c). In the second case, only visual inspection of the DTM or its derivatives make it possible to evaluate the likelihood of the elevation model. Lastly, all the above quality criteria ® nd better application when the DTM resolution (cell size) is comparable with the contour interval of the input map, namely, the ® rst should be less than or, at the most, equal to the second.


3. DTM generators

To generate a grid DTM from digital contour lines, a large variety of interpolation algorithms has been proposed or developed. Some of them are general in nature (weighted moving averages, bicubic splines, kriging, ® nite elements, etc.), by considering the measured elevations as a group of randomly distributed point observations. Other methods may be interpreted as contour-speci® c since they attempt to exploit the speci® c topological and morphological properties of contour lines. The latter were discussed by Yoeli ( 1975) and Clarke et al . ( 1982). As previously mentioned, at present many elevation models are generated using TIN structures, where the main issue does not consist in an e cient interpolation technique but in the selection of a triangulated network whose node distribution best re¯ ects the actual morphology of the ground surface under investigation ( Pries 1995). In recent years, most commercial GIS incorporate routines for producing DTMs from contour lines or spot heights either in raster or TIN format. In general, GIS producers claim their algorithms perform very well, but frequently they do not provide any signi® cant evidence of such quality. With some exceptions (cf. Carrara 1988, Hutchinson 1989, Wood and Fisher 1993, Bitelli et al . 1993, Carrara et al . 1996 ), the topic has received little attention from the research community. As a result, nowadays most DTMs are generated within a GIS, with relevant advantages and drawbacks. The ® rst refer to the fact that the resulting data set is already fully integrated with all other environmental data stored in the geographical database. The second concerns the inadequate information on how well these algorithms perform under the di erent morphological conditions of natural landscapes. In a previous investigation, two grid interpolators, implemented in low-cost, popular GIS ( IDRISI, ILWIS), one commercial TIN generator (Arc/Info) and one stand-alone interpolation algorithm (MDIP), developed by the writers (Carla’ et al . 1987 ) were compared (Carrara et al . 1996). In the present study, the analysis aims to confront two grid- and two TIN-based DTM generators using the quality criteria previously listed. To the ® rst group belong an interpolation algorithm incorporated into a widely-used, public domain GIS (GRASS) and the above mentioned MDIP interpolator. To the second group appertain the space tessellation algorithms of the two largest commercial GIS (Arc/Info and Intergraph-MGE). In the following sections of this paper, they will be named as follows: Procedure A : generator ( r.surf.contour ) of a grid-based DTM from contour lines as implemented in GRASS, version 4.1, developed by US Army CERL, U.S.A. Procedure B : generator ( MDIP ) of a grid-based DTM from contour lines, developed by R. Carla’ and A. Carrara, CNR, Italy.

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Procedure C : TIN generator (Arc T in ) from contour lines or spot heights as implemented in ARC/INFO, version 7.0, developed by ESRI, U.S.A.). Procedure D : TIN generator ( T errain Modeler) from contour lines or spot heights as implemented in MGE, version 5, developed by Intergraph, U.S.A.

As frequently occurs, technical information on the above commercial procedures for creating DTMs is rather scanty. Here it is worth outlining the main features of each technique. In procedure A, the digitized (vector) contour lines are ® rst rasterized with a resolution equal to the grid spacing of the DTM to be produced. Through a ¯ ood ® ll algorithm, the contour matrix is converted to a matrix of the distances of each grid-cell from the nearest contours and the height of each cell is then calculated by linear interpolation between each contour pair (GRASS 1996). Details on procedure B are provided elsewhere (Carla’ et al . 1987, Carrara 1988). Since the method attempts to exploit the speci® c morphological properties of contour lines, each point is interpolated or extrapolated by a method (steepest slope or moving average, etc., Leberl and Olson 1982) dependent on the morphology of the neighbouring area ( hill top, slope, valley bottom and depression). Input consists of contour lines in vector format, which are dynamically rasterized with a resolution that is independent of the spacing of the resulting grid DTM, but a function of both the input map scale and the distance between the neighbouring contour pair. In procedure C, spot heights or selected vertices of contour lines are used to build up, through Delaunay tessellation, the nodes of a triangular network; the module allows the insertion by the user of di erent breaklines to ensure a better representation of the ground surface. By means of similar criteria, procedure D calculates a triangulated network, but with a major di erence: for areas of high contour curvature (ridges or stream courses), the module can automatically generate inferred breaklines and incorporate such as ancillary heights in the ® nal network. Since all comparisons were performed in a grid-based environment, the TIN data from Arc/Info and MGE needed to be converted to a raster structure, through TINto-grid linear algorithms already available in each of these GIS modules. Since such a structure transformation may somewhat degrade the quality of these elevation models, contour lines were ® rst calculated from both the Arc/Info TIN data and the derived lattice , then plotted. By overlaying the two contour sets, only very small discrepancies resulted. Hence, the TIN-to-grid conversion did not signi® cantly altered the information content of the original structure. 4. Test areas

In order to test the quality of the elevation models produced by the above procedures three morphologically complex areas were selected. The ® rst sample area, 7´02 km2 in size, is located in Calabria (southern Italy, ® gure 1 ). Topography is rugged with steep slopes, a ¯ at ridge top and the wide ¯ ood plain of the Ortiano river. Source data, provided by the Italian Military Geographic Institute, were obtained by automatically scanning, vectorizing and interactively labelling contour lines derived from 1 : 25 000 scale topographic sheets with 25 m contour interval. For this area, four DTMs, with a grid spacing of 10 m by 10 m and georeferenced to the Italian Gauss-Boaga reference system, were generated using procedures A, B, C and D. In all cases, heights were expressed in meters with one



457

decimal digit. The ® rst and fourth elevation models were produced by ET&P Consultants ( Bologna) and PAC Srl ( Bologna), respectively; the second and third were calculated by the writers. Since in procedure A the size of the cell used in the rasterization of the input contours is set by default equal to the spacing of the DTM to be calculated, this technique cannot be successfully applied in areas, as those selected for this study, characterized by rugged topography and slopes greater than 45ß , which lead to zones of very high contour density. Under such circumstances, two or more contour lines can go through the same grid-cell causing unpredictable errors in cell coding and interpolation ( Bitelli et al . 1993, GRASS 1996 ). To overcome this severe drawback, it was necessary ® rst to calculate the DTM with a grid spacing of 5 m by 5 m and then resample the heights to 10 m by 10 m. The last operation can take place by either pixel thinning or aggregation . In the ® rst case, every n th pixel is kept and the rest are eliminated. In the second case, the new pixels represent averages of the n pixels speci® ed by the factor of resampling. To avoid undesired smoothing e ects, resampling was always accomplished by pixel/ grid-cell thinning . Procedure B did not required this extra step since contour rasterization parameters are not a function of the ® nal DTM density. The Arc/Info TIN procedure was run using a maximum arc-vertex density of 5 m and a minimum distance between triangle nodes of 1 m; this led to the generation of very dense networks. The MGE TIN was generated using a low tolerance (i.e., 2´5 m) and inferred points. As already mentioned, each data set was converted to a grid structure having a 10 m spacing, through TIN-to-grid linear conversion routines. The second and third sample areas, located in Trentino ( Northern Italy, ® gure 1 ), are 16 km2 and 36 km2 in size, respectively. The second area, located near the town of Andalo, re¯ ects a gently rolling upland of karst origin bounded by fairly steep slopes. The relief of the third area is characterized by the ¯ at, very wide, valley bottom of the Adige river, bounded by very steep ¯ anks on both sides. Such morphology resulted from two distinct events: the WuÈrm glaciation and the subsequent ¯ uvial processes. The ® rst event determined the overall shape of the area outlined by contours with long wavelength; the second caused a complex superimposed micro-relief expressed by recurving contours with high amplitude as compared to their wavelength. As part of a joint research project (Carrara 1994, Carrara et al . 1996), source data were provided by Informatica Trentina Spa. ( Trento) which scanned, vectorized and interactively labelled the contour lines, with a 10 m interval, drawn on 1 : 10 000 scale topographic sheets. For each area, four DTMs, with a 10 m by 10 m sampling space and georeferenced to the Italian Gauss-Boaga reference system, were generated using the four procedures. Elevation models A, C and D were provided by ET&P Consultants, Insiel Spa ( Udine) and PAC Srl, respectively. Model B was calculated by the writers. For sample area 2, the DTM A was ® rst calculated with a grid spacing of 5 m by 5 m and then resampled to 10 m by 10 m. For sample area 3, which exhibits an extremely high contour density ( ® gure 1 ), the GRASS DTM would have required a initial grid size smaller than half the ® nal resolution (table 1 ). Owing to the huge amount of CPU time (estimated time greater than 100 h on a Sun Sparc 20) required by the ¯ ood-® ll algorithm, the task was considered impractical. Hence, the DTM had to be directly generated with a contour rasterization grid-size equal to the ® nal resolution (i.e., 10 m by 10 m).

458 Table 1.

A. Carrara et al. Overall CPU time required for generating the DTMs of sample area 3 by procedures A, B, C and D, respectively.

Platform


CPU time

Procedure A Sparc 20

Procedure B Pentium 120

Procedure C IBM RS/6000

Procedure D IntergraphCliper 2730

23 h

12 h

2h

1´5 h

It is worth mentioning that, to minimize boundar y e ects on DTM quality, contour lines from a belt, approximately 200± 300 m in width, of the adjacent topographic sheets were incorporated in the data set of each sample area. These supplementary data enabled the algorithms to perform better in zones of low relief information, such as the northern portion of the valley bottom of sample area 1 and the southern section of the wide valley ¯ oor of sample area 3 (® gure 1). Since di erent computer platforms were used to process the data and even the processing operations were very di erent, a quantitative comparison of the performance of the four techniques is a rather di cult task. In addition, the e ciency of each procedure greatly varies depending on the morphology of the sample area to be processed. Results from one area, therefore, cannot be readily extrapolated to other regions having di erent relief characteristics. In spite of these obstacles, a tentative comparison was attempted for the largest and most complex sample zone, the Adige river test area 3 (® gure 1). Input data consisted of vector contour lines covering both the area itself ( 6000 m by 6000 m in size), and its neighbouring belt (about 500 m in width), for a total surface close to 42 km2 . In procedure A, input contour rasterization and subsequent contour interpolation took place over the total surface using a grid-size equal to the ® nal DTM resolution (namely, about 650 by 650 elevation points). The resulting grid was then resized to the test area limits. In procedure B, contour interpolation was automatically con® ned within the test area limits, leading directly to a grid of 601 by 601 height points. Procedures C and D created a triangulated network over the sample area and its neighbourhood; each TIN was then converted to a lattice, 601 by 601 spot heights in size. Regardless of the speed di erence between the four platforms used to generate the DTMs, it is clear that the performance of the two TIN algorithms is far superior (from 10 to 20 times) to that of grid-based generators. It is worth mentioning that such a huge di erence in algorithm e ciency greatly reduces as input contour density increases. In the generation of the DTMs of sample areas 1 and 2, the di erence in CPU time between TIN and grid generators reduced to a factor less than 2. 5. Analysis of DTM quality

5.1. Sample area 1 For the ® rst sample area ( 7´02 km2 in size), shaded-relief maps were produced from the four DTMs ( ® gure 2). In each image the distribution of shaded and sunlighted areas appears in agreement with the relief pattern de® ned by the original contour lines. A more careful observation, however, reveals minor artefacts. In all images the ¯ at river ¯ ood plain is characterized by an unrealistic relief pattern consisting of either triangular-shaped surfaces at slightly di erent heights ( DTMs C



459

Figure 2. Sample area 1 ( 2710 m by 2590 m in size). Shaded-relief of DTMs obtained by procedures A (a ), B ( b), C (c ) and D (d ). Area viewed from NW at an angle of 60ß . Original contour lines shown in black.

and D) or stair-step discontinuities along the search directions of the algorithms ( DTM B). For a better evaluation of data quality, elevation maps were produced by grouping height values into 25 m classes with limits corresponding to the contour interval of the input map. From visual observation of the resulting images, where the original contour lines were also added (® gure 3 ), it is clearly apparent that DTMs A, B and D faithfully ful® lled the requirements of the ® rst two criteria outlined in § 2. Conversely, procedure C produced an elevation pattern of the valley bottom and the hill summit which does not match the spatial distribution of input contours. For a closer inspection of the four DTMs, contours were calculated with a 5 m interval and were plotted along with the original input contours for a small subzone corresponding to an isolated hill top ( ® gure 4). If all the four procedures performed almost equally well on the sloping sides of the hill, only generators B and D were capable of extrapolatin g elevations within the area bounded by the highest contour ( 925 m). In addition, as shown by the contours drawn as dashed lines, the elevations inferred by these algorithms are surprisingly close to the actual hill top


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Figure 3. Sample area 1. DTMs obtained by procedures A (a ), B ( b), C (c ) and D (d ). Heights grouped into 25 m classes with limits corresponding to contour (white lines) interval of input map.

height ( 936 m) reported on the topographic sheet. Procedure A created an unrealistic ¯ at hill top and procedure C produced signi® cant artefacts. This limitation, common to both grid interpolators and TIN generators, may constitute a relevant obstacle for the application of such terrain models to many theoretical and development issues. In order to quantitatively assess how well each DTM ful® ls criteria (a) and (b), the input map area, bounded by each contour pair, was calculated and compared with the corresponding area (expressed as the number of grid-cells) in each DTM (table 2). Since the di erences between such areas may vary locally in a positive or negative way, the values listed in table 2 constitute overall results that may well underestimate the actual discrepancies. Nevertheless, these values indicate that procedure D ranks ® rst in terms of areal agreement ( RMS error less than 10 gridcells); procedures B and A yielded slightly less accurate outcomes, while procedure C was not very successful in meeting these quality criteria. To facilitate the display of data and enhance the detection of potential errors, heights were grouped into 1 m intervals, and reclassi® ed as relative elevations from

461



Figure 4. Sub-zone (610 m by 810 m in size) of sample area 1. Contour lines, with 5 m interval, calculated from DTMs obtained by procedures A (a ), B ( b), C (c ) and D (d ). Contours obtained from extrapolated heights ( b and d ) shown as dashed lines. Input map contours, with 25 m interval, shown as thick black lines.

the nearest lower contour line. In other words, elevation values included between each contour pair (say, 600± 625) were recalculated as classes, with values 0, 1, 2, . . ., 24, corresponding to the actual height classes (say, 600± 601, 601± 602, . . ., 624± 625; ® gure 5 ). This simple transformation, already used elsewhere ( Reichenbach et al .

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Table 2. Sample area 1. Di erence (in 10 m by 10 m grid cells) between areas bounded by each input contour pair and obtained from each DTM of procedures A, B, C and D.


Contour interval (m) 275± 300± 325± 350± 375± 400± 425± 450± 475± 500± 525± 550± 575± 600± 625± 650± 675± 700± 725± 750± 775± 800± 825± 850± 875± 900± 925±

300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 775 800 825 850 875 900 925 950

RMS error

Area between contour pair (as grid-cells)

Di erence DTM A (grid-cells)

2961 2423 3621 3861 2946 2092 2496 2563 2646 2787 2828 2990 3050 2317 2238 2544 2525 2492 2743 2529 2475 2225 2341 2458 2092 2188 1759

57 38 23 17 4 12 2 3 11 3 2 11 7 12 11 17 2 4 4 20 5 7 9 10 22 0 62 Õ

Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ

Õ

Õ

Õ

Õ

20´7

Di erence DTM B (grid-cells) Õ Õ

Õ Õ

Õ Õ Õ Õ Õ

Õ

Õ

Õ

Õ

39 21 22 35 39 2 2 1 20 17 4 5 6 16 4 16 0 11 10 20 8 9 16 1 14 16 49 19´6

Di erence DTM C (grid-cells) 1723 681 Õ 12 30 Õ 952 Õ 60 18 62 66 Õ 150 26 32 Õ 16 Õ 28 38 172 Õ 78 Õ 93 Õ 52 Õ 1 9 Õ 27 43 Õ 5 Õ 34 Õ 47 18

Di erence DTM D (grid-cells)

Õ

405´2

Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ

Õ

Õ Õ

11 4 9 10 17 3 3 6 0 12 10 0 3 7 3 15 15 13 7 3 12 7 13 6 17 0 3 9´4

1993 ), clearly highlights possible systematic errors in the height interpolation procedure, which were already reported by various investigators (cf. Thelin and Pike 1991 ). Clearly, when no bias a ects the data set, the resulting histogram should be nearly rectangular in shape; if modes occur in the frequency distribution, they indicate lack of linearity in the interpolation algorithm. In particular, high modal values corresponding to contour interval would indicate an unrealistic, terraced , landscape characterized by ¯ at areas which systematically occur where contour lines lie, and by steep slopes which are located in the space between contours. This is the case for the DTMs obtained by procedures C. DTM A shows a more complex pattern characterized by two modal values; while DTM D and, to a lesser extent, B are virtually free from systematic errors. As discussed below, these outcomes re¯ ect the logic behind the four algorithms under examination. 5.2. Sample area 2 Sample area 2 is characterized by a wide karst depression and gently rolling uplands. It is worth noting that a short closed contour, located in the northeastern portion of the area (near the spot height 1003; ® gure 6), was labelled as 1020 m

463



Figure 5. Sample area 1. DTMs generated with procedures A, B, C and D. Frequency distribution of relative heights from the nearest lower contour line for each contour pair. Input map contour interval equal to 25 m.


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Figure 6. Sub-zone ( 1440 m by 1700 m in size) of sample area 2. DTMs obtained by procedures A (a ), B ( b), C (c ) and D (d ). Heights grouped into 10 m classes with limits corresponding to contour (white lines) interval of input map.

instead of 1010 m. However, the error was not corrected to investigate its e ect on the di erent DTM algorithms. For a sub-zone (about 2´5 km2 in size) elevations of each DTM were grouped into 10 m interval classes, with limits corresponding to the contour interval of the input map, and displayed along with the original contour lines (® gure 6). In addition, for the upper-left portion of ® gure 6, contour lines calculated from the four DTMs were plotted along the original contour lines (® gure 7). By inspecting the resulting images and drawings, it is apparent that DTM A is a ected by various errors; ® rst the karst depression was not detected by the algorithm

465



Figure 7. Sub-zone (700 m by 1030 m in size) of sample area 2. Contour lines calculated from DTMs obtained by procedures A (a ), B ( b), C (c ) and D (d ). Contours obtained from extrapolated heights ( b and d ) shown as dashed lines. Input map contours, with 10 m interval, shown as thick black lines.


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which set all the elevations to a constant value ( 1000 m), namely the height of the contour outlining the depression, and the incorrectly labelled contour has caused widespread errors in its neighbourhood. Procedures D and B performed better: no signi® cant artefacts are present. In DTM B the wrong contour did not propagate elevation errors in the adjacent zones. Both detected the karst sink by extrapolating height information from the surrounding zones; the ® rst algorithm guessed better ( 996 m) the actual depth ( 993 m) of the depression than the second ( 998 m) but in a perhaps less realistic fashion. Lastly, procedure C yielded the worst result in terms of artefacts and smoothing e ects. Owing to the rather complex morphological setting of the investigated area, only procedures B and D ful® lled the ® ve requirements de® ned in § 2. A statistical analysis was also carried out on the elevation data of this sample area, using the previously described technique (® gure 8). As expected, the results obtained were very similar to those derived from sample area 1. 5.3. Sample area 3 The last test was extended to a large portion of the valley bottom of the Adige river. Here, the morphology of the river ¯ ood plain is outlined only by few contour lines several kilometres apart, while the very steep (over 45ß ) valley ¯ anks are characterized by a very high contour density. The occurrence of adjacent areas at strongly contrasting relief information constitutes a major obstacle to any TIN or grid based generator. To capture the intricate morphology of the steeply sloping areas, a dense TIN or grid are needed which are likely to be, however, unable to cope with the ¯ at morphology of the valley bottom. Conversely, large triangles or grid cells, enabling to reproduce correctly the valley area, may well overgeneralize the local relief of sloping zones. To verify how well the four algorithms perform under such complex morphological conditions, the heights of the four DTMs were grouped into 2 m interval classes up to an elevation of 230 m and lumped into a single class above this value, then displayed together with the original contour lines (® gure 9). The resulting images indicate that none of the procedures could handle such a morphological pattern. Widespread artefacts, among which the relief inversion of the valley bottom (® gure 9 (a )), were created, particularly along the search directions, by procedure A, and, to a lesser extent, B, while the whole valley was placed at the same elevation by method C which also generated major artefacts in the southern section of the image. Better results were obtained with method D which however produced a triangular relief pattern largely inherited from its original structure. Consequently, no DTM algorithm could satisfy all the ® ve criteria and, in particular, the third, fourth and ® fth. 6. Discussion

The results of the comparison of the DTMs of the three test areas, generated by the four techniques selected, can be summarized as follows. The ® rst and second criteria of quality were fully honoured by procedures D and B in all test areas (® gures 2± 9), and largely satis® ed by procedure A. The third criterion was largely ful® lled by procedures D, B and A, with the exception of the valley bottom of sample area 3 (® gure 9). Likewise, all techniques but B and D were unable to extrapolate heights on the hill tops (® gure 4) or depressions (® gure 7 ).

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Figure 8. Sub-zone of sample area 2. Frequency distribution of relative heights of DTMs generated with procedures A, B, C and D. Histograms obtained as in ® gure 5. Input map contour interval equal to 10 m.


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Figure 9. Subzone of sample area 3 ( 5500 m by 6000 m in size). DTMs obtained by procedures A (a ), B ( b), C (c ) and D (d ). Heights grouped into 2 m classes below 230 m, and lumped into a single class above this elevation. Input map contours lines in white.

The fourth and ® fth criteria were honoured by procedures D and B, once again with the exception of the ¯ at river course of area 3 (® gure 9). The DTM generators selected for this study do not cover the very wide spectrum of techniques designed or implemented for producing terrain models. They can be considered, however, a fairly representative sample of the current algorithms implemented in widely-used GIS products available on the market. Therefore, this investigation, along with the outcomes of a previous study on the topic (Carrara et al . 1996 ) allow some general comments and conclusions on advantages and limitations of such spatial operators. 6.1. Grid-based interpolator s Most grid interpolators are clearly a ected by a major constraint: the size of the grid-cell used for converting input vectorized contours into a raster structure. When



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the selected grid cell is very small (say, equal to or less than 5 m by 5 m), unmanageable CPU and mass storage problems arise if relatively large regions are to be processed (say greater than 1000 km2 ); if the cell is kept large in comparison to the input map contour spacing or density, the resulting DTM is frequently a ected by artefacts due to cell collisions and mislabelling ( Bitelli et al . 1993, Detti and Pasqui 1995 ). This is con® rmed by the overall better results obtained by procedure A in sample area 1 as compared to those derived from sample area 3. In the ® rst, where input map contour interval is 25 m, contour rasterizing took place with a grid cell of 5 m by 5 m. In the second, in spite of a much narrower input map contour interval ( 10 m), rasterization had to be performed with a coarse grid-cell ( 10 m by 10 m) that led to an overall failure of the algorithm. Grid-cell size in contour rasterization is also the cause of the high modal values, corresponding systematically to each contour label, in the DTM height frequency distributions obtained from procedure A (® gures 5 and 8). Such an unrealistic pattern has been reported by many investigators ( Thelin and Pike 1991, Reichenbach et al . 1993 ), but attributed to unclear and undocumented failures of the computer algorithms. In order to readily demonstrate the linear dependence of the shape of the DTM frequency distribution on cell-size, ® rst an e cient grid-based contour interpolator ( ILWIS, version 1.41) was selected. Previous work proved that the algorithm ful® ls criteria (a ), (b ) and (c) when contour rasterization is accomplished by means of a grid-cell much smaller than contour interval (Carrara et al . 1996). Then, three DTMs were generated on a steeply sloping sub-zone of sample area 1. They were obtained using a decreasing contour rasterization cell-size, namely: 10 by 10, 5 by 5 and 2 by 2 m (i.e., approximately half, one ® fth and one tenth the input map contour interval ), and the last two resampled ( by pixel thinning) to a common 10 by 10 m grid spacing. The results, displayed in ® gure 10, clearly con® rm what is stated above. The anomalous modal value corresponding to the contour label (relative height

Figure 10. Comparison of DTMs generated through the same grid-based interpolating algorithm, but using di erent grid-sizes in contour rasterization. The last two were resampled to a common 10 m by 10 m grid-spacing. Histograms obtained as in ® gure 5.


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equal 0) fades out completely as the rasterization cell-size reduces to nearly one tenth the input map contour interval. Since many DTM interpolators (GRASS, IDRISI, ILWIS, etc.) rasterize contour lines at the same resolution as the ® nal DTM, which is commonly in the range of 20 by 20± 50 by 50 m for projects concerning large regions, the resulting contour matrix is too coarse, even for gently sloping terrain. To minimize this drawback, for sample areas 1 and 2 DTMs A were generated at 5 m by 5 m and resampled to 10 m by 10 m. Owing to the increase in CPU time and the huge temporary disk store requirements, this approach is impractical when applied to large regions or even to small zones with areas at low relief (® gure 9). To overcome the problem, the input region can be split into subdomains (tiling) and the resulting DTMs eventually merged. In order to minimize the boundary e ects, the task needs a careful joining of the adjacent tiles which should partially overlap. An alternative solution is provided by procedure B, where contour rasterization takes place piecewise; each tile is sequentially processed, using a variable pixel size (cf. Carla’ et al . 1987, Carrara 1988). Other well-known, and somewhat trivial, limitations of many grid interpolators refer to their lack of ability in extrapolating heights on the top of hills (® gure 4). The task would be algorithmically fairly simple, but in most DTM generators would require a relevant increase of the total CPU time, since the input data set should be processed twice. As clearly witnessed by the artefact patterns shown in ® gure 9, in the grid models directions parallel to the matrix rows ( E± W ), columns ( N± S) and diagonals ( NW± SE and NE± SW) are privileged as compared to the other directions. Hence, DTM values and their derived products (slope or aspect maps, etc.) will be somewhat dependent on how the DTM matrix is aligned to the geographical reference system. 6.2. T IN generators During the past decade, TIN generators have became very popular, mainly because triangulated network structures can be fully integrated within a vector GIS environment. TIN supporters have always maintained that such a structure is more e cient and ¯ exible than that of raster models ( Burrough 1986, Arono 1989, Weibel and Heller 1991). When source data consist of irregularly distributed spot heights, this may be largely true. When input data are made up by contours, most of the advantages of TINs fade out. First, most TIN generators, such as the Procedure C, cannot correctly handle a valley bottom morphology (® gure 3 and 9), minor variations in the relief, hill tops and, in general, any morphological con® guration leading to so called ¯ at triangles. The latter are the main cause of the unrealistic modal values observed in the frequency distributions of all DTMs obtained with procedure C ( ® gures 5 and 8 ). To overcome this inherent shortcoming, procedure D generates inferred breaklines and recreates a network whose nodes will also lie along such breaklines ( Tonelli 1995 ). However, this approach also exhibits some pitfalls. First, if the ¯ at area increases in size above a certain limit which is linked to the resolution of the triangulation, it may be expected that inferred breaklines will assume unrealistic or even false patterns, leading to artefacts in the ® nal elevation model, as witnessed by the outcomes of test area 3 (® gure 9). Second, TIN supporters claim that such a structure is superior to any grid-based elevation model in terms of data quality and compression (cf. Burrough 1986). However, a very dense triangulated network is generally required to capture the


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micro-relief as expressed by contour crenulations; this leads to a ® nal number of triangles which is close to the number of pixels of an equally detailed grid DTM. This is clearly witnessed by the tests carried out on sample area 1 (2710 m by 2590 m in size) where 70 189 grid heights, calculated by procedure B, yielded a relief information similar to that obtained by procedure D which generated a network of approximately 60 000 triangles, the latter requiring much more topological information than the ® rst. Consequently, TIN generators cannot readily be applied to large regions, without a preliminary subdivision of the region into tiles of appropriate size and the subsequent careful merging of the sub-TINs, a task not accomplished by the majority of the systems available on the market. 6.3. D T M f rom contour lines Besides the respective advantages and limitations of the grid interpolators and TIN generators, a major issue deserves further discussion and investigation; namely, the use of contour lines from existing topographic maps to generate terrain models. As already mentioned, this is still the most common approach followed by many institutions in order to produce large elevation databases within major GIS projects. The reasons for this policy are economic and functional. In many developed countries, detailed, recently produced, topographic maps are available. By exploiting automatic scanning and vectorization technology, contours can be cost-e ectively digitized and used as source data for DTMs. The extent to which these contours re¯ ect the real ground morphology will greatly vary depending on many factors that cannot be readily assessed. By generating DTMs from such contours, the original data are further degraded regardless of the e ciency of the DTM generator selected. Therefore, new direct approaches to the automated acquisition, storage and analysis of ground relief need to be developed. The direct derivation of the DTM from traditional photogrammetric analysis of stereo aerial photographs at the time of map production can certainly provide the best results, but the costs involved would be una ordable when dealing with high-resolution terrain models over large regions. An alternative, direct approach for producing high-® delity terrain models would be the digital processing of stereo satellite/aerial data using softcopy image correlation systems ( Krzystek and Ackermann 1995, Kolbl 1996). Since the accuracy of DTMs obtained by this new technology does not appear fully documented as yet, their potential was tested in sample area 1. A DTM was extracted from scanned aerial photographs using a softcopy photogrammetric system ( Helava by Leica). As previously outlined, by comparing this model with a DTM carefully generated by traditional analytical plotting, advantages and pitfalls of the approach were highlighted. From this experiment, it appears that the digitallyderived DTM faithfully re¯ ects the actual relief of most of the ground surface; however, the whole process is still costly and, most importantly, it may lead to large local errors where dwellings or other arti® cial structures occur, slopes are steep, ground is mantled by thick forest, and aerial photographs are masked by shadows ( Bitelli et al . 1996 ). Hence, the approach needs further development and re® nement. 7. Conclusions

Five simple criteria for evaluating the quality of DTMs derived from digitized contour lines were de® ned. Their application to terrain models produced by four di erent techniques in three sample areas, has highlighted the major drawbacks which a ect the DTM grid interpolators and TIN generators selected for this investigation.


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The best grid interpolator (MDIP) and the best TIN generator ( IntergraphMGE) provided outcomes almost equally good in terms of accuracy. The accuracy of the ® rst lies in the adaptive nature of the technique: depending on the morphology of the neighbouring area, it uses a di erent interpolator algorithm. Other advantages of the approach refer to its ability to process input data sets of any size, and the variable size of the grid-cell used in rasterizing dynamically the original contour lines. However, this procedure has a very severe pitfall, common to most grid-based interpolators: it requires an impractical amount of CPU time for processing areas at low relief or low contour density. The good results provided by Intergraph TIN are due to the generation of inferred breaklines in areas of low relief with recurving contours; its limitations include the need for large central memory and disk space volume for processing wide regions, and the somewhat unrealistic triangulated look of the relief produced. Lastly, no procedure can fully handle extreme morphological conditions such as those of the Adige valley bottom in sample area 3. Under such circumstances, the application of local ® ltering techniques may appear a simple, attractive way to reduce artefacts ( Weibel and Heller 1991 ). In general, however, any type of DTM smoothing is not suitable, since it will invariably lead to a undesirable loss of micro-relief information. In the future, high-resolution DTMs will likely be extracted from sophisticated softcopy image processing systems of aerial photographs or even of hyper-spectral, high resolution imagery of space-borne sensors. However, in the immediate coming years, contour lines will continue to be a primary source for the generation of DTMs over large regions. Hence, the relevance for improving the quality and performance of the existing grid interpolators and TIN generators. Acknowledgm ents

Franca Giovannini, Informatica Trentina Spa, calculated the DTMs of sample areas 2 and 3 using the ArcTin generator. Elena Toth, ET&P, and Gabriele Tonelli, PAC Srl, calculated the DTMs of the three sample areas using the GRASS interpolator and Intergraph MGE generator. The Province of Trento made available the contour lines of sample areas 2 and 3 in digital format. Insiel Spa ® nancially supported part of this investigation. The authors are grateful to Andrew Hansen, Geotechnical Engineering O ce, Hong Kong, for a critical review of the manuscript. References A ckermann, F . , 1978, Experimental investigation into the accuracy of contouring from DTM. Photogrammetric Engineering and Remote Sensing , 44, 1537± 1548. A ronoff, S ., 1989, Geographic Information Systems: A Management Perspective (Ottawa: WDL

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