detecting dominant landscape objects through multiple...

Research article

Detecting dominant landscape objects through multiple scales: Anintegration of object-specific methods and watershed segmentation

Ola Hall1,*, Geoffrey J. Hay2, André Bouchard3 and Danielle J. Marceau2

1Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91 Stockholm,Sweden; 2Geocomputing Laboratory, Département de géographie, Université de Montréal, C.P. 6128,succursale Centre-Ville, Montréal, Québec, Canada, H3C 3J7.; 3IRBV, Université de Montréal, 4101Sherbrooke Est, Montréal, Québec, Canada, H1X 2B2; *Author for correspondence (e-mail:[email protected])

Received 17 September 2002; accepted in revised form 8 July 2003

Key words: Complex system, Critical landscape threshold, Feature detection, Hierarchy, IKONOS, Marker-con-trolled watershed segmentation, Multiscale, Object-specific analysis, Object-specific upscaling, Scale domain

Abstract

Complex systems, such as landscapes, are composed of different critical levels of organization where interactionsare stronger within levels than among levels, and where each level operates at relatively distinct time and spatialscales. To detect significant features occurring at specific levels of organization in a landscape, two steps arerequired. First, a multiscale dataset must be generated from which these features can emerge. Second, a proce-dure must be developed to delineate individual image-objects and identify them as they change through scale. Inthis paper, we introduce a framework for the automatic definition of multiscale landscape features using object-specific techniques and marker-controlled watershed segmentation. By applying this framework to a high-reso-lution satellite scene, image-objects of varying size and shape can be delineated and studied individually at theircharacteristic scale of expression. This framework involves three main steps: 1� multiscale dataset generationusing an object-specific analysis and upscaling technique, 2� marker-controlled watershed transformation to au-tomatically delineate individual image-objects as they evolve through scale, and 3� landscape feature identifica-tion to assess the significance of these image-objects in terms of meaningful landscape features. This study wasconducted on an agro-forested region in southwest Quebec, Canada, using IKONOS satellite data. Results showthat image-objects tend to persist within one or two scale domains, and then suddenly disappear at the next,while new image-objects emerge at coarser scale domains. We suggest that these patterns are associated to sud-den shifts in the entire image structure at certain scale domains, which may correspond to critical landscapethresholds.

Introduction

It is now widely recognized that landscapes are com-plex systems having a hierarchical structure wheredominant patterns and processes exist at specificscales �O’Neill 1988; Meentemeyer 1989; Malanson1999; Hay et al. 2001; Wu and Marceau 2002�. Tobetter appreciate and understand how such systemsinteract, useful theoretical concepts have been devel-

oped. For example, from Complex Systems theory,we recognize that a system is ‘complex’ when a mul-tiplicity of spatial patterns and processes, non-linearinteractions among components, and spatial heteroge-neity exist �Waldrop 1992�. In addition, Hierarchytheory provides a conceptual framework for explain-ing such multiscale patterns and processes �Allen andStarr 1982�. In this theory, complex systems �such aslandscapes� are regarded as being composed of dif-

Landscape Ecology 00: 1–19, 2003.© 2003 Kluwer Academic Publishers. Printed in the Netherlands.

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XPS 0120378 — ms-code land2139r2 — PIPS 5145185 — 1 Sep 2003 — Grafikon 203001121

ferent critical levels of organization where interac-tions are stronger within levels than among levels,and where each level operates at relatively distincttemporal and spatial scales.

More recently, the Hierarchical patch dynamicsparadigm �HPDP� has provided an organizational andoperational framework that integrates the verticalcomponents of Hierarchy theory and the horizontalcomponents of Patch dynamics theory to express therelationships among pattern, process, and scaleexplicitly within the context of landscapes �Wu andLoucks 1995�. In the HPDP, the hierarchical structureof a system is conceptualized as a ‘scaling ladder’,where each rung corresponds to a threshold within thescale continuum. A scale threshold defines the end orbeginning of a scale domain, that is, a segment of thescale spectrum where patterns do not change, orchange monotonically with changes in scale �Meen-temeyer 1989�. Consequently, scale is fundamental tothe realization of hierarchy �Levin 1992�. In generalterms, ‘scale’ corresponds to a ‘window of percep-tion’. As the size �i.e., grain and extent� of the win-dow is changed, new patterns and structures emerge;thus, the conclusions drawn by the observer arestrongly influenced by the scale of observation. Theterm ‘grain’ refers to the smallest distinguishablecomponent i.e., spatial resolution, while ‘extent’refers to the total area or time under analysis.

To detect dominant objects occurring at differentscales �i.e., hierarchical levels of organization� withina landscape, two fundamental components are re-quired. First, it is necessary to generate data that re-present a range of scales �i.e., multiscale� from whichobjects can be detected. Second, feature detectors areneeded to delineate individual objects and identifythem as they change through scale �Hall 2002; Hayet al. 2003�.

During the last four decades, a number of compu-tational techniques have been developed that allowfor the generation of multiscale representations�Starck et al. 1998�. These include fractals �Mandel-brot 1967�, quadtrees �Klinger 1971�, pyramids�Klinger and Dyer 1976�, wavelets �Daubechies1988�, scale space �Lindeberg 1994; Hay et al.2002a�, and object-specific analysis �OSA� andupscaling �OSU� �Hay et al. 1997; Hay et al. 2001�.Among these, the last set of methods exhibit novelcharacteristics that are of significant importance formultiscale landscape analysis. First, the object-specific framework has been developed for the par-ticular spatial sampling context provided by remote

sensing imagery where it explicitly considers pixelsas parts of objects, thereby addressing the hierarchi-cal structure of landscape components. Second, as in-dividual objects rather than arbitrarily selectedentities are the basis for upscaling �i.e., resampling tocoarser scales�, the effects of the modifiable areal unitproblem �MAUP� are reduced �Openshaw, 1984; fora comprehensive review of MAUP, see Marceau 1999and Marceau and Hay 1999�. Third, the frameworkautomatically identifies significant scale domains andgenerates multiscale datasets based on the spatial at-tributes of the varied objects composing an image.However, at the time this study commenced, the ob-ject-specific framework did not provide an automatedmechanism for feature detection at multiple scales.

Once an appropriate methodology has been appliedto generate a multiscale representation, feature detec-tors are necessary for isolating entities of interestwithin either individual layers/scales, or within allscales of the multiscale output. Several techniquesthat are typically used include edge detectors �Marrand Hildreth 1980; Canny 1986�, thresholding �Ridlerand Calvar 1978�, template matching �van derHeijden 1994; Brunelli and Poggio 1995� and math-ematical morphology �Serra 1982; Haralick et al.1987�. This last technique represents a class of non-linear neighbourhood operators that aim at extractingrelevant structures from an image. A typical applica-tion is a watershed transformation, where image pix-els are grouped around a regional minimum, andboundaries are created around the edge of these pixelgroups �Soille 1999�.

A common limitation of many of these feature de-tection techniques is that the user is required to apriori define the size, shape and location of the op-erator�s� to be used �i.e., threshold limits, filter sizes,template shapes� which is a non-trivial task when theobjects in a complex scene are of varying size, shape,and spatial distribution. However, these characteris-tics are not required of watershed transformations.

Based upon the preceding information, the primaryobjective of this study is to integrate object-specificmethods and watershed segmentation to automati-cally detect dominant landscape features within a finespatial resolution remote sensing image through mul-tiple scales. More generally, this study aims ataddressing two recent issues in landscape analysis�Turner 2001�:

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1. the automatic delineation of the varying sized,shaped and spatially distributed objects within alandscape at their characteristic scales of expres-sion �rather than at the arbitrariness of a user�, and

2. the development and use of multiscale techniquesto evaluate how dominant landscape objects evolvethrough scale.

Study site and dataset

The study site is located in the Haut-Saint-Laurentregional county municipality, in the southernmost partof the Province of Quebec, Canada �Figure 1�. It isbounded by the St.-Lawrence River to the north, andNew York State to the south. During the 19th century,the region was extensively exploited for timber �Si-

mard and Bouchard 1996; Bouchard and Domon1997�. Today, agriculture is the primary activity con-sisting of dairy farming, and grain and cereal produc-tion. The vegetation is typical of the hickory-mapleregion of the deciduous forest region of the GreatLakes-St.-Lawrence river system �Bouchard andDomon 1997�. Remnant forest patches stand on mo-raine islets and morainic ridges, while cultivatedcrops are located in lowlands that are rich in marineclay deposits. Occasionally, biogenic deposits canalso be found �Pan et al. 1999; De Blois et al. 2001�.A major powerline right-of-way, brought into servicein 1978, crosses the study area �Mercier et al. 2001�.

A 4.0 m, four channel-multispectral �MSS� sceneand a single channel 1.0 m panchromatic �pan�IKONOS-2 scene with a spatial extent of 11�11 kmand a spectral range of 0.45 � 0.90 �m �Table 1�was acquired over this area on August 5, 2001. For

Figure 1. Study site map.

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the purpose of this study, the panchromatic image wasresampled �i.e., upscaled� from 1.0 m to 4.0 m tomatch the extent and spatial resolution of the multi-spectral channels. Resampling was performed withOSU, which is considered a robust upscaling tech-nique �Hay et al. 1997�. For this study a 4.0�4.0 km�1000�1000 pixels� subset was extracted from theoriginal 11 km scene �Figure 2�. In the following sec-tions the notation IKONOSall refers to all five chan-nels while IKONOSc refers to a specific channel, e.g.,IKONOSpan. All channels were included in the analy-sis.

The study site spatially represents a complex agro-forest scene composed of an agricultural matrix tex-tured with forest patches of varying size and shape�Figure 2�. Three dominant land-use classes, namelyAgriculture, Fallow land and Forest can be found inthe IKONOS images. In the true-color sub-image,white, blue and green-blue tones are visually associ-ated with rectangular shaped agricultural fields�marked ‘A’ in Figure 2a�. In the false color compos-ite agricultural fields are associated with red and blue�marked ‘A’ in Figure 2b�. Red represents variousstates of vegetation while blue corresponds to baresoil. Fallow land is a dynamic class that represents atransition from Agriculture to Forest �marked ‘Fa’ inFigure 2a, Figure 2b�. This category is apparent in thefalse color composite where faint pink corresponds tolimited vegetation cover and green tones representunder story and soil reflectance. Forest is associatedwith dark green colors in the true color image �Fig-ure 2a� and dark red tones in the false color compos-ite �Figure 2b� �marked with ‘Fo’ in 2a and 2b�.

Methods

The methodological framework developed in thisstudy integrates techniques from remote sensing and

mathematical morphology, with data analysis beingconducted in three main steps: 1� multiscale datasetgeneration within an iterative OSA/OSU framework,2� marker-controlled watershed segmentation to de-lineate image-objects, and 3� landscape feature iden-tification using automated classification. Each ofthese steps required the use of different methods andtechniques: OSA/OSU software were developed inIDL 5.5 �http://www.rsinc.com/idl�; marker-con-trolled segmentation was written in Matlab 5.1�http://www.mathworks.com� and classification, accu-racy assessment, and image analysis were performedusing ENVI 3.5 �http://www.rsinc.com/envi�. Each ofthese steps are described in the following sections.

Generating a multiscale dataset: Object-specificanalysis

Object-specific analysis �OSA� is a recent multiscaletechnique that defines unique spatial measures spe-cific to the individual image-objects composing a re-mote sensing scene �for a detailed description of thistechnique, see Hay et al. 1997; Hay et al. 2001�.These object-specific measures may then be used asweighting functions to representatively upscale�OSU� an image to a coarser resolution by taking intoaccount the spatial influence of the image-objectscomposing the finer resolution scene.

Object-specific analysis is based on threefundamental concepts:

1. an ‘image-object’ is a perceptual entity that visu-ally represents an object in an image composed ofsimilar digital numbers,

2. spatially near objects tend to be more alike thanspatially distant objects �Tobler 1970; Curran andAtkinson 1998�, and

3. all pixels within an image are considered as partsof the spatially corresponding image-objects theymodel. Consequently, parts of objects �i.e., pixels�are used to define the extent of corresponding im-age-objects that exist at their next �coarser� scales.

From an applications perspective, Hay et al. �1997�described an object-specific technique based on theobservation that when plotting the digital variance ofsamples �pixels� located within increasingly largerkernels while centred on an image-object of knownsize, the resulting plots tended to produce a curvewith a distinct break, or threshold in variance as the

Table 1. IKONOS spectral and spatial resolution.

Channel Spectral range �� Spatial resolution*�m2�

Panchromatic 0.45-0.90 1Blue 0.45-0.52 4Green 0.52-0.60 4Red 0.63-0.69 4Near IR 0.76-0.90 4

*Nominal resolution at � 26° off nadir.

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pixels than the smallest kernel can discern, its spatialcharacteristics cannot be defined.

Since the �¼� resampling heuristic describes howthe signal of real-world components are modelled bya sensor, we adopt it for automatically defining ap-propriate upscale resolutions in the following manner:

upscale_res = pixel_size + �pixel_size×min_win

×res_heur� �1�

Upscale_res represents the length �i.e., diameter�of the square upscale kernel defined in pixel units thatare equivalent to those of the original image �i.e.,IKONOSall�. Pixel_size initially is the value 1, whereit represents a single pixel �regardless of its spatialresolution� in the original image. Min_window repre-sents a value of 3, i.e., a 3�3 window, and in thisstudy, res_heur equals 0.20. Rather than using the ¼�i.e., 0.25� minimum as previously discussed, wechose to err on the side of prudence by over-samplingthe data with a 0.20 minimum. This approach

provided a larger number of multiscale image-setshaving a finer grain, and wider extent than if 0.25were used. It was also adopted by Hay et al. �2001�.

Based on Equation 1, the first upscale_res equals1.6 �i.e., 1 � �1�3�0.2��. That is, each pixel in thefirst upscale image has a grain equal to 1.6 pixels inIKONOSall. This represents a spatial resolution of 6.4m/pixel �i.e., 4 m�1.6 pixels�. The extent of this newupscale image is obtained by dividing the length ofIKONOSall �i.e., 1000 pixels� by 1.6, resulting in 625pixels.

To determine the upscale resolution for coarserscales, this process is iterated using upscale_res as thenew pixel_size. Consequently, the next upscale_resequals 2.56 �i.e., 1.6 � �1.6�3�0.2��. That is, at thesecond upscale iteration, a single upscale pixel is nowequivalent to 2.56 IKONOSall pixels – with a spatialresolution of 10.24 m/pixel �i.e., 4 m�2.56 pixels�,and an image extent of 391 pixels. When applied fortwo more iterations, the resulting upscale resolution,

Table 2. Image information and object-specific procedures for generating a multiscale data set

SDn�IStComponents

OSAt OSUn � 1 Upscale Resolution �OI pixels� Grain �m2� Extent �pixels2� # Pixels

SD1�OI

IS1= V1, A1, M1

IS2= V2, A2, M2

1.0 4.0 1000 1000000

1 4.0 1000 1000000

2 4.0 1000 1000000

SD2�IS3= V3, A3, M3

IS4= V4, A4, M4

1 1.6 6.4 625 390625

3 6.4 625 390625

4 6.4 625 390625

SD3�IS5= V5, A5, M5

IS6 = V6, A6, M6

2 2.56 10.24 391 152881

5 10.24 391 152881

6 10.24 391 152881

SD4�IS7= V7, A7, M7

IS8= V8, A8, M8

3 4.1 16.38 244 59536

7 16.38 244 59536

8 16.38 244 59536

SD5�IS9= V9, A9, M9

IS10= V10, A10, M10

4 6.55 26.21 153 23409

9 26.21 153 23409

10 26.21 153 23409

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and grain and extent of the upscaled images are de-fined in Table 2.

The result of this iterative object-specific analysisand upscaling approach is a nested hierarchy of im-age-sets �ISt� composed of VI, AI and MI that havemembership in a unique scale domain �SDn�, where nindicates the location of each scale domain within thenested hierarchy. Within each SDn, all images sharethe same grain and extent, and represent the result ofmultiscale analysis specific to the image-objectscomposing them. The combination of all SDn gener-ated from a single image/channel is referred to as ascale domain set �see Table 2�.

In this study, iterative OSA and OSU �in automaticmode� were individually applied to each of the fiveimages comprising IKONOSall. This resulted in fivescale domain sets. Due to the size limitations of thisdata set, processing was halted after five scaledomains were generated from each image. If upscal-ing were conducted several iterations further, wewould eventually end up with the study siterepresented by a single pixel with a 4000 m�4000 mspatial resolution. For each of the five scale domainsets generated, there are five scale domains �SD1-5�,each of which are composed of two image-sets. Andeach image-set is further composed of three images.Consequently, 150 images were automatically gener-ated to represent the evolution of this study sitethrough scale. Only even-numbered image sets wereused for further analysis, as they correspond to thebeginning scale of all newly emergent objects �Hayet al., 2001�. This reduced the working dataset to 75multiscale images. Processing of each scale domainset on a dual processor Pentium III 500 MHz com-puter with 512 MB of ram required approximately 13minutes.

Marker-controlled segmentation

Once a multiscale dataset has been generated, the re-maining problem to be solved is how to automaticallydelineate individual image-objects and identify themas they change through scale. To do so, an algorithmbased on the watershed transformation �Beucher etal., 1990� was used. In watershed analysis, an imageis viewed as a topographic surface, where bright pix-els represent peaks and dark pixels constitute valleys.More specifically, a peak corresponds to a localmaximum and a valley to a local minimum.

One of the appealing features of the watershedtransformation is that it provides closed contours

�Beucher and Lantuéjoul 1979�. Consider for a mo-ment that we pierce a hole in a topographic surfacewhere the minima �i.e., valley� are located. Whenwater is forced upwards into these valleys a floodingprocess begins. During this process, two or morefloods originating from different minima may merge.To prevent this, dams are erected between them. If thewater continues to flood until the image surface iscompletely covered, eventually, only the dams willremain. These dams define image watersheds byseparating the various catchment basins �i.e., minima��Figure 3�.

However, the standard watershed transformation isknown to produce an over-segmentation of an image.The minima responsible for this are often smallvariations due to noise and not to real image-objects.Filtering could reduce the influence of noise but isoften based on subjective decisions. To resolve theover-segmentation problem, Meyer and Beucher�1990� introduced the concept of marker-controlledsegmentation �MCS�. Marker-controlled segmenta-tion is a region-based technique that detects regionsimilarities as opposed to boundary-based techniquesthat detect local changes. Markers are used as spatialidentifiers �or ‘seed’� for significant image-objects�i.e., regions�. Instead of risking ‘piercing’ holes inthe topographic surface at the location of noise, holeswill only be pierced at the location of the markers.Flooding will then produce as many catchment basinsas there are markers. A common approach is to usethe regional minimum as the marker of image objects

Figure 3. Watershed transformation. In this example a single rowin a digital image is illustrated as a 1-D signal. Black boxes repre-sent grey-level values. R- represent regional minima from whereno descending path exists. R� represent regional maxima fromwhere no ascending path exists. Full vertical lines illustrate water-sheds. Dotted vertical lines represent watersheds caused by over-segmentation, i.e., noise. The white circles illustrate marker-controlled segmentation. The only minima considered by themarker-controlled segmentation process are those defined by thewhite circular markers. The resulting segmentation produces threeobjects illustrated as regions.

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�Beucher et al., 1990�. A point belongs to a regionalminimum if there exists no descending path startingfrom the same point. Similarly, a point belongs to aregional maximum if there is no ascending path start-ing from the same point.

The general procedure associated with marker-controlled segmentation �Beucher and Lantuéjoul1979; Meyer and Beucher 1990; Beucher 1992 andRivest et al. 1993� encompasses three principal steps.First, intensity variations in an image are enhancedwith an edge detector. This type of detector is oftenreferred to as a ‘gradient operator’, and the resultingimage as the ‘gradient image’. Second, a relevantmarker set is obtained and applied to this gradientimage. Third, watersheds are delineated from thiscombination of markers and edges.

In this study, MCS was implemented in the follow-ing way. Instead of haphazardly generating gradientimages for each scale �which would require the non-trivial task of determining the best filter type�s� andkernel size�s� for each scale of data�, each of the evennumbered Variance images �V2,4,6,8,10� automaticallygenerated by OSA/OSU were used as gradientimages. Within each SDn, the Variance image repre-sents a threshold image; it illustrates where edges ofdifferently sized objects have been reached. Brighttones correspond to high variance �edges� and darktones to object interiors �Figure 4�. Next, marker setswere automatically obtained from each Area image�A2,4,6,8,10� by using a regional-minima algorithm inMatlab.

Each marker set is essentially a binary image wheremarkers equal 1, and the background equals 0. Basedon how OSA/OSU is designed, these markersconceptually represent the centre of an image-object.To define each image-object, the appropriate markersets were ‘imbedded’ within the corresponding gradi-ent image. That is, the location of each marker set wasdefined within the appropriate gradient image using asimple logical operator. Thus, markers now representthe local minimum value within the correspondinggradient image. Next, the Matlab watershed algorithm�Vincent and Soille, 1991� was applied to each ‘im-bedded’ image. This resulted in the generation of 25watershed boundary images, each containing ‘empty’polygons. Only the boundaries �i.e., ‘dams’� separat-ing image-objects were generated with this algorithm.

With delineated image-objects in hand, the nextstep was to associate them with their correspondingspectral values. This process is called ‘object label-ling’. Recall that every pixel found in a Mean image

represents a member of a newly detected image-ob-ject. Because these images are generated from aver-age values calculated within specific threshold ker-nels, they represent the dominant image structuredefined at a specific spatial resolution within a uniquescale-domain �Hay et al. 2001�. Therefore, eachnewly defined – though empty – polygon was used asa mask, to generate a value equal to the average ofthe corresponding MI pixels within its perimeter. Inessence, each watershed polygon now spatially repre-sents the average grey-tone, and areal extent of aunique image-object. The output of this step repre-sents the automatic delineation of topologicallydefined multiscale objects for each of the five chan-nels in each of the five scale domains �MCS1-5�. Thus,25 newly defined MCS images were generated. Fig-ure 4 illustrates five MCS images produced from thepanchromatic channel. A complete description ofthese images is provided in the Results section.

Landscape feature identification

Now that multiscale image-objects have been delin-eated, the final step involves assessing their signifi-cance in terms of meaningful landscape features. Thisstep was performed using a semi-automated classifi-cation procedure commonly used in remote sensingthat involves: 1� a reduction of the data dimensional-ity, 2� the identification of the classification scheme,3� the selection of training and test pixels, and 4� theaccuracy assessment of the classification results.

Reducing data dimensionality

Correlation between adjacent remote sensing spectralchannels is often high, and the averaging operationsinvolved in OSU and MCS appear to further increasecorrelation. Thus, to reduce the dimensionality of thedata while preserving the information content�Mather 1999�, principal component analysis �PCA�was applied to all five MCS1 images as a separategroup. This was because they shared the same spatialresolution, and resulted from the five spectrally cor-related IKONOSall channels. PCA was then appliedin the same manner, to all five MCS2-5 images, eachas separate groups depending upon their spatial reso-lution. This produced 25 new PCAMCS images. PCAwas then applied to the five IKONOSall channels re-sulting in five new PCAIKONOS�all� channels. PCA is amathematical procedure that transforms a number ofcorrelated variables into a smaller number of uncor-

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related variables called ‘principal components’ thataccount for the majority of the variability in thedataset. The first three principal components fromeach of the five PCAMCS image groups, and the fivePCAIKONOS�all� images were then selected for furtherprocessing, after an analysis of eigenvalues indicatedthat they contained more than 98% of the initial vari-ability of the assessed data. This step reduced the to-tal number of original MCS images from 25 to 15 andIKONOSall from five channels to three.

Defining a classification scheme

To create the classification scheme, three dominantobject categories �land-cover types� were identified,namely Agriculture, Fallow land and Forest. Agricul-ture was then divided into four sub-classes, Fallowland into three sub-classes, and Forest into four sub-classes �Table 3�. Each sub-class was delineatedbased on their visual appearance in the true color andfalse color IKONOS image �Figure 2a,b� and theircorresponding normalized difference vegetation index�NDVI� values. The NDVI is an image transforma-tion based on the following formula �Near-infraredchannel – red channel/Near-infrared channel � redchannel� and is related to the proportion of photosyn-thetically absorbed radiation, i.e., vegetation cover�Jensen 1996�. Here the index was used only to aid inthe discrimination of training and test samples.

All classes extracted from IKONOSall were in-spected to ensure spectral separability in an n-dimen-sion visualizer �using ENVI�. When distinct spectralclasses were obtained, they were used as training ar-eas for the classifier. Additional test pixels were alsoselected for accuracy assessment. Test pixels andtraining pixels were collected at different locations to

ensure spatial variability and valid statistical compari-son. The number of training and test pixels were es-timated according to 30p, where 30 is the minimumsample size per class and p is the number of channels�Mather 1999�.

A separate supervised maximum likelihood classi-fication was performed on the three PCAMCS imagesfor each of the five scale domains, and a single maxi-mum likelihood classification was also performed onthe three PCAIKONOS�all� images. This resulted in sixclassification maps, one for IKONOSall and one foreach scale domain. The same training and test areas�defined in IKONOSall� were used for every scale do-main, thus enabling a comparison of how class defi-nitions changed through scale. Accuracy assessmentwas conducted using the standard procedure de-scribed by Congalton and Mead �1983�, where testpixels were compared to the classification results andconfusion matrices were produced.

Results

The results are presented in two main sections. Thefirst is a detailed description of the multiscale datasetsgenerated with OSA/OSU, and the images producedwith MCS. Due to the large number of images gen-erated, and the need for simplicity in illustration, onlya 920 m�920 m subset of the panchromatic channelis displayed and discussed �Figure 4�. This channelwas chosen as it covers the spectral range ofIKONOSRGB, while also falling within the range ofhuman vision. The second section presents the clas-sified images �Figure 5� and explains their accuraciesthrough scale, based on their confusion matrices�Figure 6�.

Table 3. Description of dominant landscape features.

Class Description NDVI Density False color

Agriculture1 Non vegetated � 0.6 – Light blueAgriculture2 Cropland 0.4 – Orange/greenAgriculture3 Cropland, sparsely vegetated � 0.2 – Light blueAgriculture4 Cropland 0.4 – OrangeFallow1 Fallow land, deciduous trees 5-20 m 0.1 Low Dark greenFallow2 Fallow land, herbaceous � 0.1 – Blue/greenFallow3 Fallow land, shrub 0 – Light greenForest1 Deciduous foliage 0.5 Medium Brownish redForest2 Deciduous foliage 0.5 Low Light redForest3 Deciduous foliage 0.7 High Dark redForest4 Deciduous foliage, big tree shadows 0 Low Dark red/black

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data� using nearest neighbour resampling as this doesnot change the actual digital values �Jensen 1996�.

In every VI, �Figure 4� bright areas �high variance�represent edges �the meeting of two or more image-objects�, while dark areas �low variance� correspondto image-object interiors. In each AI, bright values in-dicate that the pixel under analysis belongs to an ob-ject that comprises a large area, while dark valuesrepresent a small area. In the Mean images, each pixelis a member of �thus an averaged value of� a new im-age-object existing at this new scale. Thus each MI

appears blurred or more diffuse through scale. In eachMCS image, all image-objects are labelled withunique grey tone values derived from the correspond-ing MI within explicit boundaries. Consequently,fewer and larger, more homogeneous polygons appearas scale increases.

The image-set generated at SD1 has an extent of1000�1000 pixels and a grain of 4 m. The large

amount of bright pixels in V2 indicates that manyedges have been defined, thus the majority of image-objects in the scene are small in size, though severallarge dark objects do appear on the image �bottomright and bottom left�. These low-variance objects arepredominantly fallow and agricultural fields. Thecenter of the utility line corridor is also visible as adark linear feature bisecting the top left of the image,while its edges, which are adjacent to agriculture andforest are bright toned due to the variation implicit atthe interface of these different object classes. A largenumber of small image-objects are further evident inA2 as the predominantly dark values indicate manyobjects composed of small areas. Interestingly, therelatively homogeneous fields noted in V2 look highlytextured in A2. Specifically, the interior of these fieldsappears homogeneous �dark� in A2, while the edgesof the fields are more variable due to their interactionwith neighbouring fields, fences, hedgerows, etc. At

Figure 6. The evolution of classes through scale based on classification accuracy.

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this scale domain, the Mean and MCS images appearvisually similar. In both cases, Forest appears less de-tailed and more coarse-textured than the original im-age; however, some of the dark Forest patchesobservable �top right and image center� are accentu-ated. Fallow land is perceived as bright flat patches.

At SD2, visual detail has begun to decline as grainhas increased to 6.4 m and the number of pixels hasbeen reduced to 625�625. In V4 and A4, new ‘edges’visually emerge of which only few were observablein SD1. This is particularly evident in the fields lo-cated at the bottom right of the sub-image. The Meanimage �M4� continues to appear more diffuse and inMCS2, image-objects have coalesced into fewerlarger structures. For example, the rectangular shapedagriculture fields of SD1 now appear as new irregularshaped objects. Many field boundaries are no longervisible, and new edge structures appear in their place.The dark forest patches previously mentioned appeareven darker and more homogeneous in M4, althoughMCS2 reveals that numerous structures still persistwithin those dark patches. The majority of the Fallowland is not identifiable without prior knowledge of thesite, though it still persists as bright flat areas.

At SD3, the grain has coarsened to 10.24 m and theimage extent is 391�391 pixels. All linear structureshave disappeared and nearly all small image-objectshave merged into larger structures. Landscape fea-tures, as we know them, e.g., Agricultural fields, haveessentially vanished and new forms have emerged.The variance and area images �V6 and A6� reinforcethis observation. In M6, the only obvious imagestructures are bright peaks �Fallow� and dark valleys�Forest�. In MCS3, spatially discrete areas appear toconnect across the image. This is apparent around thedark Forest patch in the image center, where a lighterobject has emerged. A similar tendency is noticed be-tween the two dark Forest patches at the top of theimage. There are no remaining structures that repre-sent the utility line corridor at this scale domain.

At SD4, the grain has increased to 16.38 m and theextent has been reduced to 244�244 pixels. The mainvisual patterns of SD3 have persisted, and in some re-spect appear strengthened. At the top-right corner ofM8 and MCS4, the two dark Forest patches visible inM6 and MCS3 have merged into one. In addition, thedark patch in the image center persists and has be-come surrounded by a ‘circular ridge’ of brightergrey-scale patches. In A8, there are less dark patches,indicating the presence of a few large image-objects.In general, there are six patches in M8 and MCS8 that

can be recognized within the original image. Three ofthem are primarily Forest �dark tone� and the otherthree are Agriculture �bright tone�. A significant vi-sual change is evident between A6 to A8, the latterimage indicating an increase in the size of the image-objects.

At SD5, the grain has increased to 26.21 m, and thenumber of pixels has decreased to 153�153. In gen-eral, the images of this scale domain are visually di-vided into distinct regions, composed of large objects�A10�. In comparison to the objects at SD2 it is appar-ent that not only the very dark and bright objects havepersisted through all scale domains, but more impor-tantly, those that represent a spatially large footprintupon the landscape. In-between these persistent ob-jects, smaller objects emerge and vanish at a higherfrequency.

Classification images and confusion matrices

Six classification images of the study site as it evolvesthrough scale are illustrated in Figure 5. SDO repre-sents the classification result conducted on IKONOS-

all, while the other five represent each of the scaledomains �SD1-5�. The general trend of these resultsconfirms those described for OSA/OSU, namely thatlarger structures form at the expense of smaller struc-tures as we move through scale. In addition, theseclassification results reveal an important shift in classmembership, particularly near the center of the imagewhere Forest shifts to Fallow and Agriculture. Over-all, these results indicate that landscape configurationand land cover considerably change as we movethrough scale.

SDO represents the ‘truth’ or reference image. Thatis, it forms the basis upon which the other classifica-tion images are evaluated. For more in-depth resultsof each class, confusion matrices have been summa-rized in a bar diagram for each class and scale do-main, enabling a graphical analysis of how classesemerge, persist and disappear through scale �Figure6�. We note that the overall classification accuracy isrelatively high, ranging from 68% to 89%, with anaverage slightly above 82%. This high accuracy �lowconfusion� is visually perceived as a relativelyuniform first bar for all classes. As we move throughscale �i.e., SD1-5�, some bars are partitioned, indicat-ing the emergence of another class.

In general, the classification accuracy for each Ag-riculture class in SDO is very high �85%�, with asmall amount of confusion �5-9%� between Agricul-

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ture2 and two Forest classes. Fallow classes are lessaccurate with �20%� confusion between Fallow1 andtwo Forest classes. The other source of error �45%� isbetween Fallow2 and Fallow3. Agricultural classesare well represented with the main errors being be-tween other Forest and Fallow classes. This is due tothe fact that some Fallow classes �1 and 3� includesparse shrub/forest vegetation.

In Figure 5, SD1 classes visually appear morehomogeneous than those of SDO and represent a 4%increase in overall accuracy �89%�. Small groups ofpixels are absorbed within dominant objects thus re-ducing error. Forest and Fallow land are spatiallydominant while Agriculture appears more dispersed.Forest dominates the top of the scene, Fallow landdominates the center of the scene, and Agriculture isconcentrated at the bottom. Overall, the classified im-age appears very similar to SDO. In Figure 6, all Ag-riculture classes are well defined, with a small amount�5%� of Fallow3 misclassified as Agriculture1.Fallow1 has not changed, however there still exists aproblem with Fallow2 and Fallow3, suggesting thatthese two classes could be combined. Forest classesare also well represented with 10% error in Forest3due to miss-classified Forest4 and an 18% error inForest4 due to Fallow1 �Figure 6�.

In Figure 5, the visual pattern of SD2 considerablychanges from SD1, becoming increasingly texturedwith Agriculture and Fallow classes. In part, this isdue to the fewer number of pixels resulting from up-scaling to a new scale domain, but also to the spatialvariation of these classes. Agricultural classes stilldominate the lower section of the image, but have in-creased around the image center. The previous Forestclass at the top left of the image has changed to Fal-low, and those Forest classes that do exist have re-ceded almost exclusively to the left of the image. TheAgriculture classes are still well classified �Figure 6�,and there is an improvement in Fallow1 and Fallow2;however, the largest errors are reported in Forest4,which has been reduced to an accuracy of 28%. Themajority of the error is due to Fallow2 �45%� andFallow3 �20%�.

In SD3, Fallow land increases around the centerand the left portion of the image, while Forestre-emerges in the top-right image but is reduced al-most everywhere else �Figure 5�. Agriculture be-comes more consolidated into two primary classes�Agriculture1 and 4� located in the lower portion ofthe image. The impression of the landscape in SD3 isno longer that of a forested landscape. This land-

cover change is plainly visible in the error informa-tion shown in Figure 6. All agricultural classes arestill well classified, though the primary confusion isbetween Agriculture3 and 4, and Fallow3 �10%� andFallow2 �17%� in Agriculture3. The Fallow classesshow serious problems. Fallow1 – which containslarge trees �see Table 1� – is confused with Forest1,and Fallow2 is completely composed of Fallow1�3%�, Fallow3 �90%�, and Agriculture3 �7%�. Impor-tant changes have also occurred within the Forestclasses. Forest1 is miss-classified as Agriculture3�45%�, and Forest4 is composed of Fallow1 �15%�,Fallow2 �47%�, Agriculture3 �6%�, and Forest2 �3%�.At this scale domain, the Forest contribution to thevisible landscape structure is at its lowest.

In SD4, Forest expands in the left portion of theimage �Figure 5� and persists �from the previous scaledomain� in the top-right of the scene. Fallow classescontinue to dominate the center of the image, andAgriculture remains dominant in the lower portion ofthe landscape. In Fig 6, Agriculture1-3 shows seriouserrors that are represented by an increase ofmiss-classified Fallow2 and Fallow3. Errors in theFallow classes tend to be within themselves exceptfor small appearances of Agriculture2, Agriculture3,and Forest1.

SD5 represents a very different scene than any ofthe previous classified images. The Forest classes inthe top-left and top-right of the image have persistedand expanded �Figure 5�. Fallow land has decreasedand becomes concentrated into several large patcheslocated primarily in the image center and at the rightof the image. A single Agriculture class �Agricul-ture4� has grown to dominate nearly the entire lowerquarter of the image. Error results are similar to thoseof SD4 �Figure 6�, with the principal confusion beingFallow land incorrectly classified as Agriculture �i.e.,65% Fallow2 as Agriculture3�, Agriculture incor-rectly classified as Fallow �i.e., 25% Agriculture3 inFallow3�, and Forest classified as Fallow �i.e., 15%Fallow1, and 23% Fallow2 as Forest4�. When com-pared to the other classified images, nearly all thesmall structures have been removed and only largerobjects dominate the landscape.

Based upon a visual analysis of the classificationresults as they appear in Figure 6, the largest errorsin the Agriculture classes result from being incor-rectly classified as Fallow – particularly Fallow2 andFallow3. In the Fallow classes, the most common er-rors are those resulting from a misclassification be-tween Fallow2 and Fallow3, and Agriculture1 �i.e.,

14


25% in Fallow3� and Agriculture3. In the Forestclasses, the principal errors arise from Forest beingmisclassified as Fallow land and small amounts ofAgriculture3.

Discussion

The general trend of image-objects through scale�Figure 4� reveals that neighbouring image-objectstend to coalesce into new objects, with the larger im-age-objects �not necessarily the brightest or darkest�persisting through scale at the expense of theirsmaller constituents. In addition, a number of image-objects tend to persist within one or two scaledomains, and then suddenly disappear at the next do-main. This is apparent in SD1-2 where the utility linecorridor �linear feature bisecting the top left of theimage� is plainly visible then abruptly disappears inSD3. The opposite observation can also be made. Thatis, several structures emerge at specific scale domainswhere they did not exist before. This is evident inMCS5 where a long light coloured diagonal object�ranging from the bottom right of the image to themiddle left� composed predominantly of Fallow landsand Agricultural fields does not exist in MCS4. Wesuggest that these types of results are related to sud-den shifts in the entire image structure at certain scaledomains, which may correspond to the detection ofcritical landscape thresholds.

Detecting critical landscape thresholds withOSA/OSU

To better understand if a critical landscape thresholdhas been reached, and to more fully appreciate thescale dynamics that are illustrated in Fig 4, we haveplotted the total scene variance of the Variance im-ages, and the average of the Area, Mean and MCSimages resulting from OSA/OSU being applied toIKONOSpan over SD1-5 �Figure 7�

The total scene variance represents the overall dif-ference in the variation resulting from the individualimage-objects composing a scene, through all possi-ble object-specific scales of analysis �Hay et al.2001�. This procedure corresponds to defining asingle measure of variance for each of the VI �instandard deviations� per scale domain, and thengraphing their combined results �see Figure 7�.Essentially, this is scale variance analysis as de-scribed by Moellering and Tobler �1972� and local

scene variance as described by Woodcock andStrahler �1987�, but adapted and applied within anobject-specific framework. Here, the primary differ-ence is that we define a measure of variance for each�odd numbered� variance image, while in the previ-ous references the measures of variance are extractedfrom the original data sets.

In Figure 7, total scene variance for SD1 is high,indicating that the landscape �IKONOSpan� is com-posed of many different image-objects. At SD3, vari-ance is the lowest, thus from an object-specificperspective, a minimum variance threshold has beenreached, indicating that this scene represents the be-ginning of a new ‘landscape-object’. While at SD5,variance has increased – though due to data limita-tions it is not possible to determine if it has reached amaximum – suggesting that the images composingSD4-5 are still part of the new landscape object thatwas detected at SD3. This interpretation is based onhow image variance is used to detect object-specificthresholds, where pixels are part of image-objects. Inthe case of total scene variance, the entire scenethrough scale appears to be part of a largerlandscape-object that exists beyond the extent definedby the image. In Fig 4, this change in variance at SD3

is plainly visible in M6 when compared to M4, sug-gesting that a critical landscape threshold, as de-scribed in Hierarchy theory �Alan and Starr, 1982�has been reached at SD3�. Therefore, it would be fea-sible to directly upscale this image from SD1 to scalesdefined at SD3, but not from SD1 to SD5, as doing sois likely to result in significant scaling errors due tothe nonlinear changes that occur by crossing criticalthresholds as discussed by Gardner et al. �1982� and

Figure 7. Total scene information content through scale. Statisticsis derived from the area �AI�, mean �MI�, variance �VI�, andmarker-controlled segmentation �MCS� images. To better under-stand the total scene variance and corresponding landscape struc-ture through scale, the values are modeled by a high orderpolynomial curve �Poly. �VI��.

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King �1990� �see Hay et al. 2001 for detailed discus-sion.

Is information content conserved through scale eventhough visual patterns change?

The MI at each scale represents the source fromwhich unique object-specific information is obtained.Therefore, we suggest that the plotted average of eachMI depicts the overall ‘information content’ of theentire scene through scale �Figure 7�. In particular, wenote that these plotted MI values remain essentiallyconstant through each SDn, though we recognize thatthere is a slight decline �less than one half of one per-cent� between SD1-5, which we attribute to roundingerrors during OSU/OSA processing. Therefore, wesuggest that the OSA/OSU methodology is capable ofconserving the average information content throughscale even though the spatial distribution and classmembership of image-objects change through scale,as do the grain and extent by which they are mod-eled.

The average value calculated for each MCS imagethrough each SDn are also relatively stable, howeverthey are lower than the corresponding MI values. Thisis expected, because they represent averaging, thusgeneralization over larger areas which tend toincrease in size with an increase in scale-domain pro-cessing. This trend is supported in the plot of the AI,where the average area values increase through scale,and the number of unique image-objects decreases.This decrease in the number of image-objects is alsovisible in the MCS images in Figure 4, as well as theclassification maps of Figure 5.

Since the average information content of the entireimage is maintained through each SDn, this furtherstrengthens the validity of using an object-specificweighting scheme for upscaling. This is because the‘object information’ or influence of image-objects atone scale is ‘embedded’ or hierarchically integratedwithin the structure of the objects at coarser scales�i.e., conservation of information through scale�. ThusOSA/OSU effectively models the hierarchical struc-ture of the landscape from a bottom up approach.

Hierarchical scale manifolds vs. a scaling ladder

While discrete levels or SDn have been generatedwhere each image in these sets has the same grain andextent, the size of the window used to determine thespatial characteristics of individual image-object are

of varying size. Thus, while it is simple to imaginehow the images in Figure 4 may be hierarchicallylayered upon each other in a manner similar to the‘scaling ladder’ conceptualized in the HPDP �Wu1999�, the reality is that in object-specific analysis the‘spaces’ between the rungs of the ladder – which re-present the ‘optimum’ scale of analysis – are notequal. Instead, they are of varying size, dependentupon the spatial characteristics of the object underanalysis. Consequently, there should be a separateladder for each image-object through scale. If thiswere the case, then it would be more plausible to vi-sualize the hierarchical levels as stacked 2.5 dimen-sional layers or manifolds as modeled by Hay et al.�2002b�.

Conclusion

Landscapes are complex systems that are composedof a large number of heterogeneous components thatinteract in a non-linear way, are hierarchically struc-tured, and scale dependent. To more fully understandthe processes behind such complexity we need mul-tiscale methods and theory that will allow us to visu-alize and link the spatial patterns, and interactions ofdominant landscape components through scale.

In an effort to reach this goal, we report on an in-novative ‘proof of concept’ that comprises anintegration of object-specific analysis, object-specificupscaling, and marker-controlled watershed segmen-tation applied to fine spatial resolution satellite data�Figure 2�. The result of this integration is a multi-scale approach capable of automatically detecting andlabeling spatially dominant landscape objects at theircorresponding scale�s� of expression �Figure 4�. Inorder to associate meaning to these labeled objects sothat they can be evaluated through scale, a standardsupervised classification is applied to the first threeprincipal components of the marker-controlled seg-mentation images generated at each scale domain.The resulting images �Figure5� indicate that a num-ber of landscape objects persist within one or twoscale domains and then disappear, while others sud-denly emerge at other scales. The classification results�Figure 6� also reveal a considerable shift in classmembership as we move through scale, indicatingthat each scale domain represents a particular land-scape configuration. When the information content ofthe entire landscape �i.e., full image� through scalewas investigated, a critical threshold was detected at

16


scale domain three �Figure 7�. Overall, these resultsare in accordance with the concepts developed in Hi-erarchy theory and the Hierarchical patch dynamicsparadigm that describe a landscape as being com-posed of different levels of organization where eachlevel operates at distinct scales.

Visual interpretation of the upscaled images andthe classification results from the first two of fivescale-domains correspond to our expectation of theimage-objects composing the original IKONOS im-ages. Therefore, a precedent exists upon which to as-sess OSA and OSU results at coarser scales where wehave no experience i.e., SD3-5. We also note that theOSA/OSU framework is capable of conserving theaverage information content of a scene through scale,even though the spatial distribution, class member-ship, and grain and extent of image-objects changethrough scale.

In this study, we have reported on the use of anobject-specific framework applied to high-resolutionIKONOS data; however, an object-specific approachcan be applied to data of any spatial resolution. Thisis because, implicit to the object-specific approach, isthe condition that ‘all pixels within an image areconsidered as parts of the spatially correspondingimage objects they model’. Thus, the user must beaware that the types of image-objects that will be de-fined are based on the relationship between pixelgrain, the size/shape of the analyzing kernel�s�, andthe size of the image-objects composing the fixed ex-tent of the image/scene. If coarse grain data are usedbthen relatively coarse grain image-objects will bedelineated.

This study represents one of the first attempts todevelop an operational approach to automatically de-lineate dominant landscape features at their character-istic scales of expression, and to assess how theyevolve through scale. Such a realization has beenidentified as a primary goal in Landscape Ecology forat least a decade �Turner et al. 1989�, and along withother scale and scaling issues remains an importantand challenging field of research today �Wu andHobbs 2002�. We envision that as different resolu-tions of imagery are evaluated within an object-spe-cific framework �Hall and Hay 2003�, our understand-ing of landscape processes through scale will beenhanced, along with our ability to define criticallandscape thresholds, domains of scale and theappropriate scale�s� at which object-based ecologicalmodels should be applied.

Acknowledgements

This research has been supported by a team grantfrom FCAR, Gouvernement du Québec, awarded toDr André Bouchard and Dr Danielle Marceau, by aMarc Bourgie Foundation Ph.D. scholarship and aBiology graduate scholarship of excellence from theUniversity of Montreal awarded to Dr Geoffrey Hay,by a grant awarded to Dr Hall by the Swedish Foun-dation for International Cooperation in Research andHigher Education and a scholarship from the Foun-dation for Strategic Environmental Research �MIS-TRA�. We also wish to express appreciation to twoanonymous referees for their constructive comments.

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