Geomorphology 129 (2011) 183–189

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Geomorphology

j ourna l homepage: www.e lsev ie r.com/ locate /geomorph

Review

Object representations at multiple scales from digital elevation models

Lucian Drăgut, a,b,⁎, Clemens Eisank a

a Department of Geography and Geology, University of Salzburg, Hellbrunnerstraße 34, Salzburg 5020, Austriab Department of Geography, West University of Timişoara, V. Pârvan Blv. 4, Timişoara 300223, Romania

⁎ Corresponding author at: Department of GeographSalzburg, Hellbrunnerstraße 34, Salzburg 5020, Austrifax: +43 662 8044 5260.

E-mail address: lucian.dragut@sbg.ac.at (L. Drăgut,).

0169-555X/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.geomorph.2011.03.003

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 August 2010Received in revised form 3 March 2011Accepted 6 March 2011Available online 10 March 2011

Keywords:GeomorphometryLandformLandform elementsLocal varianceSegmentationPattern analysis

In the last decade landform classification and mapping has developed as one of the most active areas ofgeomorphometry. However, translation from continuous models of elevation and its derivatives (slope,aspect, and curvatures) to landform divisions (landforms and landform elements) is filtered by two importantconcepts: scale and object ontology. Although acknowledged as being important, these two issues havereceived surprisingly little attention.This contribution provides an overview and prospects of object representation from DEMs as a function ofscale. Relationships between object delineation and classification or regionalization are explored, in the context ofdifferences between general and specific geomorphometry. A reviewof scales issues in geomorphometry—rangingfrom scale effects to scale optimization techniques—is followed by an analysis of pros and cons of using cells andobjects in DEM analysis. Prospects for coupling multi-scale analysis and object delineation are then discussed.Within this context, we propose discrete geomorphometry as a possible approach between general and specificgeomorphometry. Discrete geomorphometrywould apply to and describe land-surface divisions defined solely bythe criteria of homogeneity in respect to a given land-surface parameter or a combination of several parameters.Homogeneity, in its turn, should always be relative to scale.

y and Geology, University ofa. Tel.: +43 662 8044 5293;

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© 2011 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1832. Object ontology—from cells to landforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1843. Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1854. Discrete geomorphometry? Coupling multi-scale pattern analysis and object delineation . . . . . . . . . . . . . . . . . . . . . . . . . 1865. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

1. Introduction

DEMs (Digital Elevation Models) are used for the extraction ofland-surface parameters and objects through geomorphometricanalysis (Pike, 2000; Pike et al., 2009). As ‘general geomorphometry’applies to continuous land surface, ‘specific geomorphometry’ appliesto discrete landforms (Evans, 1972). Most land-surface parameters andobjects vary with spatial scale, which in the digital realm is widelyunderstoodas a functionof cell size or grid resolution (WilsonandGallant,2000). However, grid resolution is not a particularly appropriate

representation of scale (Gallant and Hutchinson, 1996). The dependenceof land-surfaceparameters ongrid resolutionhasbeendescribedbyEvans(1972) as ‘a basic problem in geomorphometry’ (Shary et al., 2002). Sincemost geomorphometric algorithms work through a fixed neighborhoodoperation (Pike et al., 2009)—usually within a 3×3 kernel—the scale ofanalysis is tied to the resolution of the input DEM and changes as theresolution changes (Zhu et al., 2008). In the absence of scale optimizationtechniques (Li, 2008), the geomorphometric analysis is conducted atrather arbitrary scales, which rely on the user's experience. In fact, thescale of analysis often depends on data availability asmany users performwhat Schmidt and Andrew (2005) called the ‘let's take a DEM…

approach’, without much concern for scale effects in analysis. Obviouslythere is no sound scientific justification for a direct linkage betweennatural phenomenaanddata acquisition techniques (Strobl, 2008). Lately,a large amount of literature has developed particularly relevant to

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applications of geomorphometric analysis (terrain-based environmentalmodeling), underpinning the impact of scale mismatches between thetarget variable and the explanatory ones leading to statistical bias. Withthe advent of increasingly high resolution DEMs, scale is becoming animportant issue in geomorphometry (MacMillan et al., 2003).

Particularly when mapping landforms from gridded land-surfacemodels such as DEMs, scale-related shortcomings are partly gener-ated by the implicit assimilation of data model elements (cells orpixels) to geographic objects (Fisher, 1997). Thus, in a somehowcounter-intuitive manner, most landform classification systems workthrough the classification of cells, which are clustered to define theextents of objects—instead of delineating the objects first and thenclassifying them. The approach of classifying cells directly is limited inseveral aspects, including the scattered aspect of classification in theso-called ‘salt-and-pepper effect’, tying the scale of analysis to theraster resolution, difficulties in including topological relationships inclassification and also in developing hierarchies of landforms.Although delineation techniques have been proposed, quantitativeevaluations of their performance have only recently been done (vanNiekerk, 2010). Still, fundamental questions pertinent to the nature ofobjects and their delineation relative to scale have only been touchedupon. Minar and Evans (2008) provided a useful review on objectontology, showing the limitations of cell-classification approach inmapping landforms and introducing segmentation of elementaryforms as an alternative. Deng (2007) and Hengl and Reuter (2009)reviewed contributions pertinent to scale and object representationfrom DEMs, but rather in wider contexts. Goodchild (2011) presentedan overview of scale in GIS.

This paper provides an overview and prospects for object represen-tation fromDEMs as a function of scale. In the next section, relationshipsbetween object delineation and classification or regionalization areexplored, in the context of differences between general and specificgeomorphometry. Rather than being an exhaustive overview, thissection will complement Minar and Evans (2008) with a focus ongenerating objects with the aid of a multi-resolution segmentation(MRS) algorithm. A review of scales issues in geomorphometry—ranging from scale effects to scale optimization techniques—is followedbyananalysis of pros and consof using cells andobjects inDEManalysis,in Section 3. This section focuses onmethods to establish non-arbitraryscales in the landsurface. Prospects for couplingmulti-scale analysis andobject delineation are then discussed, in Section 4.

2. Object ontology—from cells to landforms

Specific geomorphometry applies to discrete spatial features orgeomorphic objects (Evans, 1972). Landforms and landform elements(see MacMillan and Shary, 2009 for a detailed review) are particularcases of geomorphic objects. Extracting landform divisions (landformelements, landforms, etc.) from DEMs usually involves applying anobject model on a raster data structure, which is the most popularformat for spatial modeling (Pike et al., 2009). This is because rasterelements themselves, i.e. cells or pixels, do not have any meaning inreality regardless of their size (Fisher, 1997). Cells as artificial, discreteunits exist merely for the purpose of representation (Goodchild et al.,2007). Clearly, footprints of cells have nothing to do with the size andshape of real-world entities such as landforms. Therefore, a model totranslate from the continuous land surface to discrete entities isrequired. This is challenging as the land surface is smoother than otherterrain variables, such as vegetation (Hengl and Evans, 2009).Consequently land-surface objects are less obvious on DEMs thanland cover patches on satellite images, for instance.

In the absence of comprehensive conceptual data models for landsurfaces (Brändli, 1996), extraction of landform divisions has largelybeen based on classification schemes. A landform is rather representedas a collection of cells that exhibit similar morphometric characteristics(Schmidt and Dikau, 1999). Classification methods have been widely

applied to directly assign cells to landform classes. Although thisstrategy is straightforward two major shortcomings have beenidentified: Firstly, cells are often treated as spatially independent fromeach other, and thus adjacent cells are frequently assigned to differentclasses resulting in a highly scattered spatial representation of land-forms (Burrough et al., 2001), the so called ‘salt-and-pepper effect’.Secondly, since landforms are classified on a cell by cell basis afterapplying statistical rules, they are solely defined thematically, but notspatially (e.g. by location, context or topology) and hence, they do notrepresent spatially configured objects (Deng, 2007; Minar and Evans,2008).Often, in a kindof Procrusteanbed approach, cells are allocated toclasses following pre-defined categories of, or thresholds in, land-surface parameters (e.g. the threshold value of slope to define a flatsurface). Landform boundaries are then given by the edges of theaggregated cells (as resulting after some filtering, needed to reduce the‘salt-and-pepper’ effect). But these boundaries may not coincide withmorphologic discontinuities in a given landscape; they are merelyconceptual or fiat boundaries (Smith, 1995).

This problem of arbitrary incidence has been exemplified forcurvatures by Minar and Evans (2008). The authors observed that‘isoline boundaries may create artificial areas without sufficient respectto the natural structure of landformswith various types of homogeneity’(p. 241).We have noticed similar behavior for elevation and slope. Suchcrude representation of landscapes is part of ‘the conceptual andcomputational gap between local geometry andmeaningful landforms’,which broadens paradoxically with improving quality and resolution ofDEMs (Mark, 2009).

Moving on from collections of ‘geomorphometric points’ to‘geomorphometric objects’ (Schmidt and Dikau, 1999) requiresdelineating the objects first, then classifying them. Similar to theconcept of ‘object–field’ (Cova and Goodchild, 2002), DEMs can bepartitioned into discrete, spatially intact land-surface objects, follow-ing data-driven approaches rather than pre-defined classificationtemplates. A strategy of clustering similar cells in property space bymeans of image analysis methods to delimit form types has alreadybeen envisioned by Pike (1995) and applied by Irvin et al. (1997).While this method produces less scattered objects, the problem ofmatching land-surface discontinuities still remains, since clusters arecreated using global thresholds instead of local contrasts (vanNiekerk, 2010). The same applies to classification methods usingdynamic but global thresholds (Iwahashi and Pike, 2007).

Identification of spatial discontinuities in land-surface parametersseems to be more appropriate for object delineation. This idea waspresented by Minar and Evans (2008) as an axiom: “At a given scale,the land surface may … exhibit discontinuities; these may berecognized as natural boundaries of geomorphic objects”. A manualtechnique of mapping based on morphological discontinuities wasproposed by Savigear (1965). Dymond et al. (1995) described analgorithm for automated mapping of land components throughapproximation of slope breaks. Recently, image segmentation tech-niques have increasingly been used to generate objects based on theconcept of heterogeneity. The most known algorithm is MRS (Baatzand Schäpe, 2000) as implemented in the eCognition® software. Thisis a region-merging technique to create objects from pixels throughan optimization process that minimizes the internal weightedheterogeneity of each object at a given scale. These objects are thenmerged or split to create objects at consecutive scales, either higher,created in a bottom-up approach, or lower, created in a top-down one.Therefore, each decision of merging or splitting is based on theattributes of homogeneous structures of a recent scale (Baatz andSchäpe, 2000) and on the user-defined heterogeneity threshold,called scale parameter. Drăguţ and Blaschke (2006) and van Asselenand Seijmonsbergen (2006) introduced this algorithm to the analysisof DEMs. This approach has lately been increasingly used indelineation of landforms or land entities (Drăguţ and Blaschke,2008; Möller et al., 2008; Schneevoigt et al., 2008; Anders et al., 2009;

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Blanco et al., 2009; Kringer et al., 2009; Martha et al., 2010). Whilesegmentation relies on local contrasts in drawing meaningfulboundaries of objects, classification uses global thresholds to facilitateinterpretation of landform classes.

Van Niekerk (2010) recently found that an MRS algorithm is moresensitive tomorphological discontinuities than two other alternatives,ALCoM and ISODATA, and he proposed it as the most suitabletechnique for delineating land components from DEMs. An imagesegmentation approach should not be confused with landformsegmentation as used by Pennock and Corre (2001), which is actuallya classification procedure based on pre-defined morphometriccategories. Other segmentation algorithms have also been success-fully applied for geomorphological mapping or delineation ofhomogeneous areas from DEMs. For instance, Miliaresis (2001a,b,2006) used a region-growing algorithm for extraction of bajadas fromDEMs and satellite imagery, and for geomorphometric mapping atregional scales; Lucieer and Stein (2005) proposed a region-growingsegmentation procedure based on texture to extract landform objectsfrom LiDAR data; Stepinski et al. (2006, 2007), Stepinski and Bagaria(2009), and Ghosh et al. (2010) developed a segmentation approachcombined with Artificial Intelligence to automatically map planetarysurfaces; Jellema et al. (2009) applied a region-growing algorithm tocharacterize and evaluate landscapes. A particularly simple andappealing procedure for watershed segmentation of curvature wasproposed by Romstad and Etzelmüller (2009) for the purpose ofgeomorphological mapping.

3. Scale

Due to increasing availability and easier access to DEMs at a broadrange of spatial resolutions (from LiDAR at several centimeters up toGTOPO30 at approx. 1 km), multi-scale analysis of the land surface isbecoming more feasible. The modeling of scale effects with respect toboth changing resolution and varying window size for surfacecalculations has been identified as a major research topic not onlyin geomorphometry, but rather in all disciplines dealing with DEMsincluding hydrology, soil science, and geomorphology. In a recentpaper Li (2008) provided a valuable review on the numerousapproaches that examine scale dependencies in terrain-basedmodeling, and has outlined a general strategy for their analysis.

As has been shown parameters such as slope (Deng et al., 2008)and curvatures (Schmidt and Andrew, 2005), do not only change inmagnitude, but may even shift their topographic meaning, as for signof curvature. Surface roughness also varies with scale (Grohmannet al., 2010). Moreover, scale dependencies in terrain analysis aredriven by terrain characteristics (e.g. simple or complex, Carter,1992), and also vary across different landform types (Gao, 1997; Denget al., 2007). An important development in examining scale effects isthat scale has become an integrated part of terrain analysis (Deng,2007). For example, Wood (1996, 1998) proposed calculating surfaceparameters at various window sizes for a constant resolution, and foreach cell recording the results as a series of values linked with scaleinformation. His open-source software package LandSerf for ‘multi-scale surface characterization’ offers powerful visualization tools forexploring scale effects. Following Wood's approach several research-ers focused on exploring the effects of neighborhood size oncomputed terrain parameters as well as on the application of variouswindow sizes for multi-scale characterization of landforms (Fisheret al., 2004; Schmidt and Hewitt, 2004; Schmidt and Andrew, 2005;Reuter et al., 2006; Deng and Wilson, 2008). Lately, it has been foundthat parameters are less sensitive to DEM resolution changes than tovariations in neighborhood size (Zhu et al., 2008).

Pure modeling of scale effects barely gives clues on how to selectnon-arbitrary scales for given analyses. Hence, researchers started toexamine strategies for scale optimization and scale detection. Theyconducted either experimental testing in the context of terrain-based

environmental modeling, or theoretical analysis in data-drivenapproaches (for a review see Li, 2008).

In terrain-based environmental modeling it is essential to fit thespatial scale of the terrain data to the scale of the processes or featuresunder investigation in order to obtain valid model results. In doing so,several authors compared results from multi-resolution terrainanalysis with reference data such as field measurements of alandscape property (Bian and Walsh, 1993; Florinsky and Kuryakova,2000; Hengl, 2006; Drăguţ et al., 2009a), or model outputs (Smithet al., 2006; Zhang et al., 2008). Through statistical analysis they wereable to identify the grid size or resolution range with the mostpowerful predictions. However, the optimal grid size might bedifferent for different target variables, so that one can hardly selecta single optimal resolution (Hengl, 2006). Especially in soil-landscapemodeling, recent efforts have been made towards optimizingneighborhood sizes for the prediction of soil classes (Smith et al.,2006; Zhu et al., 2008; Behrens et al., 2010).

Indeed, it is more desirable to develop methods that work data-driven, and without reference to dependent variables outside theDEMs. Depending on themethod one obtains ameasure for each scale,and when plotting all these measures or simply the results fromterrain analysis against scale, one finally gets a ‘scale signature’, whereextremes mark ‘characteristic scales’ (Wood, 1996, 2009). Schmidtand Andrew (2005) introduced a spatially adaptive scale detectiontechnique exemplified for curvatures in order to recognize dominantscale ranges of landforms. Gallant and Dowling (2003) proposed analgorithm to produce a multiresolution index of valley bottoms basedon their topographic signatures at multiple scales.

A particularly appealing concept to describe aspects of scaledependency in spatial objects is fractals (Mandelbrot, 1975). However,empirical evidence (Chase, 1992; Evans and McClean, 1995; Perronet al., 2008) suggests that fractal models are not appropriate to the landsurface, which has a statistically multidimensional character (Evans,1998). Deficiencies of unifractal and multifractal models are summa-rized by Evans (1998). Tate andWood (2001) provide a comprehensivereview on fractals and scale dependencies in the land surface.

Probably the most promising approach for data-driven scaledetection is the method of local variance (LV). This method wasoriginally developed in image analysis for the purpose of scaledetection (Woodcock and Strahler, 1987). The approach is based onthe relationship between the size of objects in the real world and pixelresolution, as expressed by the spatial structure of images. Theinformation on spatial structures of images is coded in the localvariance measures. Thus, in a high-resolution scene (Strahler et al.,1986), objects in the real world are represented by multiple pixels,hence spatial autocorrelation is high (Fig. 1, top). Local variance,computed as average value of standard deviation measured in a smallneighborhood (3×3 moving window), is therefore small. Whensuccessive coarser scales are produced from the initial datasetthrough resampling, local variance increases with the scale levels upto the point where pixels start approximating the representativeobjects in the scene (Fig. 1, top). At this scale level themaximumvalueof local variance is recorded as the likelihood of neighbors beingsimilar decreases. At coarser pixel sizes local variance decreases againas a consequence of including more objects within a pixel, hence thespectral difference between neighbor pixels is reduced (Fig. 1, top).

Despite its simplicity and usefulness this method was not widelyadopted in remote sensing and GIS (Cao and Lam, 1997). Li (2008)suggested the LV method could prove useful as a scale detectiontechnique in DEM analysis. Two recent studies tested the suitability ofthe LV method for multi-scale pattern analysis in geomorphometry(Drăguţ et al., 2009b, in press). Scale levels were simulated from thesame high-resolution datasets through resampling and imagesegmentation respectively, in a bottom-up approach. The authorsfound that the LV method performed better when scale levels werecreated with image segmentation as compared to cell aggregation.

Fig. 1. Rationales of the method of local variance (LV) as applied on cells (top) and objects (bottom).

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Up-scaling through resampling induces an isotropic smoothing thatlevels out spatial patterns at coarser resolutions. In contrast, imagesegmentation maintains distinct boundaries of objects (Karl andMaurer, 2010) by steadily adding heterogeneity to objects at eachcoarser scale level (Fig. 1, bottom). Thus, at each coarser scale levelcontiguous objects with similar property values are merged intolarger ones. The merged object preserves the external boundaries ofthe previously independent objects.

4. Discrete geomorphometry? Coupling multi-scale patternanalysis and object delineation

Talking about the specific geomorphometry, Mark (1975, p. 165)observed that ‘the specific approach can only be applied once an areahas been identified as a drainage basin, an alluvial fan, a drumlin, etc.’.This means that delineation of objects that satisfy the condition ofmaximizing internal homogeneity and external differences is not aspecific approach, as long as the objects do not bear a meaning otherthan statistical. As Minar and Evans (2008, p. 238–239) pointed out‘segmentation of the land surface can provide a transition from thefieldmodel to the object model, and from general geomorphometry tospecific geomorphometry, thus connecting the continuous andatomistic hypotheses’. The main issue is that this transition has notbeen conceptualized in geomorphometry so far. Therefore, wepropose discrete geomorphometry as a possible approach to specificgeomorphometry.

Discrete geomorphometry would apply to and describe land-surface divisions defined solely by the criteria of homogeneity inrespect to a given land-surface parameter or a combination of severalparameters. Homogeneity, in its turn, should always be relative toscale. The main aim of discrete geomorphometry is to producemorphometrically meaningful objects. This approach has a generaland objective character as general geomorphometry; however thetwo approaches are framed into different conceptual models–field vs.object. On the other hand, discrete geomorphometry shares the objectmodel with specific geomorphometry; however, in the specificapproach the character of objects is defined before segmentation,while in the discrete the meanings are assigned after or along withsegmentation.

Discrete geomorphometry thus centers on objects, defined ashomogeneous areas delineated by discontinuities in land-surface

parameters, either on individual or combined layers, which reveal theland-surface patterns at a given scale or across scales. Therefore,spatial pattern, which ‘has been missing frommost quantitative work’(Evans, in press) would come into focus. Possible candidates for suchobjects have been called land components by Dymond et al. (1995),terrain facets by Rowbotham and Dudycha (1998), elementary formsby Minar and Evans (2008), pattern elements by Drăguţ et al. (2009b),andmorphometric primitives by Gessler et al. (2009). These objects canbe seen as intermediate building blocks in the translation from cells tolandform divisions. Once the objects are delineated in the digitalrealm, further statistical, relational and semantic rules can be appliedto map each object to the landform concept to which it comes closest(MacMillan et al., 2004; Minar and Evans, 2008; Bishop, 2009; Eisank,2010), by incorporating expert knowledge (MacMillan et al., 2005), orto use terrain objects as basic areal divisions for the study of land-surfaceprocesses (Rowbotham and Dudycha, 1998). Once the objects areassigned to classes of elementary form, or given interpretations such as‘terrace’, ‘fan’ or ‘drumlin’, we havemoved into specific geomorphometry.

Segmentation is a good candidate as the main method of discretegeomorphometry. In the second section of this paper we presented itsadvantages over clustering in property space and cell classification(also see Minar and Evans, 2008 for a comprehensive discussion onsegmentation techniques). Two main strategies of segmentation canbe followed: segmentation into pre-defined types and degrees ofhomogeneity (Minar and Evans, 2008) and data-driven approach(Drăguţ et al., in press).

In the first strategy, homogeneity is expressed by ‘constant valuesof altitude or its derived morphometric properties’ (Minar and Evans,2008, p. 244). These constant values are named the form-definingproperties. A unified system of elementary forms was predefinedbased on variation in the general fitted function. The forms are data-based and assigned to a form class after or along with delimitation.This approach is potentially likely to facilitate the reference of terraindivisions to process or genesis. Although the approach should be inprinciple independent of scale, the authors acknowledge that manyaspects of the land surface are scale dependent (Evans, 2003, 2009,2010), therefore further investigation is needed before applying it atbroader scales (Minar and Evans, 2008).

The data-driven approach was developed with the aid of themultiresolution segmentation algorithm (see Section 2 of this paper).Homogeneity is controlledbyauser-defined factor called scale parameter.

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Selection of the scale parameterwas turned into anobjective choice,withthe aid of the ESP tool (Estimation of Scale Parameters), by using theconcept of local variance (Drăguţ et al., 2010). Segmentation of land-surface parameters such as slope gradient (Eisank andDrăguţ, 2010)wasperformed with the ESP tool in a bottom-up approach, where objects atfiner scale were steadily merged into more heterogeneous objects atbroader scales (Fig. 1), by changing the scale parameter in a constantincrement. Thus, ever coarser object patterns were produced. For eachpattern LV was measured by first calculating the standard deviation ofobjects, and then averaging object values to obtain the pattern mean.Values of LVwere plotted against scale parameter; breaks in the LV graphand its rate of change indicated the scales where the probability thatdelineated land-surfaceobjectsmatchagroupof similar-sized real-worldforms should be higher than for other scales (Drăguţ et al., in press).

Although the two methods are in incipient stages, they offer goodprospects for delineating homogeneous morphometric primitiveseither independent of scale, or at multiple scales, through multi-scalepattern analysis. However, much work lies ahead before they can befully operational for what Olaya (2009) called the ‘discrete analysis ofthe land surface’. Object ontology needs particular attention. Forinstance, more research on relationships between real land-surfacefeatures and segmented objects across scales is required. This is tomake sure that we delineate real objects and do not create artificialconstructs; arbitrary partitions at various scales would represent aparticular case of the Modifiable Area Unit Problem (MAUP) with allits acknowledged shortcomings (Openshaw and Taylor, 1979). Apossible strategy for linking object ontologies of segmented objectswith concepts of real landforms is semantic modeling (Eisank et al.,2010) as was originally proposed by Dehn et al. (2001).

Another important research topic would be on the nature ofboundaries. Since land-surface features show smooth transitions, howcanwe account for fuzziness on both conceptual and spatial domains?Preliminary results (Drăguţ et al., in press) show that discontinuitiesin land-surface parameters seem to relate to the quality of objectboundaries: sharper contrasts are expressed by smoother lines, whilesoft transitions give more indented boundaries. If this proves true, thedegree of fuzziness could be measured via edge analysis. Models likecore vs. transitional areas (Drăguţ and Blaschke, 2008), attractors(Minar and Evans, 2008), or spatial gradation of slope positions (Qinet al., 2009) would be further useful in classification of objects.

Here we presented methods producing non-overlapping objects,potentially amenable to nested hierarchies. However, overlappingareas might be better suited for given applications. Romstad andEtzelmüller (2009) proposed an interesting approach based onoverlapping convexities and concavities.

5. Summary

This paper has provided a critical review on object representationfrom digital elevation models. Translation from continuous models ofelevation and its derivatives (slope, aspect, and curvatures) tolandform divisions (landforms and landform elements) is filtered bytwo important concepts: scale and object ontology.

Scale has been acknowledged as a basic problem in geomorphometry.Dependingon theDEMresolution andon the sizeof the analysiswindow,land-surface parameters have different values at the same location;consequently one landscape can be represented in multiple ways. Thus,scale impacts heavily on the results of geomorphometric analysis.Whereas scale effects on geomorphometric analysis are now relativelywell understood, scale optimization techniques remain a priority forfuture research. Scale becomes more important with increasing DEMresolution (MacMillan et al., 2003): while the number of landscaperepresentations from a low resolution dataset is limited, many moreversions of the landscape can be represented from a single very highresolution DEM through up-scaling. Which of those representations arebest suited for a given purpose? The answer to this question prompts a

reliance either on expert knowledge (Gustavsson and Kolstrup, 2009), oran exploratory attitude in the use of local land-surface parameters (Deng,2007). An exploratory attitude is unfortunately hindered by poortechnical implementation of scale issues in most GIS software packages.LandSerf (Wood, 1996) is a remarkable exception, providing a suite ofsolutions for scale/multi-scale analysis (Wood, 2009).

Although landform divisions are discrete features by definition(Evans, 1972; MacMillan and Shary, 2009; Pike et al., 2009), most ofthe procedures to produce them in the digital era have essentially beentributary to a field model: individual cells are allocated to pre-definedclassification schemes. Objects emerge then as aggregations of cellsthrough decisions that are not easily applicable to other landscapes.Boundaries of such aggregates are likely to fail inmatching land-surfacediscontinuities. Image segmentation procedures create the technicalframework for delineating homogeneous objects delimited by realdiscontinuities in land-surface parameters. ‘Abstracting complex sur-faces as objects is innately human’ (Gessler et al., 2009), so that thistechnique can bridge the gap between a pixel-based approach andmanual mapping based on visual interpretation, while preserving theadvantages of speed and objectivity given by computers. Still, theconceptual basis of specific geomorphometry should be improved. Herewe proposed discrete geomorphometry as a possible approach betweengeneral and specific geomorphometry. Discrete geomorphometrywould apply to and describe land-surface divisions defined solely bythe criteria of homogeneity in respect to a given land-surface parameteror a combination of several parameters.Homogeneity, in its turn, shouldalways be relative to scale.

The emerging idea of smoothing local variability in land-surfaceparameters into homogeneous entities looks promising for futuredevelopments. Delineation of such objects should produce morpho-metric patterns that match landscape patterns at given scales. Thisapproach does not incorporate a priori knowledge on a specificlandscape, therefore results are transferable. Landform classificationcan further give meaning to the resulting building blocks (elementaryforms, pattern elements or morphometric primitives) by addingsemantics. Minar and Evans (2008) set up the stage by creating aunified system of geometric primitives. Coupling multi-scale patternanalysis—with the help of local variance—with object delineation isanother promising approach towards hierarchies built on suchobjects.

Acknowledgments

This research was supported by the Austrian Science Fund (FWF)through a Stand-alone project (FWF-P20777-N15), and by a MarieCurie European Reintegration Grant within the 7th EC FrameworkProgramme (FP7-PEOPLE-ERG-2008-239312). Reviews by Ian Evansand Tom Farr led to important improvements in the manuscript.

References

Anders, N., Seijmonsbergen, A., Bouten, W., 2009. Multi-scale and object-orientedimage analysis of high-res LiDAR data for geomorphological mapping in Alpinemountains. In: Purves, R., Gruber, S., Straumann, R., Hengl, T. (Eds.), ProceedingsGeomorphometry 2009. University of Zurich, Zurich, pp. 61–65.

Baatz, M., Schäpe, A., 2000. Multiresolution segmentation—an optimization approach forhigh quality multi-scale image segmentation. In: Strobl, J., Blaschke, T., Griesebner, G.(Eds.), Angewandte Geographische Informationsverarbeitung. Wichmann-Verlag,Heidelberg, pp. 12–23.

Behrens, T., Zhu, A.X., Schmidt, K., Scholten, T., 2010. Multi-scale digital terrain analysisand feature selection for digital soil mapping. Geoderma 155, 175–185.

Bian, L.,Walsh, S.J., 1993. Scale dependencies of vegetation and topography in amountainousenvironment of Montana. The Professional Geographer 45, 1–11.

Bishop,M.A., 2009. A generic classification for themorphological and spatial complexity ofvolcanic (and other) landforms. Geomorphology 111, 104–109.

Blanco, P.D., Metternicht, G.I., Del Valle, H.F., 2009. Improving the discrimination ofvegetation and landform patterns in sandy rangelands: a synergistic approach.International Journal of Remote Sensing 30, 2579–2605.

Brändli, M., 1996. Hierarchical models for the definition and extraction of terrain features.In: Burrough, P.A., Frank, A.W. (Eds.), Geographic Objects with IndeterminateBoundaries. Taylor & Francis, Bristol, Pennsylvania, USA, pp. 257–270.

188 L. Drăguţ, C. Eisank / Geomorphology 129 (2011) 183–189

Burrough, P., Wilson, J., van Gaans, P., Hansen, A., 2001. Fuzzy k-means classification oftopo-climatic data as an aid to forest mapping in the Greater Yellowstone Area,USA. Landscape Ecology 16, 523–546.

Cao, C., Lam, N.S.N., 1997. Understanding the scale and resolution effects in remotesensing and GIS. In: Quattrochi, D.A., Goodchild, M.F. (Eds.), Scale in RemoteSensing and GIS. CRC Press, Boca Raton, pp. 57–72.

Carter, J.R., 1992. The effect of data precision on the calculation of slope and aspectusing gridded DEMs. Cartographica: The International Journal for GeographicInformation and Geovisualization 29, 22–34.

Chase, C.G., 1992. Fluvial landsculpting and the fractal dimension of topography.Geomorphology 5, 39–57.

Cova, T.J., Goodchild, M.F., 2002. Extending geographical representation to includefields of spatial objects. International Journal of Geographical Information Science16, 509–532.

Dehn, M., Gärtner, H., Dikau, R., 2001. Principles of semantic modeling of landformstructures. Computers and Geosciences 27, 1005–1010.

Deng, Y., 2007. New trends in digital terrain analysis: landform definition, represen-tation, and classification. Progress in Physical Geography 31, 405–419.

Deng, Y., Wilson, J.P., 2008. Multi-scale and multi-criteria mapping of mountain peaks asfuzzy entities. International Journal of Geographical Information Science 22, 205–218.

Deng, Y., Wilson, J.P., Bauer, B.O., 2007. DEM resolution dependencies of terrainattributes across a landscape. International Journal of Geographical InformationScience 21, 187–213.

Deng, Y., Wilson, J., Gallant, J., 2008. Terrain analysis. In: Wilson, J., Fotheringham, S.(Eds.), Handbook of Geographic Information Science. Blackwell, Malden, USA, a.o.,pp. 417–435.

Drăguţ, L., Blaschke, T., 2006. Automated classification of landform elements usingobject-based image analysis. Geomorphology 81, 330–344.

Drăguţ, L., Blaschke, T., 2008. Terrain segmentation and classification using srtm data.In: Zhou, Q., Lees, B., Tang, G.-A. (Eds.), Advances in Digital Terrain Analysis.Springer, Berlin, Heidelberg, pp. 141–158.

Drăguţ, L., Schauppenlehner, T., Muhar, A., Strobl, J., Blaschke, T., 2009a. Optimization ofscale and parametrization for terrain segmentation: an application to soil-landscape modeling. Computers and Geosciences 35, 1875–1883.

Drăguţ, L., Eisank, C., Strasser, T., Blaschke, T., 2009b. A comparison of methods toincorporate scale in geomorphometry. In: Purves, R., Gruber, S., Straumann, R., Hengl,T. (Eds.), Proceedings Geomorphometry 2009: Geomorphometry 2009. University ofZurich, Zurich, pp. 133–139.

Drăguţ, L., Tiede, D., Levick, S., 2010. ESP: a tool to estimate scale parameters formultiresolution image segmentation of remotely sensed data. International Journalof Geographical Information Science 24, 859–871.

Drăguţ, L., Eisank, C., Strasser, T., in press. Local variance for multi-scale analysis ingeomorphometry. Geomorphology. doi:10.1016/j.geomorph.2011.03.011.

Dymond, J.R.,Derose, R.C.,Harmsworth,G.R., 1995.Automatedmappingof land componentsfrom digital elevation data. Earth Surface Processes and Landforms 20, 131–137.

Eisank, C., 2010. A hierarchical system for multi-scale and object-based landformclassification. In: Wallgrün, J.O., Lautenschütz, A.-K. (Eds.), Proceedings of theGIScience 2010 Doctoral Colloquium. Akademische Verlagsgesellschaft AKA GmbH,Heidelberg, Zurich, Switzerland, pp. 17–22.

Eisank, C., Drăguţ, L., 2010. Detecting characteristic scales of slope gradient. In: Car, A.,Griesebner, G., Strobl, J. (Eds.), Geospatial Crossroads @ GI_Forum '10: Proceedingsof the Geoinformatics Forum Salzburg. Wichmann, Berlin, pp. 48–57.

Eisank, C., Drăguţ, L., Götz, J., Blaschke, T., 2010. Developing a semantic model of glaciallandforms for object-based terrain classification—the example of glacial cirques. In:Addink, E.A., Van Coillie, F.M.B. (Eds.), GEOBIA 2010-Geographic Object-BasedImage Analysis. ISPRS Vol.No. XXXVIII-4/C7, Archives ISSN No. 1682–1777, GhentUniversity, Ghent, Belgium, 29 June–2 July.

Evans, I.S., 1972. General geomorphometry, derivatives of altitude, and descriptivestatistics. In: Chorley, R.J. (Ed.), Spatial Analysis in Geomorphology. Methuen & Co.Ltd, London, pp. 17–90.

Evans, I.S., 1998. What do terrain statistics really mean? In: Lane, S., Richards, K.,Chandler, J. (Eds.), Landform Monitoring, Modelling and Analysis. Wiley,Chichester, pp. 119–138.

Evans, I.S., 2003. Scale-specific landforms and aspects of the land surface. In: Evans, I.S.,Dikau, R., Tokunaga, E., Ohmori, H., Hirano, M. (Eds.), Concepts and Modelling inGeomorphology: International Perspectives. Terrapub, Tokyo, pp. 61–84.

Evans, I.S., 2009. Allometric development of glacial cirques: an application of specificgeomorphometry. In: Purves, R., Gruber, S., Straumann, R., Hengl, T. (Eds.),Proceedings Geomorphometry 2009: Geomorphometry 2009. University of Zurich,Zurich, pp. 248–253.

Evans, I.S., 2010. Allometry, scaling and scale-specificity of cirques, landslides and otherlandforms. Transactions of the Japanese Geomorphological Union 31, 133–153.

Evans, I.S., 2010. Geomorphometry and landform mapping: what is a landform? Paperfor 41st International Binghamton Geomorphology Symposium (BGS), GeospatialTechnologies and Geomorphological Mapping, Oct. 15-17, 2010, Columbia, SouthCarolina.

Evans, I.S., McClean, C., 1995. The land surface is not unifractal: variograms, cirque scaleand allometry. Zeitschrift fur Geomorphologie N.F. Supplement Band 101, 127–147.

Fisher, P., 1997. The pixel: a snare and a delusion. International Journal of RemoteSensing 18, 679–685.

Fisher, P.,Wood, J., Cheng, T., 2004.Where isHelvellyn? Fuzziness ofmulti-scale landscapemorphometry. Transactions of the Institute of British Geographers 29, 106–128.

Florinsky, I.V., Kuryakova, G.A., 2000. Determination of grid size for digital terrainmodelling in landscape investigations exemplified by soil moisture distribution at amicro-scale. International Journal of Geographical Information Science 14,815–832.

Gallant, J., Dowling, T., 2003. A multi-resolution index of valley bottom flatness formapping depositional areas. Water Resources Research 39 ESG 4-1 - ESG 4-13.

Gallant, J.C., Hutchinson, M.F., 1996. Towards an understanding of landscape scale andstructure. Third International Conference/Workshop on Integrating GIS andEnvironmental Modeling, Santa Fe, USA.

Gao, J., 1997. Resolution and accuracy of terrain representation by grid DEMs at a micro-scale. International Journal of Geographical Information Science 11, 199–212.

Gessler, P., Pike, R., MacMillan, R.A., Hengl, T., Reuter, H.I., 2009. The future ofgeomorphometry. In: Hengl, T., Reuter, H.I. (Eds.), Geomorphometry—Concepts,Software, Applications: Developments in Soil Science, vol. 33. Elsevier, Amsterdam,pp. 637–652.

Ghosh, S., Stepinski, T., Vilalta, R., 2010. Automatic annotation of planetary surfaceswith geomorphic labels. IEEE Transactions on Geoscience and Remote Sensing 48,175–185.

Goodchild, M.F., 2011. Scale in GIS: an overview. Geomorphology. doi:10.1016/j.geomorph.2010.10.004.

Goodchild, M.F., Yuan, M., Cova, T.J., 2007. Towards a general theory of geographicrepresentation in GIS. International Journal of Geographical Information Science 21,239–260.

Grohmann, C.H., Smith, M.J., Riccomini, C., 2010. Multiscale analysis of topographicsurface roughness in theMidland Valley, Scotland. IEEE Transactions on Geoscienceand Remote Sensing, pp. 1–14.

Gustavsson, M., Kolstrup, E., 2009. New geomorphological mapping system used atdifferent scales in a Swedish glaciated area. Geomorphology 110, 37–44.

Hengl, T., 2006. Finding the right pixel size. Computers and Geosciences 32, 1283–1298.Hengl, T., Evans, I.S., 2009. Mathematical and digital models of the land surface. In:

Hengl, T., Reuter, H.I. (Eds.), Geomorphometry—Concepts, Software, Applications:Developments in Soil Science, vol. 33. Elsevier, Amsterdam, pp. 31–63.

Hengl, T., Reuter, H.I. (Eds.), 2009. Geomorphometry—Concepts, Software, Applications:Developments in Soil Science, 33. Elsevier.

Irvin, B.J., Ventura, S.J., Slater, B.K., 1997. Fuzzy and isodata classification of landformelements from digital terrain data in Pleasant Valley, Wisconsin. Geoderma 77,137–154.

Iwahashi, J., Pike, R.J., 2007. Automated classifications of topography from DEMs by anunsupervised nested-means algorithm and a three-part geometric signature.Geomorphology 86, 409–440.

Jellema, A., Stobbelaar, D.-J., Groot, J.C.J., Rossing, W.A.H., 2009. Landscape characterassessment using region growing techniques in geographical information systems.Journal of Environmental Management 90, S161–S174.

Karl, J., Maurer, B., 2010. Multivariate correlations between imagery and fieldmeasurements across scales: comparing pixel aggregation and image segmenta-tion. Landscape Ecology 25, 591–605.

Kringer, K., Tusch, M., Geitner, C., Rutzinger, M., Wiegand, C., Meißl, G., 2009.Geomorphometric analyses of LiDAR digital terrain models as input for digitalsoil mapping. In: Purves, R., Gruber, S., Straumann, R., Hengl, T. (Eds.), Proceedingsof Geomorphometry 2009. University of Zurich, Zurich, Switzerland, pp. 74–81.

Li, Z., 2008. Multi-scale digital terrain modelling and analysis. In: Zhou, Q., Lees, B.,Tang, G. (Eds.), Advances in Digital Terrain Analysis. Springer, Berlin, Heidelberg,pp. 59–83.

Lucieer, A., Stein, A., 2005. Texture-based landform segmentation of LiDAR imagery.International Journal of Applied Earth Observation and Geoinformation 6, 261–270.

MacMillan, R.A., Shary, P.A., 2009. Chapter 9 Landforms and Landform Elements inGeomorphometry. In: Hengl, T., Reuter, H.I. (Eds.), Geomorphometry—Concepts,Software, Applications: Developments in Soil Science, vol. 33. Elsevier, Amsterdam,pp. 227–254.

MacMillan, R., Martin, T., Earle, T., McNabb, D., 2003. Automated analysis andclassification of landforms using high-resolution digital elevation data: applicationsand issues. Canadian Journal of Remote Sensing 29, 592–606.

MacMillan, R.A., Jones, R.K., McNabb, D.H., 2004. Defining a hierarchy of spatial entitiesfor environmental analysis and modeling using digital elevation models (DEMs).Computers, Environment and Urban Systems 28, 175–200.

MacMillan, R.A., Pettapiece, W.W., Brierley, J.A., 2005. An expert system for allocatingsoils to landforms through the application of soil survey tacit knowledge. CanadianJournal of Soil Science 85, 103–112.

Mandelbrot, B.B., 1975. Stochastic models for the Earth's relief, the shape and the fractaldimension of the coastlines, and the number-area rule for islands. Proceedings ofthe National Academy of Sciences of the United States of America 72, 3825–3828.

Mark, D., 1975. Geomorphometric parameters: a review and evaluation. GeografiskaAnnaler. Series A. Physical Geography 165–177.

Mark, D.M., 2009. From land form to landforms: bridging the quantitative—qualitative gapin a multilingual context. In: Purves, R., Gruber, S., Straumann, R., Hengl, T. (Eds.),Proceedings of Geomorphometry 2009. University of Zurich, Zurich, pp. 13–16.

Martha, T.R., Kerle, N., Jetten, V., van Westen, C.J., Kumar, K.V., 2010. Characterisingspectral, spatial and morphometric properties of landslides for semi-automaticdetection using object-oriented methods. Geomorphology 116, 24–36.

Miliaresis, G.C., 2001a. Extraction of bajadas from digital elevation models and satelliteimagery. Computers and Geosciences 27, 1157–1167.

Miliaresis, G.C., 2001b. Geomorphometric mapping of Zagros Ranges at regional scale.Computers and Geosciences 27, 775–786.

Miliaresis, G.C., 2006. Geomorphometric mapping of Asia Minor from GLOBE digitalelevation model. Geografiska Annaler Series a-Physical Geography 88A, 209–221.

Minar, J., Evans, I.S., 2008. Elementary forms for land surface segmentation: the theoreticalbasis of terrain analysis and geomorphological mapping. Geomorphology 95,236–259.

Möller, M., Volk, M., Friedrich, K., Lymburner, L., 2008. Placing soil-genesis and transportprocesses into a landscape context: a multiscale terrain-analysis approach. Journal of

189L. Drăguţ, C. Eisank / Geomorphology 129 (2011) 183–189

Plant Nutrition and Soil Science-Zeitschrift Fur Pflanzenernahrung Und Bodenkunde171, 419–430.

Olaya, V., 2009. Basic land-surface parameters. In: Hengl, T., Reuter, H.I. (Eds.),Geomorphometry—Concepts, Software, Applications: Developments in Soil Science,vol. 33. Elsevier, Amsterdam, pp. 141–169.

Openshaw, S., Taylor, P.J., 1979. A million or so correlation coefficients: threeexperiments on the modifiable areal unit problem. In: Wrigley, N. (Ed.), StatisticalApplications in the Spatial Sciences. Pion, London, pp. 127–144.

Pennock, D.J., Corre, M.D., 2001. Development and application of landform segmenta-tion procedures. Soil and Tillage Research 58, 151–162.

Perron, J.T., Kirchner, J.W., Dietrich, W.E., 2008. Spectral signatures of characteristicspatial scales and nonfractal structure in landscapes. Journal of GeophysicalResearch 113, F04003.

Pike, R.J., 1995. Geomorphometry—progress, practice, and prospect. Zeitschrift furGeomorphologie Supplementband 101, 221–238.

Pike, R.J., 2000. Geomorphometry—diversity in quantitative surface analysis. Progressin Physical Geography 24, 1–20.

Pike, R.J., Evans, I.S., Hengl, T., 2009.Geomorphometry: a brief guide. In:Hengl, T., Reuter, H.I.(Eds.), Geomorphometry—Concepts, Software, Applications: Developments in SoilScience, vol. 33. Elsevier, Amsterdam, pp. 3–30.

Qin, C.-Z., Zhu, A.X., Shi, X., Li, B.-L., Pei, T., Zhou, C.-H., 2009. Quantification of spatialgradation of slope positions. Geomorphology 110, 152–161.

Reuter, H.I., Wendroth, O., Kersebaum, K.C., 2006. Optimisation of relief classificationfor different levels of generalisation. Geomorphology 77, 79–89.

Romstad, B., Etzelmüller, B., 2009. Structuring the digital elevation model into landformelements through watershed segmentation of curvature. In: Purves, R., Gruber, S.,Straumann, R., Hengl, T. (Eds.), Proceedings of Geomorphometry 2009. Universityof Zurich, Zurich, Switzerland, pp. 55–60.

Rowbotham, D.N., Dudycha, D., 1998. GIS modelling of slope stability in Phewa Talwatershed, Nepal. Geomorphology 26, 151–170.

Savigear, R.A.G., 1965. A technique ofmorphological mapping. Annals of the Associationof American Geographers 55, 514–538.

Schmidt, J., Andrew, R., 2005. Multi-scale landform characterization. Area 37, 341–350.Schmidt, J., Dikau, R., 1999. Extracting geomorphometric attributes and objects from

digital elevation models—semantics, methods, future needs. In: Dikau, R., Saurer, H.(Eds.), GIS for Earth Surface Systems. Borntraeger, Berlin, pp. 153–173.

Schmidt, J., Hewitt, A., 2004. Fuzzy land element classification from DTMs based ongeometry and terrain position. Geoderma 121, 243–256.

Schneevoigt, N.J., van der Linden, S., Thamm, H.-P., Schrott, L., 2008. Detecting Alpinelandforms from remotely sensed imagery. A pilot study in the Bavarian Alps.Geomorphology 93, 104–119.

Shary, P.A., Sharaya, L.S., Mitusov, A.V., 2002. Fundamental quantitative methods ofland surface analysis. Geoderma 107, 1–32.

Smith, B., 1995. On drawing lines on a map. In: Frank, A.U., Kuhn, W., Mark, D.M. (Eds.),Spatial Information Theory. Proceedings of COSIT '95: Lecture Notes in Computer

Science. Springer Verlag, Berlin, pp. 475–484. Heidelberg, Vienna, New York,London, Tokyo.

Smith, M.P., Zhu, A.X., Burt, J.E., Stiles, C., 2006. The effects of DEM resolution andneighborhood size on digital soil survey. Geoderma 137, 58–69.

Stepinski, T.F., Bagaria, C., 2009. Segmentation-based unsupervised terrain classifica-tion for generation of physiographic maps. IEEE Geoscience and Remote SensingLetters 6, 733–737.

Stepinski, T., Ghosh, S., Vilalta, R., 2006. Automatic recognition of landforms on Marsusing terrain segmentation and classification. In: Todorovski, L., Lavrac, N., Jantke,K. (Eds.), Discovery Science Lecture Notes in Computer Science. Springer, Berlin,pp. 255–266. Heidelberg, New York.

Stepinski, T.F., Ghosh, S., Vilalta, R., 2007. Machine learning for automatic mapping ofplanetary surfaces. Proceedings 19th Innovative Applications of Artificial Intelli-gence Conference (IAAI-2007), pp. 1807–1812.

Strahler, A.H., Woodcock, C.E., Smith, J.A., 1986. On the nature of models in remotesensing. Remote Sensing of Environment 20, 121–139.

Strobl, J., 2008. Segmentation-based terrain classification. In: Zhou, Q., Lees, B., Tang, G.-a.(Eds.), Advances in Digital Terrain Analysis. Springer, Berlin, Heidelberg, pp. 125–139.

Tate, N.J., Wood, J., 2001. Fractals and scale dependencies in topography. In: Tate, N.J.,Atkinson, P.M. (Eds.), Modelling Scale in Geographical Information Science. Wiley,Chichester, pp. 35–51.

van Asselen, S., Seijmonsbergen, A.C., 2006. Expert-driven semi-automated geomor-phological mapping for a mountainous area using a laser DTM. Geomorphology 78,309–320.

van Niekerk, A., 2010. A comparison of land unit delineation techniques for landevaluation in the Western Cape, South Africa. Land Use Policy 27, 937–945.

Wilson, J., Gallant, J. (Eds.), 2000. Terrain Analysis: Principles and Applications. Wiley,Chichester.

Wood, J., 1996. The geomorphological characterisation of digital elevation models, PhDThesis. University of Leicester, Leicester.

Wood, J., 1998. Modelling the continuity of surface form using digital elevationmodels. Proceedings of the 8th international Symposium on Spatial DataHandling, pp. 725–736.

Wood, J., 2009. Geomorphometry in LandSerf. In: Hengl, T., Reuter, H.I. (Eds.),Geomorphometry—Concepts, Software, Applications: Developments in Soil Science,vol. 33. Elsevier, Amsterdam, pp. 333–349.

Woodcock, C.E., Strahler, A.H., 1987. The factor of scale in remote-sensing. RemoteSensing of Environment 21, 311–332.

Zhang, J.X., Chang, K.-T., Wu, J.Q., 2008. Effects of DEM resolution and source on soilerosion modelling: a case study using the WEPP model. International Journal ofGeographical Information Science 22, 925–942.

Zhu, A.X., Burt, J.E., Smith, M., Wang, R., Gao, J., 2008. The impact of neighbourhoodsize on terrain derivatives and digital soil mapping. In: Zhou, Q., Lees, B., Tang,G.-a. (Eds.), Advances in Digital Terrain Analysis. Springer, Berlin, Heidelberg,pp. 333–348.