Landscape Ecology 16: 471–490, 2001.© 2001 Kluwer Academic Publishers. Printed in the Netherlands.

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Research Article

A multiscale framework for landscape analysis: Object-specific analysisand upscaling

G.J. Hay1,∗, D.J. Marceau1, P. Dube1 and A. Bouchard2

1Geocomputing Laboratory, Department de geographie, Universite de Montreal, C.P. 6128, succursaleCentre-Ville, Montreal, Que, Canada, H3C 3J7; 2IRBV, Universite de Montreal, Jardin Botanique de Montreal,4101 Sherbrooke Est, Montreal, Que, Canada. H1X2B2; ∗Author for correspondence (Tel: (514) 343-8073; Fax:(514) 343-8008; E-mail: ghay@sympatico.ca)

Received 15 October 1999; Revised 10 April 2001; Accepted 5 April 2001

Key words: domains of scale, image-objects, landscape thresholds, MAUP, multiscale, object-specific analysis,OSA, OSU, remote sensing, scale, upscaling

Abstract

Landscapes are complex systems that require a multiscale approach to fully understand, manage, and predicttheir behavior. Remote sensing technologies represent the primary data source for landscape analysis, but sufferfrom the modifiable areal unit problem (MAUP). To reduce the effects of MAUP when using remote sensing datafor multiscale analysis we present a novel analytical and upscaling framework based on the spatial influence ofthe dominant objects composing a scene. By considering landscapes as hierarchical in nature, we theorize howa multiscale extension of this object-specific framework may assist in automatically defining critical landscapethresholds, domains of scale, ecotone boundaries, and the grain and extent at which scale-dependent ecologicalmodels could be developed and applied through scale.

Introduction

To better understand, manage, and predict the be-havior of the complex systems that provide life onearth, we require an improved understanding of thescale-specific interactions responsible for landscapemetabolism (Levin 1992), robust techniques for vi-sualizing and deciphering multiscale processes frompatterns (Turner et al. 1991), and appropriate scalingstrategies for linking and modelling data at multi-ple scales (King 1990; Ehleringer and Field 1993).To assist landscape ecologists in these tasks modernremote sensing technologies provide multi-resolutiondata sources for analysis and hypothesis testing overboth large and small areas, and hierarchy theory pro-vides a useful analytical framework for describing thelandscape’s composition within these scenes.

According to hierarchy theory, ecological sys-tems are considered as ‘nearly decomposable’ hier-archically organized entities resulting from (different)

structuring processes exerting their influence over de-fined ranges or domains of scale (Allen and Starr1982; O’Neill et al. 1986; Holling 1992). Concep-tually, the decomposability of these systems impliesthat their analysis and understanding can be enhancedby organizing their numerous components into fewerdiscrete, interactive units at different levels based ondifferences in process rates (O’Neill et al. 1989; King1999). When these ideas are considered in relation tothe spatial, spectral, temporal, and radiometric prop-erties inherent to remote sensing data (Marceau andHay 1999a), the keys to fully unlock the complex re-lationships between scale-specific landscape patternsand processes appear close at hand. For example,Moody and Woodcock (1995), Benson and MacKen-zie (1995), O’Neill et al. (1996), and Pax-Lenneyand Woodcock (1997) describe the influence of remotesensing resolution on detecting landscape patterns andprocesses. Bian and Walsh (1993), Souriau (1994)and Walsh et al. (1997) discuss the identification of

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Table 1. List of general terms and abbreviations.

AVHRR Advanced very high resolution radiometer

AVIRIS Airborne Visible Infra-Red Imaging Spectrometer

C.Cut Clear-cut

CASI Compact Airborne Spectrographic Imager

CCD Charged-couple device

DNs Digital numbers or gray-scale values

FPAR Fraction of photosynthetically active radiation

HPDP Hierarchical Patch Dynamics Paradigm

H-res High resolution

IFOV Instantaneous field of view

LAI Leaf area index

L-res Low resolution

MAUP Modifiable areal unit problem

MODIS Moderate-resolution Imaging Spectroradiometer

PSF Point-spread function

RMSE Root mean square error

SPOT Satellite pour l’Observation de la Terre

TM Landsat Thematic Mapper

landscape scale-thresholds and domains of scale asviewed in remotely sensed data. Caldwell et al. (1993),Ustin et al. (1993), Friedl et al. (1995), Cullinan et al.(1997), DeFries et al. (1997), and Stewart et al. (1998)describe the challenges of scaling remote sensing dataand the implementation of multiscale approaches forecosystem models.

In addition to the remote sensing platforms morefamiliar to landscape ecologists such as AVHRR⊗ ,TM⊗ and SPOT⊗, lesser-known hyperspectral air-borne sensors like CASI⊗ and AVIRIS⊗ have been inoperation for over a decade providing unique oppor-tunities to diagnostically examine landscape patternsand processes at very fine spatial and spectral scales(Wessman et al. 1989). These sensors allow for thediscrimination of landscape structures that are absentin coarser imagery, thus providing opportunities tolink field data with patterns at much coarser scales(Treitz and Howarth 2000). They also serve as ex-cellent test-beds for conducting fine-scale landscapeanalysis in preparation for data available from thenew high-resolution satellites such as Ikonos (with itscommercially available 1 m2 panchromatic and 4 m2

multispectral channels), MODIS⊗ (with its 36 co-registered channels ranging from 250 m2–1 km2), andHyperion (launched in November, 2000 with a capac-

⊗See Table 1.

ity to acquire 220 spectral bands (from 0.4 to 2.5 µm)at a 30 m2 spatial resolution).

It is becoming increasingly apparent that in orderto fully understand the complexity of landscape dy-namics we require the ability to recognize broad-scalepatterns and processes, and relate them to those at finerscales where we are most familiar (Wu and Qi 2000).These high-resolution sensors provide critical data andperspectives that will assist in bridging this knowledgegap.

While remote sensing data hold great promise, it isalso important to recognize their limitations. In partic-ular, all remote sensing data represent a unique formof the modifiable unit areal problem or the MAUP (fora comprehensive review see Marceau 1999). Thoughthe importance of MAUP has previously been notedin landscape ecology (Jelinski and Wu 1996), its rela-tionship to remote sensing data remains poorly recog-nized and understood (Wu et al. 2000). In particular,the effects of MAUP can be especially devastatingduring scaling, where arbitrarily extrapolating site-specific measurements to coarser scales can result insubstantial error (Gardner et al. 1982; King 1990).Thus the ramifications for inappropriately using re-mote sensing data to understand multiscale landscapepatterns/processes are profound. This is especially rel-evant in landscape ecology, where multiscale studiesare increasingly conducted (Wu and Qi 2000), andwhere land-cover classifications generated from satel-lite imagery are frequently used to characterize theecology of large areas and to make generalizationsabout the distribution of species and communities(Townsend 2000).

The primary objectives of this paper are to de-scribe a novel approach for analyzing and upscalingremotely sensed data, and a multiscale extension tothis approach, both of which are based on the spa-tial influence of the dominant objects composing thescene, rather than relying solely on user bias. Thesenovel approaches incorporate object-specific analysisand solutions to the MAUP. Together they representa framework for spatially defining critical landscapethresholds and domains of scale, ecotone boundaries,and the grain and extent at which scale-dependentecological models could be developed, and applied.

Theoretical background

The following two sections briefly provide a theo-retical background on scale, scaling, the relationshipbetween remote sensing imagery and MAUP, and the

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fundamentals of object-specific analysis and object-specific upscaling, and their relationship with otherscaling techniques.

Scale, scaling, remote sensing imagery and MAUP

Conceptually, scale represents the ‘window of percep-tion’, the filter, or measuring tool with which a systemis viewed and quantified. As scale changes, so do theassociated patterns of reality, which has obvious im-plications for understanding any organism, place, orsystem. An important characteristic of scale lies inthe distinction between grain and extent. Grain refersto the smallest intervals in an observation set, whileextent refers to the range over which observations ata particular grain are made (O’Neill and King 1998).Within a remote sensing context, grain is equivalentto the spatial resolution of the pixels composing animage, while extent represents the total area that animage covers.

Associated with multiscale analysis is the termdomain of scale (or scale domain). This refers to aregion of the scale spectrum over which, for a partic-ular phenomenon, patterns do not change or changemonotonically with changes in scale. Such domainsare separated by scale thresholds - relatively sharptransitions or critical points along the spatial scalecontinuum where a shift in the relative importance ofvariables influencing a process occur (Meentemeyer1989; Wiens 1989).

To analyze objects, or entire scenes at differ-ent scales, and to utilize information between thesescales, appropriate scaling methods are required. Scal-ing refers to transferring data or information fromone scale to another. It requires the identification ofthe factors operational at a given scale of observa-tion, their congruency with those on the lower andhigher scales, and the constraints and feedbacks onthose factors (Caldwell et al. 1993). As noted by Jarvis(1995), scaling represents a real challenge because ofthe non-linearity between processes and variables, andheterogeneity in properties that determines the ratesof processes. In practice, scaling can be performedfrom a ‘bottom-up’ or a ‘top-down’ approach: upscal-ing consists of using information at smaller scales toderive information at larger scales, while downscalingconsists of decomposing information at one scale intoits constituents at smaller scales.

Allen and Hoekstra (1991) suggest that scale is nota property of nature alone but rather is something as-sociated with observation and analysis, and that the

scale of a process is fixed only once the observer hasspecified the actors in the system. So what happenswhen the scale of observation is arbitrarily derived, asis the case with remote sensing data? Quantificationproblems resulting from such arbitrariness are knownas the modifiable unit areal problem or the MAUP(Openshaw and Taylor 1979; Openshaw 1981).

The MAUP originates from the fact that a sig-nificant number of different – often arbitrary – waysexist by which a study area can be divided into non-overlapping areal units for the purpose of spatialanalysis. In essence, the MAUP represents the sen-sitivity of analytical results to the definition of datacollection units, and is illustrated by two related butdistinct components: the scale problem and the aggre-gation problem. The former is the variation in resultsthat can be obtained when areal units are progres-sively aggregated into fewer, larger units for analysis;the latter represents the variation in results gener-ated by the use of alternative aggregation schemes atequal or similar resolutions (Openshaw 1984). Con-sequently, the potential for error in the analysis ofspatial data resulting from MAUP is significant, andhas been recognized in a number of studies (Dudley1991; Fotheringham and Wong 1991; Hunt and Boots1996).

Marceau (1992) was among the first to demon-strate that remote sensing data represent a particularcase of the MAUP. In a remote sensing scene, an imagemay be envisioned as a regular net arbitrarily thrownover a study area where the grain and extent of themesh define the areal units measured (Figure 1). Morecorrectly, each pixel represents an integrated radiancemeasure corresponding to the spectral, spatial, tempo-ral, and radiometric influence of the real-world objectswithin the area delineated by the instantaneous fieldof view (IFOV) of the sensor (Duggin and Robinove1990). IFOV determines how much of the ground areathe sensor ‘sees’ at any given instant in time. This re-sults in three general situations: the ground featuresof interest are smaller than, approximately equal to, orlarger than the spatial sampling unit. It should be notedthat within a single image, each of these samplingcombinations are possible, and in fact very probable.In the first situation, this type of image is referred to aslow resolution or L-res, in the second and third cases,as high resolution or H-res (Woodcock and Strahler1987). Consequently, every image is characterized bya scale and aggregation level, which determines itsstructure and information content. Recognizing this iscritical for determining what information can be ex-

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Figure 1. The relationship between grain and extent in remote sensing imagery.

tracted from an image, and how reliable it is (Marceauet al. 1994).

Fortunately, several solutions to MAUP have beensuggested (Fotheringham 1989). In particular we notetwo important concepts related to these solutions.First, the MAUP does not exist if analysis is performedwith basic entities. The term basic entity refers to anobject composed of similar parts that are different thanitself. For example, if we consider a tree-crown as abasic entity, conceptually it may be composed of, oris an aggregate of leaves, and branches, each of whichindividually belongs to classes that are themselves, ba-sic entities. Thus, identifying basic entities providesthe clearest way out of the MAUP, as a user works withspatially discrete entities rather than arbitrarily definedareal units (for additional information see Fothering-ham, 1989). Second, while the MAUP certainly posessignificant challenges, it can also reveal critical in-formation for understanding the structure, function,and dynamics of complex real world systems if it isrecognized and dealt with explicitly (Jelinski and Wu1996). Part of the challenge in recognizing MAUP is

that there is no unique ‘MAUP statistic’ to quantify itsinfluence, though correlation analysis and other tech-niques have been used (Amrhein and Reynolds 1996;Hunt and Boots 1996). Instead, users of spatial datamust be cognizant of the fact that spatial analysis ofarbitrarily defined areal units can produce results thatmay not necessarily represent the content of the orig-inal units, but rather, the associations between them(i.e., aggregation problem) and the scale at which theywere assessed (i.e., scale problem).

The fundamentals of Object-Specific Analysis (OSA)and Upscaling (OSU)

Object-Specific Analysis (OSA) is a multiscale tech-nique that defines unique spatial measures, specificto the individual objects composing a remote sens-ing scene. These object-specific measures are thenused in weighting functions for upscaling an image toa coarser resolution. The resolution of the upscaledimage can either be defined manually by the user(see further), or automatically by statistical proper-ties of the objects composing the image (see further).

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Figure 2. Tree-crown image-objects. This CASI sub-image hasbeen magnified to illustrate the relationship between individualpixels (gray-tone squares) and the tree-crown image-objects theyperceptually represent. Individual crown centers are defined by asingle black pixel. The spatial resolution of each pixel is 1.5 m2.

Both forms of upscaling are referred to as Object-Specific Upscaling (OSU) because they incorporateobject-specific weights. Thus, MAUP effects are mini-mized in both OSA and OSU, as object-specific spatialinformation is incorporated throughout the analysis.

An underlying premise of OSU is that H-resimage-objects should have more influence on an up-scaled signal than a single L-res pixel – which signal isalready regularized1 . The term ‘image-objects’ refersto basic entities, located within an image that are per-ceptually generated from H-res pixel groups, whereeach pixel group is composed of similar digital values,and possesses an intrinsic size, shape, and geographicrelationship with the real-world scene component itmodels [e.g., a tree crown (Figure 2)].

The heuristics determining this threshold of ‘sim-ilarity’ are based on the novel concept that all pixelswithin an image are explicitly considered H-res sam-ples of the scene-objects they model, even though (aspreviously described) each pixel many represent bothH- and L-res object information. The importance ofthis rule is that by biasing for H-res samples only,we explicitly seek objects that exist at, or over, alarger spatial extent than the area covered by the in-dividual pixels that compose them. Essentially, weare using parts of objects (grain) to define the ex-tent of objects that exist at their next (coarser) scales.

1Regularization is a signal-processing term describing the integra-tion of signals generated by objects that are no longer individuallydiscernable (thus L-res), due to the physical limitations of thesensing device in relation to the size of the objects being assessed.

The spatial extents defined are then used as weightsto representatively upscale the image to a coarserresolution.

Similar to Mandelbrot’s famous question concern-ing the length of a coastline, the answer is dependenton the precision of the measuring tool (Mandelbrot1967). In the case of OSA, the maximum sized objectthat can be defined is represented by the relationshipbetween the spatial resolution of pixels composing theobjects within a scene, and the ability of the heuristicsto define this object’s edges. As a result, this tech-nique can be applied to any type of remote sensingdata from H-res data such as the CASI (airborne), andIkonos (satellite), to medium resolution TM and low-resolution AVHRR. The only difference in each caseis to appreciate the relationship between the pixel size,and the geographic size of the object of which the pixelis a component. In a CASI data set, pixels could beconsidered parts of individual trees, trees being theobject of analysis. In TM data, individual pixels maybe considered parts of a particular forest stand, and inAVHRR data, individual pixels may represent parts ofa larger extent, more general landscape entity such asa deciduous broad-leaf forest class.

Though sharing similarities with other scaling andscale detecting techniques (Turner et al. 1991; Gard-ner 1998), OSA is unique, in that it incorporates anexplicit multi-resolution (i.e., hierarchical) samplingand evaluation of each pixel in relation to the (differ-ent sized) coarser grain objects of which it is a nestedconstituent. For example, while scale variance analy-sis (Moellering and Tobler 1972) is also a hierarchicalapproach, there is no consideration of pixels as parts ofindividual objects composing a scene. Instead, pixelscomposing the image are aggregated by systematicallyincreasing grain size (for the entire image), resultingin a nested hierarchy of images with the same extent,but with different spatial resolutions. A measure of thetotal scene variance is then evaluated for each imagein the hierarchy, and the results are plotted illustratingpotential scale thresholds at specific resolutions withinthe entire scene. A similar approach is described byWoodcock and Strahler (1987), where local scene vari-ance is graphed as a function of increasing spatialresolution, and also by Marceau et al. (1994) wherea minimum spectral variance threshold is used to de-fine the optimal spatial resolution of different forestclasses.

In OSA, a ubiquitous ‘optimal’ resolution is neverfound, as none exists in images representing com-plex heterogeneous environments (Hay et al. 1997).

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Instead, different ‘optimal’ resolutions or thresholdsare defined based on the different objects being as-sessed (Hay et al. 1996). In the previous examples,the described techniques are used for scale explorationonly. They do not explicitly consider individual pixelsas parts of variously sized, shaped, and spatially dis-tributed objects, and they do not include facility forupscaling, or provide information indicating where inthe image such spatial thresholds exist. OSA does notshare these limitations.

Materials and methods

Study site

Our initial interest in scale issues was based on under-standing the spatial evolution of individual trees andforest gaps through scale (Marceau and Hay 1999b),particularly as it relates to changes in landscape frag-mentation. To facilitate this we applied OSA andOSU to H-res CASI data, which allowed us to followthe evolution of familiar image/site structures throughscale. The CASI (Compact Airborne SpectrographicImager) is a pushbroom sensor designed to operatefrom light aircraft and helicopters, with data capturecapabilities based on a two-dimensional frame transferCCD array. 16 bit signed data were collected dur-ing 20:10–21:40 h (GMT) over the Sooke Watershed,Vancouver Island, British Columbia, Canada on Au-gust 1, 1993 (Figure 3). The data were radiometricallycorrected to 1.5 m2 pixels, and a study site (Fig-ure 4a) was located along Rithet Creek and extractedfrom a channel centered at 0.66 µm (+/− 0.05 µm).This scene was then corrected for geometry andatmosphere, and all subsequent analyses were per-formed on it. Ancillary data include 1:10,000 forestinventory maps, numerous field surveys, and 1:12,000color near-infrared (NIR) aerial photography (1993).In this area, the very dry maritime Coastal WesternHemlock biogeoclimatic subzone dominates, though asmall component of moist maritime Coastal Douglas-Fir subzone also exists.

In Figure 4a, three principal stand types are vis-ible, each of which illustrates the dominant seraltree species - Coastal Douglas-Fir [(Pseudotsuga men-ziesii) (Mirb.) Franco var. menziesii]. Located in thecenter of this image is a mature stand (141–250 yrs)with a crown-closure of 56–65%. Below it (bottomcenter) is a dense young stand (21–30 yrs) with acrown-closure of 76–85%. Surrounding these two, no-tably on the image left, is a stand of mixed-immature

and mixed-young individuals (1–20 yrs), with crownclosures ranging from 0–45%. Three gravel roadstransect the scene and are represented as bright lin-ear features. An exposed sparsely vegetated clear-cut(C.Cut) lies adjacent to a gravel road at the upper rightquadrant of the scene, and a small, partially vegetatedmarsh is located at the bottom right. Throughout thesite, many exposed soil, and soil-grass patches are vis-ible. In the Thematic Map (Figure 4b), these patcheshave been classified as C.Cut.

OSA and user-defined OSU

In the earth sciences it is generally observed that ob-jects closer to each other are more alike than thosefurther apart (Curran and Atkinson 1998). Similarly,in a remotely sensed image, spatially near pixels tendto elicit a strong degree of spectral autocorrelation.Therefore, plotting the digital variance of samples(pixels) located within increasingly larger kernels,while centered on an image-object of known size tendsto produce a distinct break, or threshold in varianceas increasing sized kernels contact the image-object’sedges. The unique window size (VTw) defined atthis variance threshold location (VTij) correspondsexplicitly to the object’s known size, and is a keycomponent for determining object-specific weightingvalues [i and j represent row and column within theoriginal CASI image (OI)]. Conceptually, VTw maybe considered similar to lag as described when usingsemivariance. For example, the window size at loca-tion (A) in Figure 5 represents the maximum scalefor defining the (inset) tree-crown2. Locations B-C,D-E, and F-G, represent an object-specific range of‘optimal’ window sizes for defining the nested image-objects, of which the center tree-crown pixel (whitedot) is a member. Locations B, D, and F representthe local variance minima corresponding to the scaleswhere the next set of ‘nested’ objects are first manifest.Minimum variance indicates that the pixels composingthis measure are locally the most spectrally similar,thus they are the most ‘object-like’, while variancemaxima located at C, E, and G, respectively, representthe maximum spatial extents of these nested objects.Locations A-B, C-D, and E-F are explained in theDiscussion section.

The window size at one iteration prior to VTij isused to define the maximum area (Aij) at which the

2The inset image has been extracted form the mature-stand in OI,and the corresponding curve represents the actual variance valuesdetermined at each incremented widow size.

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Figure 3. Rithet Creek study site map.

Figure 4. Remote sensing image and thematic map of the study site. A). CASI image illustrating the study area (36 ha2) at a spatial resolutionof 1.5 m2. B). Thematic site map and legend (same scale).

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Figure 5. Variance characteristics of a single tree-crown pixel defined through multiple scales. The curve of this graph results from plottingthe variance of the digital values of all pixels located within increasing sized square windows. In this illustration, varying sized windows arecentered over an individual tree-crown (circular image-object) that is located within the white bars of the inset image. The crown center isdefined by a single white pixel that represents the apex of the tree. As the window size increases, the resulting variance value is plotted. Inpractice this form of multiscale analysis is applied to all pixels composing a scene. The maximum window size specified for each pixel is definedwhen variance measures meet unique object-specific heuristics that correspond to the spatial extent of the real-world objects they model.

central pixel under analysis is spectrally and spatiallyrelated to its neighbours. At the same time that Aij isdefined, the corresponding mean (Mij) and variance(Vij) values are also defined for the central pixel withinVTw. These procedures are then applied to all remain-ing pixels in OI, resulting in corresponding variance(VI), area (AI), and mean (MI) images.

Once VI, AI, and MI have been generated, twosteps are required to complete user-defined OSU. Thefirst involves determining an object-specific weight(Wij) for each (∀) pixel (Pij) in OI, which is repre-sented by WijK .

∀Pij ∈ OI (1)

WijK = (AijK /SK)

WijK defines the object-specific weight for each Aijwithin an upscaling kernel (K) [of a (k∗k) user-defineddimension], where SK is the sum of all Aij within K

(see equation 2).

SK =k∑i

k∑j

Aij (2)

The second step is to apply the object-specific weightto produce a new upscaled image.

∀UPLM ∈ UI

UPLM =[

k∑L

k∑M

(Oij

∗Wij)] (3)

UPLM represents an upscaled pixel located at row L,column M , in the resultant upscaled image UI. Oijis the DN (digital number) of the pixel located inthe original image at row i, column j , that is evalu-ated within the upscaled kernel. UPLM and the pixelswithin rows (i − k, j + k) and columns (i + k, j − k)represent the same real-world extent. Thus UI is com-posed of fewer pixels than OI, though both representthe same geographic area. Resampling within the up-scaling kernel is represented by the double summationof all DNs to a single object-weighted pixel valuethat is located within the new upscaled image. Thenon-overlapping kernel is then moved a distance of K

pixels across OI, and the process is iterated until a newupscaled image UI is generated.

A multiscale extension: Iterative OSA and OSU

Although a single remote sensing scene represents aunique instance of all discernible objects within itsextent, we hypothesize that it also contains additionalinformation related to image-objects (IOs) that exist

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over a ‘limited’ range of coarser, non-immediately dis-cernible spatial scales, located within the same extent.Support for this comes from three sources:

1. Appreciating that both H- and L-res informationexists within an image collected at a single resolu-tion (Woodcock and Strahler 1987)

2. Understanding the intimate relationship betweenIFOV and object size (Slater 1980)

3. Recognizing that previous work illustrates the abil-ity of OSU methods to reveal patterns that consis-tently model the spatial extent of differently sizedobjects existing at coarser scales (i.e., tree crowns,canopy gaps, etc, Hay et al. 1997).

To exploit this range of multiscale informationwithin a single image, we hypothesize that by itera-tively applying OSA to define object-specific (max-imum and minimum) variance-thresholds within MI,dominant landscape objects will emerge through the it-eration process. In essence we are applying principlesof non-linear feedback to ascertain if self-organization(Kay and Schneider 1995) – in the form of patternscorresponding to the spatial extent of dominant land-scape objects – will ‘emerge’ at each new scale. Wenote that our goal in developing and applying object-specific techniques is to allow for previously existingself-organized patterns (i.e., image-objects) to be de-tected within the image/landscape at different scales.It is not to generate new self-organizing patterns. Thissubtle difference is important to clarify, because astrict requirement of self-organization includes tem-poral evolution (Nicolis and Prigogine 1989; Coveneyand Highfield 1991), while a single remote sensingimage – and all analysis performed on it – can onlyrepresent an instance in time.

The result of this iterative approach is a nested hi-erarchy of image-sets (ISt) composed of VI, AI andMI that have membership (∈) in a unique scale do-main (SDn). Within this SDn, each image has thesame grain and extent, and represents the results ofmultiscale analysis specific to the individual image-objects composing it. Following this logic, each SDn isa member of a scale-domain super set (SDS) that rep-resents the entire range of object-specific multiscaleanalysis (OSA) and scaling results (OSU) evaluatedwithin the fixed spatial extent of a unique digital land-scape (OI). This hierarchical structure (outlined inFigure 6) may be described in the following manner:

Pij ∈ IOs ∈ ISt ∈ SDn ∈ SDS (4)

Figure 6. Hierarchically nested components of iterative ob-ject-specific analysis (OSA) and object-specific upscaling (OSU).

A digital landscape is composed of pixels (Pij)that are parts of image-objects (IOs), that are definedwithin a specific image-set (ISt), that is a member of ascale-domain (SDn), which populates a scale-domainset (SDS).

To operationalize this framework with minimaluser-bias, we apply object-specific concepts to se-lect the most appropriate images for upscaling. Tominimize the scale problem resulting from arbitraryscaling, we apply a resampling heuristic (Rh) basedon the relationship between image-objects and pixelsize, and apply OSU as our upscaling algorithm (Hayet al. 1997). This combination of iterative OSA andOSU constitutes an object-specific multiscale frame-work for landscape analysis that is further discussedin the following sections.

Selecting an iterated MI to upscale

Through the iteration process, MI pixels increasinglybecome parts of objects existing over larger and largerextents, yet the spatial resolution of the pixels repre-senting each new image-object remains constant. Toreduce unnecessary computation, an appropriate MImust be evaluated within each ISt to determine if up-scaling is necessary. In the first OSA iteration, theexact process described in section ‘OSA and user-defined OSU’ is applied. That is, each Pij is assessed

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within larger windows until a local maximum variancethreshold (VTw(max)) is reached that corresponds to a‘peak’ location as illustrated by (A) in Figure 5. Whenapplied to the entire image, this process generates thefirst image-set (i.e., V1, A1, M1).

In the second iteration, each Pij (in the newlygenerated M1) is assessed within larger windows un-til a local minimum variance threshold (VTw(min)) isreached. This results in the generation of a secondimage-set (i.e., V2, A2, M2) that represents the be-ginning scales of all newly emergent image-objects.Conceptually, each pixel in M2 will be representedby a local variance saddle or pit, as illustrated by (B)in Figure 5. Therefore, odd-numbered OSA iterationsdefine scales representing the ‘end’ of objects, whileeven-numbered OSA iterations define the beginningscale of the next emergent object(s). As a result, all MIgenerated from even-numbered OSA iterations will beselected for upscaling.

Defining an upscale resolution (Rh)

Once an appropriate image has been selected for scal-ing, the upscale resolution will be defined by a resam-pling heuristic (Rh) that is based on the relationshipbetween pixel size, and the size of the minimum dis-cernible image-object for which VTw was initially de-veloped. Rh is similar to recommendations by O’Neillet al. (1996), who suggest a grain size 2 to 5 timessmaller than the spatial features of interest, and asample area 2 to 5 times larger than the patches as-sessed. We note that this grain size recommendationcorresponds to a reference by Slater (1980) regardingthe point-spread function (PSF)3 of the sensor. Essen-tially, if an object is less than 1

4 the size of the sensor’sIFOV, its influence in the corresponding pixel is equalto the sensor PSF. In modern sensors this value is ex-ceptionally small, though it can be defined for eachsensor, and included within the model. For the pur-pose of this study, Rh equals the resampling resolutionwhere the minimum area (Amin) of all pixels compos-ing the image-objects defined in AI must be four timeslarger than the spatial resolution of the current image.This ensures not only detection (as implied by the 1

4PSF rule), but also identification (Jensen 1986). Byadopting this 4:1 relationship we are again erring onthe side of caution (i.e., under-sampling).

3The PSF defines the spatial influence or ‘spread’ of a zero-dimensional point of light resulting from lens aberrations in thesensor.

We also note, that if 14 represents detection, and

4:1 represents identification, then a fuzzy (i.e., notspecifically defined) range of scales (a maximum of)16 times an object’s minimum detectable size exists,where part of an object’s spatial influence is poten-tially discernible within a single image. This furthersupports the hypothesis in the above section regardinga limited range of object-specific spatial informationwithin a single image.

Upscaling strategy

In a previous study, Hay et al. (1997) evaluated OSUagainst four resampling or scaling techniques tradi-tionally included in remote sensing image-analysissoftware. Over a gigabyte of data were analyzedand upscaled from 1.5 m to 3 m, 5 m, and 10 m,respectively, using nearest neighbor, bilinear inter-polation, cubic convolution, non-overlapping averag-ing, and OSU. All upscaled images were evaluatedagainst (non-upscaled) data of the same scene orig-inally collected at a 10-m spatial resolution. Thetechnique producing an upscaled image most visuallyand statistically similar to the original 10-m imagewas considered the most appropriate upscaling tech-nique. Six thousand samples representing six differentforest classes were evaluated using the smallest root-mean-square-error (RMSE) results to represent thebest technique. Results indicate that OSU producedthe most visually and statistically accurate upscaledimages of those tested, with the lowest RMSE in 10out of 18 classes over all forest types and ranges ofscale tested. In the eight times it did not obtain thelowest RMSE, it produced six values with the secondlowest errors. Based upon these results OSU is con-sidered the most appropriate upscaling technique, thusit is used to resample the selected MI to a resolutionspecified by Rh. To accomplish this, Rh is appliedto Equation 1, replacing the user-defined upscalingkernel size (K). This iterative OSA and OSU strat-egy is then applied until VTw is larger than the imagedimensions.

Results

The original CASI image (OI) spatially represents acomplex forest scene spanning a geographic extentof 600 × 600 m. Spectrally it represents both the

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Table 2. Image information and object-specific procedures for generating Figure 7.

SDn

{ISt Components OSAt OSUn MI Dimensions Grain (m2) # Pixels

SD0

OI

IS1 = V1, A1, M1

IS2 = V2, A2, M2

1

2

0 400 × 400

400 × 400

400 × 400

1.5

1.5

1.5

160000

160000

160000

SD1

U1

IS3 = V3, A3, M3

IS4 = V4, A4, M4

3

4

1 250 × 250

250 × 250

250 × 250

2.4

2.4

2.4

62500

62500

62500

SD2

U2

IS5 = V5, A5, M5

IS6 = V6, A6, M6

5

6

2 156 × 156

156 × 156

156 × 156

3.84

3.84

3.84

24336

24336

24336

SD3

U3

IS7 = V7, A7, M7

IS8 = V8, A8, M8

7

8

3 98 × 98

98 × 98

98 × 98

6.14

6.14

6.14

9604

9604

9604

SD4

U4

IS9 = V9, A9, M9

IS10 = V10, A10, M10

9

10

4 61 × 61

61 × 61

61 × 61

9.83

9.83

9.83

3721

3721

3721

Table 3. List of Object-Specific terms and abbreviations.

∀ For each. . .

∈ Has membership in. . .

VTw(max) Local maximum variance defined with the variance threshold window

AI, Aij, A2 Area-image, Area value defined at (i, j), Area-image generated at OSA2

EOs Edge-objects

IOs Image-objects

ISt Image-set generated at OSA iteration (t)

K, SK Upscaling kernel of (k∗k) user-defined dimensions, Sum of all Aij within K

LTDv The Landscape-threshold-domain, where (v) represents the number of landscape

thresholds defined by TSV within the SDS

MI, Mij, M2 Mean-image, Mean value defined at (i, j), Mean-image generated at OSA2

OI Original CASI image

OSAt Object-specific analysis at iteration (t)

OSUn Object-specific upscaling at the (nth) upscaling iteration

Pij Pixel located at row (i), column (j) in a 2D image

Rh Resampling heuristic

SDn Scale-domain, resulting from the (nth) OSU iteration

SDS Scale-domain-set

TSV Total scene variance

UI, U2 Upscale-image, Upscale-image generated at OSA2

UPLM An upscaled pixel located at row L, column M, in the UI

VI, Vij, V2 Variance-image, Variance value defined at (i, j), Variance-image generated at OSA2

VTw(max) Local maximum variance defined with the variance threshold window

VTw(min) Local minimum variance defined with the variance threshold window

VTw, VTij Variance threshold window, Pixel location (i, j) defined at the variance threshold

WijK Object-specific weight defined at row (i), column (j) within K

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minimum chlorophyll a reflectance signal4, and theabsorption maximum of solvated chlorophyll a (Kirket al. 1978). In this study, it is also considered asurrogate measure of vegetative ‘greenness’. Whenthe multiscale extension is applied to OI, the resultis a hierarchy of image-sets (SDn), each consistingof variance (VI), area (AI), and mean images (MI),with the same spatial resolution. As upscaling occurs,the spatial resolution of the newly generated image-sets increase as do their scale domain subscripts i.e.,SDn+1. The iteration where OSU first takes place is re-ferred to as SD1. The image-set prior to this is SD0 - asupscaling is not applied. Figure 7 illustrates image-setswithin the first four scale-domains (SD0−3), generatedfrom automatically applying 10 iterations of OSA, and4 iterations of OSU to the original CASI image. Theprocedures for producing these results are outlined inTable 2, and are summarized as follows.

OSA was applied to the OI where object-specificmeasures of maximum local variance were assessedfor every pixel resulting in the first image-set (V1, A1,and M1). OSA was then applied to the newly gener-ated M1, where object-specific measures of minimumlocal variance were similarly assessed, resulting in thesecond image-set (V2, A2, and M2). Together, theseimage-sets and OI represent the first scale domain(SD0), of which V2, A2, and M2 are illustrated in Fig-ure 7. Based on the concepts described above, M2 wasautomatically selected for upscaling to a resolutiondefined by Rh. This resulted in a grain change from1.5 m to 2.4 m and the generation of the first upscaledimage (U1). These procedures were then repeated forthe next 8 iterations, substituting in the appropriatelydefined MI, Rh, and UI variables. In all cases, the re-sulting upscale images (U2−4) were used as the ‘seed’images for OSA, from which new image-sets (IS3−10)composing the additional scale-domains (SD1−4) weregenerated. To facilitate visual comparisons5 betweenthe image-sets illustrated in Figure 7, each upscaledimage was resampled to 400×400 pixels. Resamplingwas performed using nearest neighbor so that originalDN values were not changed. As a result, images inlatter scale-domains appear more ‘blocky’ than thosein SD0.

4Though radiometrically ‘close’, the low trough in spectra asso-ciated with plants is nearer to 675 nm than to the spectral bandlocation (655–665 nm) defined in this data set.5All figures are 8 bit linearly scaled versions of 16 bit data that havebeen enhanced for illustration. In the original images, far greatervisual clarity is achieved than in print.

As the grain size increased through the upscalingprocess from 1.5 m to 9.83 m, the total number ofpixels in the image was reduced from 160,000, to3,721. Object-specific analysis was stopped at OSA10,as analyzing kernels contacted the borders of the im-age. Throughout the scaling process, the scene extentremained constant at 600×600 m, but the physical di-mensions of the generated images were systematicallyreduced from 400 × 400, to 61 × 61 pixels. The visualdifferences in information content resulting from theseprocedures are illustrated in Figure 8, where U1−4 isillustrated against the background of OI. We note thatOSU was applied to M2,4,6,8 to generate this upscalecomposite.

Within each SDn, the VI represents a threshold-image resulting from OSA. Essentially it illustrateswhere the edges of differently sized objects have beenreached. Bright tones define areas of high variance(object edges), while darker tones define areas of lowvariance (object interiors) e.g. bright road edges vs.dark young forest (image bottom) in V2. Similarly,each AI models the maximum spatial extent – or areaof influence – of its constituent objects at a specificgrain defined within the variance threshold kernel.This important measure represents the unique (scale-specific) areas over which dominant landscape objectsexist, thus it is used to determine object-specific-weights for scaling. Because image-objects are com-posed of similar pixels, they tend to be assessed withinsmaller kernels, as their accompanying variance mea-sures are small. This results in correspondingly smallarea values, which are visually represented by dark ar-eas. In A2, dark tones within the mature stand (imagecenter) clearly correspond to individual tree crowns,while the brighter surrounding values correspond toedges composed of shadow and or understory pixels.Visually, these results strongly support the validity ofobjects-specific heuristics (at least over fine scales),as individual trees illicit complex illumination/shadeeffects on either side of their crown, yet both sides areconsidered part of a single object (i.e., a dark tone).

In each MI every pixel represents a H-res memberof a newly detected image-object that exists at its next(coarser) scale i.e., branches and leaves now becomepart of a tree crown. Because these images are gen-erated from average values calculated within specificthreshold kernels, they represent the dominant imagestructure defined at a specific spatial resolution withina unique scale-domain. To enhance interpretation ofthe overall structural evolution of each MI composingSD1−4, we have applied a simple linear color table, as

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Figure 7. Scale domain sets (SDS0−3) consisting of variance (VI), area (AI), and mean (MI) images.

484

printed gray-tone gradations are more difficult to dis-tinguish. In each MI, black and purple represent high-density vegetation, dark blue represents low-densityvegetation, and light blue-green represents the gra-dient between sparsely vegetated and non-vegetatedareas. Clear-cut areas with varying amounts of vegeta-tion range from green-yellow, where colors representlow-density invading grasses and shrubs on partiallyexposed soils, to orange-red, representing the max-imum scene brightness resulting from fully exposedsoils.

As the spatial resolution of each SDn changes, eachVI, AI, and MI visually delineate newly defined scale-specific structures that represent the dominant objectsemergent at these scales. In SD0 a large amountof recognizable object structure is explicitly defined.In particular, individual tree crowns, their shadows,canopy gaps, patches of exposed soil and vegetation,road edges, and vegetation along roads are highly dis-cernible in both V2 and A2. In SD1 we see an obviousevolution from individual crown structures within themature stand (as defined in V2 and A2), to larger sizedobjects (dark patches) that correspond to areas of highstand densities and include reflective characteristicsfrom crowns, shadows, and understory. At this scale,the (highly reflective central) gravel road is influencedby the spectral characteristics of the surrounding veg-etation, causing it to change from green-yellow (asdepicted in M2) to a light blue (in M4). It is alsoimportant to note the increasing spatial effect (i.e.,larger areas of bright tones in A4) appearing alongthe edge of vegetated and non-vegetated areas. In V4,this is represented by bright linear features around(darker) objects, and will be referred to further in theDiscussion section.

In SD2−3 we see a dramatic change in the over-all scene composition from the previous scale-domainsets. Here, the images clearly illustrate a distinct evo-lution within three dominant object groups: C.Cut (in-cluding roads, grasses, and bare soil depicted), young-forest (which includes young and juvenile classes),and mature forest. The net result is an increasing spa-tial and spectral encroachment of clear-cut, and lowvegetation density areas within locations that were ini-tially densely vegetated. This is most apparent in theupper right quadrant of each image, where the spatialinfluence of C.Cut, and lower density vegetation (i.e.,young forest) increase at the expense of mature forest.

Figure 8. This upscale image (U1−4) composite illustrates the dif-ferent image extents resulting from four iterations of object-specificupscaling (OSU).

Discussion

What exists between the end of one image-object andthe beginning of another?

We suggest that multiscale image-object thresholds areoften far more ‘fuzzy’ or less discrete than the termthreshold commonly implies. This is because the pix-els used to evaluate image-thresholds are themselves ahemispherical integration of reflected light, which rep-resents the non-linear interaction of entities existingover different scales. For example, a single ‘threshold’pixel defining the extent of a tree-crown may share itscomposition with a portion of this crown’s edge, theneighboring crown shadow, understory, and partial re-flectance from near-by exposed soil. Therefore, ratherthan a pixel being part of a nested hierarchy of discreteimage-objects that spatially lie adjacent to each otherthrough scale, there exists instead, a unique range ofscales between the end of one image-object, and thebeginning of another, that is composed of integrated‘edge’ pixels. We refer to the species of objects thatpopulate this ‘edge-space’ as edge-objects (EOs), andsuggest that an example of their signal is illustrated inFigure 5, between A–B, C–D, and E–F.

Conceptually, EOs exist within a varying range ofscales located on the ‘other-side’ of discrete image-object frontiers or boundaries, but due to their digital

485

nature6 they actually share part of their spectral com-position with a non-linear integrated fraction of theedge pixels they abut. As a consequence, EOs willalways be L-res which means they will be representedby relatively large VI and AI measures, as they areunable to be defined within the range of scales com-monly used to assess image-objects (see Figure 7). Forexample, during OSA1, visual and statistical outputgenerated at each increment in window size indicatedthat 99% of OI was processed within a window size of29 × 29. Yet the remaining 1% required analysis up toa window size of 63 × 63. In addition, this 1% of pix-els did not visually correspond to spatially meaningfulimage-objects within OI. Instead, they representededge locations between recognizable IOs. A similartrend was found in all additional iterations throughoutthe OSA process.

To ensure that spatially dominant image-objectswill emerge through multiscale analysis, rather thanEOs, we confirm that inverse area values (which fa-vor image-objects) are used to define all OSU weights.And yet, EOs appear to spatially dominate at coarsergrain sizes, rather than recognizable image-objects(see Figure 7). We suggest two plausible solutionsfor this condition. Either EOs represent real land-scape structure(s), or they are artifacts resulting frominappropriate OSA heuristics.

Strong support that OSA heuristics work well onrecognizable image-objects is provided by SD0 inFigure 7, where individual tree crowns, road edges,canopy gaps, and barren areas have been explicitlydelineated. When these results are considered in re-lation to the evaluation conducted during heuristicdevelopment, we are confident that the heuristics workwell. The second solution is that EOs are actuallyimage-objects that represent real multiscale landscapestructure that we may not be familiar with from asingle-scale perspective.

If edge-objects (EOs) are real, what landscapephenomenon do they model?

As Wu and Qi (2000) point out, it is not always clearwhether the effect of changing scale is an artifact dueto the improper use of analytical methods, an indica-tion of the scale multiplicity of ecological systems, orneither of the two. If for a moment we consider that

6Within a digital scene, an image-edge or threshold is not a 1D-linecomposed of zero-dimensional points lying between two or morepixels, but rather a 3D pixel (i.e., x, y, DN) that must exist in thesame location as one of the points it is trying to segregate.

EOs are real landscape entities rather than image ar-tifacts, what do they structurally represent? By theirvery nature, we know that they are not image-objectswith obvious real-world counterparts, if they were, wewould recognize them. Obviously we need to evaluateEOs with a different conceptual perspective. What wedo know is that EOs exist in the ‘edge-space’ betweenimage-objects. Visual analysis of Figure 7 reveals aspatial evolution of increasing perimeter for C.Cut,gravel-road, and barren-ground, that extends far be-yond their initial physical boundaries (see Figure 4a).When these changes are considered in relation to thescale-dependent manner in which OSA functions, itis highly plausible that the evolution of EOs modelsthe scale-dependent change(s) occurring at, or within,ecotones.

Although the study of ecotones is complicated bythe diversity of interpretation regarding their nature,we adopt the definition of Holland (1988), where thetransition zone between adjacent patches is recognizedas an ecotone. In OSA, image-objects correspond toscale-dependent patches within a landscape mosaic,thus EOs correspond to their ecotones. A seriouschallenge with ecotone detection is the subjectivityinherent with identifying boundaries along graduallychanging ecolines. Here the difficulty involves divid-ing a zone of ‘continuous’ variation into compart-ments. As Johnson et al. (1992) indicate, even whenstatistically significant differences exist between indi-vidual compartments, the boundaries between themmay not represent true ecotones. Instead, ecotonesspan the range between these two extremes. In addi-tion, boundary distinctness is scale dependent, thususers are also faced with the subjectivity of determin-ing the most appropriate scale to assess the scene,which in turn effects the delineation of ecotones.

One of the true benefits of imaging spectrome-try is the ability to explicitly link specific spectralcharacteristics with physiological properties (Wess-man et al. 1989). If the idea of EOs as ecotones islinked with the spectral characteristics of the originalCASI image (i.e., a surrogate measure of vegetative‘greenness’) it is further plausible to hypothesize thatEOs defined in OI may be a visual analogue of whatis referred to as ‘depth-of-edge influence’, or ‘edgewidth’ (Chen 1999). Depth-of-edge influence is asso-ciated with microclimatic zones across abrupt edgesin the landscape, and can result in broad areas ofedge influence, which constitute a significant portionof (unaccounted) fragmentation in a landscape. Thephenomenon varies over time and with edge charac-

486

teristics, and can extend four to six tree heights intothe forest from a recent clear-cut edge. Notably, edge-width value varies according to different tree species,ranging from 60 m in Eastern Red Pine/White Pine toover 400 m in Pacific N.W. Douglas-fir forests (Chen1999). This ‘EO = edge-width’ hypothesis is furthersupported by the fact that OI is a high-resolution sceneof a (then) recently clear-cut site on southern Van-couver Island, where the dominant tree species in allthree-forest classes (Mature, Young and Juvenile) arePacific N.W. (Coastal) Douglas Fir. However, it isimportant to note that no microclimate data were avail-able to corroborate this hypothesis. Nevertheless, thisprovides an excellent example of how object-specificanalysis offers new insight into linking and question-ing the relationships between landscape processes andmultiscale landscape patterns, that may not have beenpossible without such a multiscale perspective.

Can an OSA perspective be used to definelandscape-scale thresholds?

Through the iterative OSA and OSU process, the pat-terns generated within a SDS represent an evolution ofimage-objects from small-scale entities such as indi-vidual tree-crowns, to larger ‘landscape’ sized objectsthat will eventually dominate the entire image. Fromthe results in Figure 7 it is clear that between SD1and SD2, recognizable image-objects stopped beinggenerated, and unfamiliar EOs began to emerge anddominate the scene. We suggest that this change inspatial dominance, from image-objects to EOs, cor-responds to crossing a landscape-scale threshold, andthat it can be defined in a similar fashion as individualimage-object thresholds.

Recall that when applying OSA to detect object-specific thresholds, each pixel is evaluated as partof an individual image-object. Therefore, to detect alandscape-scale threshold within an OSA framework,all image-objects and EOs within a scene are evaluatedas being part of a larger scene-object (i.e., a landscape-scale threshold-object) that spatially dominates theentire image/landscape being assessed. This is op-erationalized by evaluating the total scene variance(TSV) for each image in a nested hierarchy, whereeach image represents the same study area, but at adifferent grain size. The resulting signal is then plot-ted, and modeled revealing distinct saddles and peaks,which correspond to the beginning and end scales oflandscape-scale threshold-objects. Essentially this isscale variance analysis as described earlier, except

that within an OSA framework, the nested hierarchycorresponds to image-sets generated at each OSA iter-ation, and images representing different grain sizes aregenerated only at odd-numbered iterations (except forOSA1). In addition, TSV is defined for each variance-image rather than each mean-image as object-specificstructures are explicitly defined in VI, while in MIsuch structures are smoothed. In simple terms, theseprocedures correspond to evaluating the total differ-ence in the variation resulting from the individualimage-objects composing a scene through all possibleobject-specific scales of analysis.

To better understand the total scene varianceand corresponding scene/landscape structure throughscale, TSV values generated for each VI at odd num-bered iterations7 are modeled with a high order poly-nomial (R2 = 0.999), and the resulting curve [Poly.(TSV)] is illustrated in Figure 9. We note that whilethe shape of this cure is similar to that found in Fig-ure 5, it must be assessed with caution past iteration8, as OSA8−10 kernels required analysis over largerwindow sizes than the available image dimensions.This indicates that the pixels being assessed were partof a larger-scale image-object that existed beyond theextent defined by the image. Visual analysis of Poly.(TSV) reveals a saddle at iteration 3 and a peak at iter-ation 6 indicating the beginning and end range of thefirst landscape-scale threshold-object. It is also pos-sible that another landscape scale threshold begins ator after OSA11. Recall from Table 2, that OSA3−4are members of SD1. When compared with the re-sults in Figure 7, the first landscape-sized thresholdcorresponds explicitly to the visual changes betweenSD1 and SD2, supporting the idea that OSA can beused to evaluate a full-range of landscape thresholdsranging from small-scale image-objects to large-scalelandscape structures.

Conclusion

From a multiscale perspective a scale-domain set maybe visualized as a hierarchical scaling ladder (Wu1999), and each SDn may be visualized as an in-dividual rung, separated by unequal spaces that arespecific to the range of scales assessed within the IStthat composes it. Alternatively, since Figure 9 sup-ports the detection of landscape-thresholds between

7We note that values generated at even-numbered iterations pro-duced a very similar curve, transposed by one iteration in thex-axis.

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Figure 9. Total Scene Variance (TSV) defined at odd-numbered object-specific analysis (OSA) iterations. Poly.(TSV) represents TSV valuesmodeled by a high order polynomial curve (R2 = 0.999) that is similar to the curve illustrated in Figure 5.

adjacent SDn, it may be more reasonable to includeSDn as a subset of a higher-order set we refer toas a landscape-threshold-domain (LTDv), where thesubscript (v) represents the number of different land-scape thresholds defined by TSV within the SDS. Thusequation 4 should be augmented as follows:

Pij ∈ IOs ∈ ISt ∈ SDn ∈ LTDv ∈ SDS (5)

As a result, it may be more appropriate to con-sider the landscape represented by a linked group ofdifferent sized scaling ladders, where each ladder cor-responds to a specific LTDv, rather than a single hier-archical scaling ladder as Wu (1999) suggests. Thoughoriginating from different starting points, we suggestthat a multiscale OSA and OSU approach providesa methodological framework that is complimentaryto the described theory, and techniques required bythe Hierarchical Patch Dynamics Paradigm (HPDP)(Wu and Loucks 1995). HPDP provides a link be-tween the patch dynamic perspectives and hierarchytheory that emphasizes multiscale properties of patternand process dynamics in ecological systems. In thisparadigm, individual patches are considered the fun-damental structural and functional units. In OSA theseprimitives correspond to image-objects, whose spatialdimensions and influence can be defined and aggre-gated to unique coarser scales (i.e., OSU), specifiedby the dominant entities (AI) composing a scene.

If at multiple image scales, the spatial extent ofdominant AI patterns strongly corresponds to geo-graphic areas over which known processes are dom-inant (i.e., soils, slope, aspect), these areas may beselected as locations over which scale-dependent eco-logical models could be developed, or data explicitlytranslated to and from (Holling 1992). King (1990)identifies four general methods of translating ecolog-ical models to larger scales: (1) lumping, (2) directextrapolation, (3) extrapolation by expected value, and(4) explicit integration. In particular, direct extrap-olation could benefit from OSA because it involvesexplicitly running a small-scale model for a set of dis-crete elements, scaling the output of each element bythe area represented, then combining the outputs torepresent the large-scale system.

If we consider that the OSA and OSU heuristicsare sufficiently robust, and that MAUP effects are min-imized – through adopting an entity, or object-specificapproach – then the complex patterns forming at eachOSA iteration represent the emergence of real worldstructures existing, or imbedded at different scaleswithin a single scale of imagery. Good reason existsto consider this a sound supposition, as (VI) and (AI)strongly correspond to real world scene-components,thus the heuristics defining image-object thresholdsare being met. As threshold patterns emerge at eachiteration, and their specific resolutions and extents aredefined, the ideal situation would be for remote sens-

488

ing data – representing surrogate ecological measures[such as leaf area index (LAI), or fraction of photosyn-thetically active radiation, (FPAR)] – to be scaled withOSU and used as inputs into unique ecological mod-els operating over the spatial extents defined by thecorresponding AI (Freidl 1997). Alternatively, modeldevelopment and data type selection could be guidedby the OSA scale-domains and landscape thresholdpatterns generated. If iterated OSA and OSU resultscorrespond to field data over a range of known scales,precedent exits upon which to assess OSA and OSUresults at coarser unverifiable image scales. At present,object topology is not embedded within the analyzingroutines, but it is envisioned in subsequent versions,which will provide multiscale image-object output foruse in geographic information systems.

In this paper we introduce a multiscale frameworkfor analysis and upscaling that when applied to remotesensing imagery reduces the effects of MAUP by in-corporating an object-specific approach. By consider-ing landscapes as hierarchical structures and adoptingthis multiscale framework, the patterns of landscapeobjects operating at, and over, unique spatial scalesmay be thematically and numerically quantified bytheir spatial dominance. While aware that the enti-ties that emerge in a data set are scaled by virtue ofthe observation protocol and the filters applied to thedata during analysis, we suggest that multiscale OSAand OSU offers a potentially powerful framework forimproved understanding of scale-specific landscapepatterns. In particular, multiscale OSA may assistin defining critical landscape thresholds, domains ofscale, ecotone boundaries, and the grain and extentat which scale-dependent ecological models could bedeveloped and applied.

This paper provides only a small sample of thepotential of multiscale OSA tested over a relativelyfine geographic area. The next step is to apply theseideas over a larger-extent fine-grained scene, wheresufficient ancillary data exist so that results may befully verified over numerous spatial scales. To facili-tate this, analysis is presently underway in the complexagro-forested Haut-Saint-Laurent region of Quebec toexamine how landscape fragmentation and connected-ness change through scale, and what their implicationsare for landscape management (Bouchard and Domon1997; Pan et al. 2000). Our primary objective willbe to apply the described object-specific frameworkto H-res Ikonos satellite data (acquired in September,2000) that represents an 11 km × 11 km scene, andevaluate the multiscale results against a database rep-

resenting more than 15 consecutive years of intensivefield studies and research.

Acknowledgements

This work has been supported by a Biology gradu-ate scholarship of excellence from the University ofMontréal and a GREFi Ph.D. Scholarship awardedto Mr Hay, by the Ministry of Natural ResourcesCanada through its Human Resources Planning andTraining Program, and by a team grant awarded toDr A. Bouchard and Dr D. Marceau from FCAR,Gouvernement du Québec. We also express appreci-ation to Forestry Canada for the CASI imagery, DrMarie Josée-Fortin for her assistance with algorithmnotation, and to three anonymous referees for theirconstructive comments.

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