ELSEVIER

Spatial Thresholds, Image-Objects, and Upscaling: A Multiscale Evaluation

G. J. Hay,* K. 0. Niemann,” and D. G. Goodenought

W hen examining a remotely sensed signal through various scale changes, what is the most appropriate up- scaling technique to represent this signal at difierent scales? And how can this be validated? Solutions to thesg questions were approached by examining how the 660 nm signal of six forest stands vary through four different scales of same-sensor imagery, four traditional resam- pling techniques, and a new object-specifk resampling technique. Analysis of the original and modeled datasets suggests that appropriately upscaled image y represents a more accurate scene-model than an image obtained at the upscaled resolution. Results further indicate the need for a multiscale approach to feature extraction and up- scaling, as no single spatial resolution of imagery appears optimal for detecting or upscaling the varying sized, shaped, and spatially distributed objects within a scene. By employing the human eye as a model, we describe a novel object-speci$c approach for addressing this chal- lenge. Upscaling evaluation is based on visual interpreta- tion, an understanding of the applied resampling theo- ries, and the root mean square error results of 6000 samples collected from a 10 m CASI scene, and from 1.5 m, 3 m, and 5 m same site CASI images upscaled to 10 m. Potential application of this object-specific ap- proach in hierarchical ecosystem modeling is also brie$y described. OElsevier Science Inc., 1997.

INTRODUCTION

In an effort to better understand and predict how our planet functions as an integrated system, biophysical and

’ University of Victoria, Department of Geography, Victoria, Brit- ish Columbia, Canada

t Natural Resources Canada, Advanced Forest Technologies Pro- gram, Canadian Forest Service, Victoria, British Columbia, Canada

Address correspondence to 6. J. Hay, Universite of Montreal, Department de Geogmphie, C.P. 6128, Succursale Centre-We, Mon- tral (Quebec), H3C 3J7, Canada.

Receiord 25 Noaenlhsr 1995; rvz;Ced 15 Junuq 1997.

REMOTE SENS. ENVlRON. 62:1-I9 (1997) OElsevier Science Inc., 1997 655 Avrnur of the Americas, New York, NY 10010

ecological information derived at the scale of the individ- ual organism must be extrapolated to the regional and global scales of climate models (Wessman, 1992). As so- lutions for integrating multiscale data and models are sought (Turner et al., 1989), scale-related concepts are rising to the forefront in earth system sciences where they have been discussed in biology, geography, geomor- phology, hydrology, landscape ecology, and meteorology (Clark, 1990; Turner et al., 1991; Lam and Quattrochi, 1992). While a single ubiquitous definition of scale does not exist, some 15 distinct meanings do appear in the Ox$rd English Dictionary, where several more readily lend themselves to computation and hypothesis testing than others. One definition which can be applied to the time, space, and mass component of any quantity is that scale denotes the resolution within the range of a mea- sured quantity (Schneider, 1994). This is an effective definition as it encompasses two very important, inter- acting facets of scale: resolution and range. Resolution or “grain” refers to the finest distinction that can be made in an observation set, while range or “extent” refers to the span of all entities that can be detected in the data (Allen and Hoekstra, 1991).

In remote sensing, a fundamental characteristic of an image is the spatial resolution, or the size of the area on the ground from which the measurements that com- pose the image are derived. In this sense, spatial resolu- tion is analogous to the scale of the observations (Wood- cock and Strahler, 1987) and the two terms will be considered synonymous throughout this paper. Similarly, the adjectives$ne and small will be used in conjunction with scale to represent microscopic areas; coarse and large will be used to refer to macroscopic spatial extents, and high (H)- and low (L)-resolution will be used as de- scribed by Strahler et al. (1986): H-resolution refers to the cells of an image being smaller than the realworld elements composing the scene; thus the elements (i.e., tree crowns) may be individually resolved within the im- age. while L-resolution refers to the cells of the image

OOW4257/97/$17.00 PI1 SOO34-4257(97)00002-3

being larger than the elements, ancl tlic7&rc ~mresolv- able. M’e aIso definr the term irrlc~gc,-o~?j!jcc,fs (Ha!- c+ al.. 1996) as individually resolvable entities within an irnagr that arc perceptually generated from H-resolution pixel groups, wIir7-e rach group possesses an intrinsic size, shape, and geographic relationship with real-world scene Components.

Within remote sensing literature, scale-related topics include spatial structure and sampling design (M&wire

et al., 1993), pattern and statistical scale approaches (King,

1991; Turner et aI., 1991), spatial resolution strategies (Forshaw et al., 1983; Townshend and Justice, 198X), scale

and information measures (Woodcock ant1 Strahler, 1987: Jupp et al., 1988; 1989; Raffy, 1994; Wieczorek, 1992),

classification accuracy (Irons et al., 1985; Marceau et al.,

1994a,b), and upscaling (Aman et al., 1992). Here, the term upscaling refers to resampling techniclues designed to transform an image collected at a high spatial resolu-

tion (Strahlrr et al., 1986), to a lower spatial resolution representation of the same image. Ideally, such transfor-

mations are intended to reduce the data sizca of an H-rcso- lution image while maintaining its inherent information content at a lower spatial resolution. Unfortunately, this

goal is somewhat contradictory as upscaling involves gen-

eralization techniques which tend to produce more ho- mogeneous, variance reduced, thus inherrntl?~ lower in-

formation content datasets (Wieczorek, 1992). While a host of different resampling or scaling tech-

niques exist in the Iiter~ture (Meentemeyer and Box, 1987; Turner et al., 1991), few are reaclil>- available to

risers, and very little instruction regarding the appropri-

ateness of these techniques to different remote sensing data types exists. In many cases, the only available re-

sampling algorithms for remotely sensed data have been

directly copied f rom classic image processing interpoL- tion techniques and included in commercial remote sens-

ing image analysis packages, even though they are not

theoretically developed for remotely sensed imageI? (Moreno and MeIia, 1994). This often leads to an inap-

propriate use of these routines by inexperienced users, similar to that seen with computer statistical software ant1 novice users. In fact, as no proven theory of spatial

scaling exists (Schneider, 1994) the opportunity to pro-

duce large volunies of impressive nonrepresentative data is enormous. A classic example includes the upscaling routinely performed on Advanced VeF High Resolution Radiometer (AVHRR) data, where pixels representing an integrated spectral response from a nominal 1 km’ areal extent are aggregated to 20 km” pixels, for weekly use as

a global vegetation inclex (Justice et al., 1989). In a broad context, scaling requires the identification

of process nonlinearities with change in scale, the range in scales where linearity may hold, and the properties that may be coherent between scales (Wessman, 1992). While it is inaccurate to state that a process is restricted

to any particular scalc~, it is possible to point to specific

time airtl space scales at \vlCh OIIV proc’c’ss l)rcGls o\‘c’i another (Schnridc~r. 1994). All en and Starr t 19X?), O’Nc~ill Pt al. ( IWGi), Holling (1992), a11t1 others halt. s~iggestrtl

that a landscape forms a llierarchy which c,olttains l)reaks in object sizes, object proximities, and textures at partic- ular scales, resulting frolri (different) stnicturing proc’esschs

exerting their influence o\‘er defined rangrs of’ sc&. St+:- era1 remote sensing studies support these &in~s (Ror- rough, 1981; Clark. 1990; Marceau et al.. 1994a,b), and have suggested that the laTldsc%p~ poss”sse” CYiticXl thresholds at which ecological processes c.l~angc’ qualita-

tively (Pllrach, I WI: Sonriau, I C&M). Unfortunately, as spatial scales \q’. spectral varia-

tions captured by sensors differ uonlinearl~~ with a trajec- tory that is ineompIetel?- irndrrstood, often resulting in substantial sealing error when integrating data and rnod- els from different disciplines, time, and spatial scales (Gardner et al., 1982; King, 1991: Rastetter c,t al., 1992). Kimes clt al. (( 1993) have explored the reflecta~lce clrrors associated with spatial a\.eraging 1,~ using a sirmllatetl scene derived from high-quality bidirectional reflectance measurements that have beLen I~roc~ss~~l illto grid cell measures of hen~ispherical rrflectancc.. Kesults indicatri that errors could br rc~stricted to the Fj-IO%, range rcx- quired for use in global cliniak inodels if l~omoge~~eous regions within ~ch ccl1 ~ultl be identified, and thr rcl- suiting c,stimates weighted I~\- the proportional area ot each cover tlcpe. One of their greatest challenges lks in being able to divide the scww into “llolnog~,n~olIs” patches of ground cover for which drtuiletl angl~lar 111ea-

surements are available. Though originating from a completely different the-

oretical approach than that described by Kinlcs et al. (1993), this article describes a novel v~lliancp-\veightecl upscaling technique-based on il model of thr lllllllall eye (Hay, 1993)-that is capable of identifjring homoge- neous regions within an image bv defining Illultiscalr spatial thresholds at which the spectral \zrianct~ of in+ age-objects arr scale-depeIlderrt, and using tlirse SC& dependent spatial measures as weighting timctions so that fin? scale data can be rcapresentativelv Inodelrd within a user-defined upscaled image. This tc~chniquc is also able to automatically generate an image that models the maximum multiscale information within the scclle, and an image that models multiscalc~ scene c~onlponc~nts at their individually unique next coarser scalrs. with ap- plication ti)r any scalr of imagery. Thra theory behind this technique is based on an understanding of thca relation- ship between multiscale image variance and high-rrsohl- tioll image-objects, and will be flirther discusscad in thcb Methodolog>; sectioll.

The primary objectives of this study result from ask- ing the following questions: When examining a signal through various scale changes, what is the most appro- priate upscaling technique to represent this signal at dif- ferent scales? And lrow can this hc \&datrd? Solutions

Tabk 1. Multiscale Data Summary

Spatiul GPS Resampled Height (A.G. L.) Ground Speed Integration Time Re.s&ion Pixel Size

Cm) (m/7) irn?i ix, y)” ix, r/i”

12x0 79 80 1.50, 3.25 1.5. 1.5 2600 92 80 :3.04, 3.79 3.0, 3.0 2600 90 150 x04, 7.10 5.0. 5.0 3500 92 1.50 4.10. 12.45 10.0, 10.0

‘LT. y) wfers to along and ;KTOSS track positiow, respwtivrly I irl nrrttm).

to these questions were approached by examining how the 660 nm signal (wavelength center +5 nm) of six for- est stands vary through four different scales of same-sen- sor imagery and five resampling techniques.

IMAGE, GENERATION, SELECTION, AND PROCESSING

Though dramatically smaller than the terabytes of imag- ery expected daily from the Earth Observing System platforms, the 1.03 GB dataset collected for this study offers substantial storage, retrieval, manipulation, and an- alytical challenges to the user. This section summarizes the procedures involved in image acquisition, study site and wavelength selection, and the application of atmo- spheric and geometric corrections.

Image Acquisition

By varying flying height, ground speed, and sensor inte- gration times (Table l), 11 multiscale Compact Airborne Spectrographic Imager (CASI) band sets, each composed of eight channels totaling some 1.03 GB were collected during 20:10-21:40 h (GMT) over the Sooke Watershed, British Columbia, Canada on 1 August 1993 (Fig. 1). Data were collected over both north-south and south- north flight paths.

The CASI is a pushbroom sensor designed to oper- ate from light aircraft and helicopters, with data capture capabilities based on a two-dimensional (2D) frame transfer CCD array. This 2D array allows the sensor to function as both a multispectral imager (spatial mode), and an imaging spectrometer (spectral mode) sensitive in the visible and near-infrared portions of the electromag- netic spectrum (418-926 nm). In both modes, the system offers user programmable spectral band sets (in terms of wavelength and width) with a sampling interval of 1.8 nm and a 12-bit dynamic range (padded to 16 bit). In spatial mode, the sensor provides a maximum capability of 15 programmable bands, while spectral mode offers a maximum of 288 bands in up to 39 different viewing di- rections across the swath (Gower et al., 1992). Since these data were acquired, an enhanced CASI instrument has become available with up to 101 look directions, 39 user selected bands, and irradiance probes on the roof

and belly of the aircraft capable of collecting up- and downwelling hemispherical radiance measurements in addition to normal image acquisition. Data from the downwelling probe enable conversion to image reflec- tance, while the two probes in conjunction provide the potential for the direct measurement of at-sensor hemi- spherical reflectance (McDermid, 1995).

Unfortunately, data acquisition over this site was plagued by equipment difficulties and conditions of se- vere wind and turbulence resulting in image smear and distortions during aircraft rolls greater than +lO” from horizontal (0.1” precision). Data were further compro- mised by a malfunction in the aircraft pitch g)iro which removed the option for pitch correction during pro- cessing. Imagery were able to be corrected for yaw and roll errors (less than + lo”), and sensor-inherent radio- metric errors. With the addition of differential Global Positioiiing System data, a first-order geometric correc- tion (Z&arias et al., 1994) was applied to the multiscale imagery, providing for resampling into north-up square pixels at four spatial resolutions: I.5 m2, 3 ml, 5 IJI~, and 10 m" (Table 1).

Wavelength and Site Selection

As the dimensionality, spatial resolution, and volume of datasets increase, routine image analysis becomes in- creasingly more complex and time-consuming. Even when working on a dedicated workstation with 64 MB of KAM, a 21-in. monitor, and a 4 GB storage medium, the task of visually locating a plausible study site within the swath proved to be nontrivial. In total, 11 different datasets (each 8 channels deep) ranging from 500 pix- elsX800 lines (9.9 meg) to 3334 pixelsX6000 lines (327 meg) required Lisual evaluation before a location with minimal roll error through all scales of imagery could be selected.

Although the finest resolution imagery covered a swath path no larger than 9.0 kmX0.6 km, its sheer digi- tal size (327 meg at 1.5 m spatial resolution) necessitated the selection of a smaller subimage for analysis. After ex- tensive scrutiny, a single channel, 1200 pixelX900 line north-south subimage was selected and extracted from the 1.5 m band set. Its corresponding location and wave- length were also extracted within the north-south 3-m,

Figure I. Map of the study site location.

5-m, and 10-m band sets, resulting in four images cov- ering the same location at different spatial resolutions, but with equivalent spectral resolutions (wavelengths). A CASI band centered at 660 nm (?5 nm) was chosen for analysis as it represented both the minimum chlorophyll a reflectance signal and the absorption maximum of solvated chlorophyll a (Kirk et al., 1978). It should be noted that while the low trough in actual spectra associated with plants appears closer to 675 nm rather than the 655-665 nm as used, the selection of band widths and locations was limited to those predetermined for a prior mission.

Geometric Correction

Once corresponding subimages were isolated and ex- tracted from all four scales of imagery, the 10 m subimage was geocorrected to imported road and forest polygons vectors (with an inherent locational error of 210 m). The remaining 5 m, 3 m and I.5 m subimages were then geo- metrically corrected to this new 10 m image, as visual cues for ground control point (GCP) selection were more abun- dant here than in the vector data. In all channels, the loca- tional error after resampling with the nearest neighbor al- gorithm-as the original DNs remain unaltered (Jensen.

Spatial Thresholds, Image-Okject,s, and Upscaling 5

Class 1 Class 2 Class 3 Class 4 Class 5 Class 6

Description Mature Mature Young Young Immature Immature

~~,~iiii

Dominant DF DF DF DF DF DF Species

Age 141 - 250 141 - 250 33 23 17 17

) Height 55.5 - 64.4 37.5 - 46.4 19.5 -28.4 10.5 - 19.4 10.5 - 19.4 0 -10.4

(m) Canopy 6-10 6-10 3-5 2-4 l-3 l-3

Diameter (m) Crown 46 - 55 56 - 65 66 -75 16 -25 46 - 55 26 - 35

Closure (%)

Figure 2. Description of Sk Forest Class Characteristics.

1986)-was less than 210 m, and the original data resolu- tions were maintained. In this article, DN (digital number) refers to spectral values which have been converted to ra- diance measures. A large number of GCPs and a high- order polynomial resampling procedure were indepen- dently applied to all images to rectify for roll error.

Site Characteristics

With the aid of l:lO,OOO forest inventory maps (GVWD, 1993), field surveys, and 1:12,000 color near-infrared (NIR) aerial photography (1993), six forest stands domi- nated by Coastal Douglas-Fir [ (Pseudotsuga mnziesii) (Mirb.) Franc0 var. menziesii] were selected within the scene, and are described in Figure 2. Classes 1 and 2 rep- resent mature stands, differing primarily in height. Classes 3 and 4 and Classes 5 and 6 represent young and imma- ture stands, respectively, each differing in height and crown closure.

The selected subimage (Fig. 3) represents a 257 ha valley-bottom site located within the Sooke Watershed, west of the city of Victoria, British Columbia, Canada. In this area, the very dry maritime Coastal Western Hemlock biogeoclimatic subzone dominates, though a small component of moist maritime Coastal Douglas-Fir subzone also exists. Due to its longevity and the area his- tory of repeated fire and windthrow disturbances, succes- sional processes on any site unit rarely proceed to a cli- max forest; as a consequence Coastal Douglas-Fir is the dominant seral tree species (GVWD, 1992).

Atmospheric Correction

After examining the entire multiscale band set and being satisfied that all wavelengths behaved according to known scattering theory (Slater, 1980), a first-order at- mospheric correction was individually applied to each of the four channels in the form of a dark-body extraction technique (Avery and Berlin, 1992). Once applied, each of the four channels were resampled to a common I.5 m spatial resolution (using the nearest-neighbor algorithm) and then combined within a single dataset to facilitate the extraction of spatially explicit samples. This resulted in a dataset composed of four geometrically and atmo- spherically corrected, same-wavelength channels, each of which visually models the scene from different flying heights, while being digitally modeled at the same spatial resolution (i.e., 1.5 m). Since the L-resolution data were resampled into a finer scale with nearest-neighbor, the DNs were not compromised; that is, a 3 1nx3 m pixel would now be represented by four 1.5 m X I .5 m pixels, each containing the same DN. These geometrically and atmospherically corrected channels were then considered accurate representations of the scene, and all subsequent analysis was performed on them.

Due to the pushbroom nature of the CASI sensor, path radiance effects, that is, the light scattered by the atmosphere into the sensor’s field of view without being reflected from the surface, tend to produce a brightening of the across-track DNs located at the image edges due to the longer path (Kaufman, 1989). While newly devel-

lmv it arc 3 111. 5 in, and IO JJJ silt~ilriages.

oped software were available to correct for this effect (Niemann and Sykes, 1995), none were applied to the data, as two (across-track) transects sampled over all four corrected scales appeared with minimal curvature when modeled by a second-order polynomial, indicating lim- ited path radiance effects.

METHODOLOGY

The task of assessing the most appropriate resampling technique to represent a 660 nm signal at different scales

was approached in two steps. The first involved applying five different resampling strategies to three scales of im- agery (1.5 m, 3 m, and 5 m), which produced 15 unique images, each of which were upscaled to a 10 m spatial resolution. The second step required determining the root mean square error (RMSE) of samples extracted from six different forest classes within the modeled data (upscaled) and those obtained from equivalent locations within the original 10 m imagery. The upscaled image with the lowest RMSE was then considered the most ac- curate upscaling routine of those tested, as it generated

DNs with values most like the original coarse resolution image. The first of the following two subsections de- scribes the traditional resampling algorithms used, while the second describes the theory and application of the variance-weighted upscaling routine.

Traditional Resampling Algorithms

Nearest-neighbor, bilinear interpolation, and cubic con- volution were available in a commercial image processing package, while nonoverlapping averaging was written for this study.

l In nearest-neighbor (NN), or zero-order interpo- lation, the DN of the pixel closest to the loca- tion of the original input pixel is assigned to the DN value at the output pixels location.

l In bilinear (BIL), or first-order interpolation, a DN is assigned to an output pixel by interpolat- ing DNs in two orthogonal directions within the input image. Essentially, a plane is fit to the four pixel values nearest the location of the pixel in the input image; then a new output DN is computed based on the weighted distances to these points.

l In cubic convolution (CC), resampling occurs in much the same manner as bilinear interpolation, except that the weighted values of 16 pixels sur- rounding the location of the pixel in the input image are used to determine the value of the output pixel (Jensen, 1986).

l In nonoverlapping averaging (AvG), the mean of the DNs within a nonoverlapping square window (beginning at the origin) are calculated and as- signed to the first location in the output image. The window in the input image is then moved a distance equivalent to the specified window size, a new mean is calculated, assigned to the next lo- cation in the output image, and the kernel is it- erated until the original image has been com- pletely sampled.

Variance-Weighted Upscaling:

Theory and Application

Allen and Hoekstra (1991) suggest that scale is not a property of nature alone but, rather, is something associ- ated with observation and analysis and that the scale of a process is fixed only once the actors in the system are specified by the observer. But how do we define these actors in a pixelated image void of topology? And what happens when the actors are themselves multiscale, and interact in a nonlinear fashion? These are not trivial que- ries and have important implications for the development and linking of hierarchical ecosystem models driven by multiscale remotely sensed data. It is also critical to rec- ognize that spatial phenomena cannot be studied inde- pendently of the sampling system used to detect and measure them, as modifications to the sampling frame

induce changes, both in the phenomena themselves and their subsequent interpretations (Marceau et al., 1994a). To satisfy both the sampling dependent nature and multiscale variability of spatial phenomena, we have cho- sen image-objects to be our vehicle for defining scale, and employ heuristics based on the mechanics of the hu- man eye and multiscale image variability to define and upscale them. The following section briefly describes the theory and methods developed to achieve this.

By employing the human eye as a model (Hay, 1993) we propose an upscaling routine that uses variable sized object-specific windows to analyze and incorporate the influence of different sized, shaped, and spatially dis- tributed objects within the upscale image, rather than upscaling based exclusively within an arbitrary fixed sized window. We recognize that when a sensor views a scene, the recorded radiance represents an integration of the spectral reflectance characteristics of the corresponding objects in the scene convolved within the spatial resolu- tion of the sensor (Jupp et al., 1988: 1989). To model these effects within an upscaling window, we use image- objects to model real-world objects; the spatial extent of the upscaling kernel to model the sensor’s static instanta- neous field of view (IFOV); and an area weighting scheme based on the unique spatial characteristics of im- age-objects to model the spectral influence of neigh- boring cells [i.e., tl le adjacency effect (Kaufman, 1989)].

Thrb variable object-specific basis of this approach is far from new. In the early 198Os, David Marr’s (1982) pioneering theories on image processing and the human visual system indicated that intensity changes occur at different scales in an image, such that their optimal de- tection requires the use of operators of different sizes. He also theorized that sudden intensity changes produce a peak or trough in the first derivative of the image. Con- sequently, a vision filter [according to Marr (I982)] re- quires two characteristics: It should be a differential op- erator, and it should be capable of being tuned to act at any desired scale (Graps, 1995).

To meet these criteria, an image-object is considered an entity composed of primitives (in this case, individual pixels) more similar to it, than dissimilar. Where the heu- ristics determining the threshold of “similari9” are based on the novel concept that all pi& within an inmge are H-rdution samples of the .scene-objects the!/ model, ecerl though both H- and L-re.volution infommtion poten- tialhy exkt for each object within the imagr~. The impor- tance of’ this rule is that spatially near pixels elicit a strong degree of’ spectral autocorrelation. Therefore, when we plot the digital variance of samples obtained within a varying sized window while centered on an im- age-object of known size, a distinct break, or threshold, in variance is observed over increasing window sizes, which (threshold window size) strongly relates to the ob- jects known size. This is similar to analysis using linear semivariograms but is not limited by the ladaccuracy problenl (Hay et al., I996), or the difficultv of interpre-

Figure 4. This image illustrates an example of 22 individual tree crowns (bright areas) as viewed from 1.2 m CASI imagery. The small black squares, with associated numbers, are attributes which represent the center of individual trees. The large black square represents the extent within which analysis was initiated, while the small image (lower left) represents the full forest scene from which this sub-scene was extracted.

ting two-dimensional semivariograms (Jupp et al., 1989). Conceptually, this variance threshold represents the end of one scale-that is, the maximum zone of influence (i.e., area) at which the pixel under analysis is spectrally and spatially related to its neighbors-and the beginning of the next scale-which defines a new image-object, of which the mean value and pixel location of the current threshold window will be an H-resolution member (see mean dutuset in the Discussion section). For example, Class 4 tree crowns (2-4 m) are poorly suited to be mod- eled by the 5 m data, as these data are L-resolution with respect to this class [i.e., the objects (tree crowns) com- posing the class are much smaller than the spatial sam- pling scheme (pixel size)]. But if the pixels over this for-

est class are considered as H-resolution and their DN variance is examined at increasing window sizes until a threshold in variance is reached, a unique (potentially optimal) spatial extent can be determined for each H-reso- lution pixel which indicates how it (a single pixel repre- senting integrated tree and background signals) is associ- ated with a portion of an object existing at the next coarser object scale, that is, gap or stand parameters. A measure of the window area obtained at this variance threshold is then used as a weighting value to model the influence of the image-object within the upscale kernel. This is based on the supposition that when upscaling an image, the H-resolution image-objects within a scene should have more influence on the integrated signal than

Spatial Thresholds, Image-Objects, and Upscaling 9

Variance Threshold / Window Size Measures

2 4 6 8 10 12 14 16 18

winsize

Figure 5. This graph depicts plots of variance threshold measures vs. window size for individual trees nurn- bered 15-22 as illustrated in Figure 3, and also illustrates the variability within a natural scene. Values are de- rived from a varying sized window centered on their respective tree centers. Measures similar to these were used to develop .ob&ct-specific threshold heuristics.

a single bright L-resolution pixel-whose signal is already regularized-as would be the case in simple averaging. Operationally these steps may be explained in the follow- ing manner:

Variance-weighted upscaling involves two main pro- cesses: generating datasets from which weights are calcu- lated, and calculating and applying these weights within the upscaling routine. In the first process, the spectral variance of DNs within iteratively growing (i.e., 3X3, 5X5,7X7, . . .) square kernels (SUP) are calculated over each kernel center until a variance threshold is reached. This threshold is based on heuristics which relate the slope of the different variance measures and kernel sizes obtained at each increment, to the spatial extent of the image-object being evaluated. Once satisfied, the area, mean, and variance of the pixels within the current threshold kernel are individually calculated, and assigned to three different files at the same pixel coordinates as the kernel center. The iteratively growing kernel is then moved to the next pixel and the process is repeated until the full image is assessed. This results in three new im- ages: area, mean, and variance, each of which maintain the same spatial extent and resolution as the original im- age. The importance of these three images are described in the Discussion section. Image edges are assessed up to a distance of one half the kernel size.

In the second process, weighting occurs in the fol- lowing manner: A user determined, fixed-sized, square moving kernel is evaluated over the newly generated area dataset. Within this kernel, each unique area value per pixel is identified and divided by the sum of the total area values within the specified upscaling window (i.e., upscaling from 1 m2 to 10 m2 data requires a 10X10 pixel kernel). This results in an individually weighted area value per pixel. Each weighted value is then multiplied by the DN at the same coordinates in the original CASI imagery, producing an object-specific area- weighted spectral value. This process is applied to all pix- els within the upscaling kernel, which are then summed and assigned to the appropriate location in a new up- scaled image file. The kernel is then moved over the area dataset a distance equivalent to its static window size, and the process is iterated until the entire dataset has been assessed and a new upscaled image produced.

Initial analysis and heuristic development were con- ducted using 1.2 m CASI imagery from a previous study (Hay et al., 1996) which represented over 150 trees with known spatial locations (Fig. 4), and corresponding men- suration data (Hay and Niemann, 1994). Due to the high variability exhibited in this natural scene (Fig. 5), a digi- tal forest model was generated-composed of 373 ob- jects (tree crowns) with known sizes-and the described

c*oimt for tllc, inherent variabilit), within thr natural scent”, wt‘ returned to the II-rrsohltion imagen and filr- thrlr developed and r&ned the ~,arianc~/k~~mel-siz~, II~II-

ristics to agree with known forest Inrusuration data. Ll’rl

then applied these refined methods to this stidy t;)r tilr- tiler analysis.

lna1l~ ul’“‘d~Yl t;,r the Ire%? le\Yl ot’ (%Cll 01’ tllck Illi(ll\

unique sized image-object composing it. as h I(’ algoritlrl~~ allows tlir statistics of wch inragcl-objr*ct within the. swne to tlctcrrninc its Jiest JIIost ol~tirnal spatial cstrwt,

rather than bring arbitrarilv ulm&tl 1~ ii cmr\-eiiirrlt

static kerucl. In esseI~~. we are Iming grain (piwl sizcl)

to define extent (obiect influence or fbtpriirt ). whicli

RESULTS AND DISCUSSION

Area, Mean, and Variance Datasets

The nrc?a dataset (Fig. 6) models (both numerically and thematically) the relationship between each pixel (grain), and the spatial area of influence, or structural en-tent of the image-object it is presently an H-resolution member of’. While it does not indicate that the processes which produce these unique spatial extents (and corresponding thematic patterns) are related, inference may be possible with more detailed ancillary data. In Figure 6, the brighter the tone, the larger the area of influence. In the 1.5 m area image (top left inset), several tones corre- sponding to different sized tree crown-which include both illuminated and shadowed portion-are repre- sented within homogeneous spatial units, whereas typical edge detecting algorithms would segregate the two. Other thematically defined areas directly correspond to canopy gaps, forest classes, forest stands, road systems. and logged areas. In the 3 m, 5 m, and 10 iii area datw-

sets, each increase in scale reveals less overall tonal varia- tion within the same spatial extent, and may he indicative of how specific landscape structuring processes with uiiiclue spatial extents dominate others as resolution changes. We are currently investigating techniques to map these varying spatial fields over increasing scales in an effort to link them with appropriate scale-specific bio- physical models, in part, by using output generated from the niean dataset.

In the ?~c:nn dataset (Fig. 7) each pixel represents arr average spectral value of all the pixels within the unique maximum spatial extent (or area) of the image-object it resides in. Though only briefly mentioned in this paper, its generation provides an important juncture in this up- scaling paradigm. By adopting the human eye model, dis- carding the concept of a user-defined &tic upscaling window, and iteratively generating upscale images de- rived from the mean of the pixels within the threshold window, we can produce an object-specific upscaled irn- age which hierarchically models the next scale(s) of im- age-objects within a digital scene (at multiple resoh- tions) as the human eye would see it, rather than as a sensor would arbitrarily define it. Iterations on mean da- tasets will produce corresponding area and variance im- ages, each with their unique spatial patterns, which, when compared over different scales, can be used to de- scribe how th(a extent of different structures, or objects, dominate over others with changes in scale. It is impor-

II I

then defines the scale of the iipxt (coarser resohition) iJIJ-

age-object it is presentlv an H-resolution mc,lnber ot’. Obviouslv, it will be critical to cxamint\ and tlefinr the exact spatial resolution each pixel represents as it JJIo\~

through this hierarchy of object-specific hcalcl changes. While aware that thr entities that eniergc~ in a data-

set are scaled by virtue of the obse~ation protocol aid the filters applied to the dataset during analysis (Allen and Star. 1982), WC believe that if this hmi~n visiorl ap- proach proves appropriate, then the changiiq pattcariis generated at path new scale of image-objects. in combi- nation with ancillary data, that is, soils, slope. aspect, \q- etation co\-er. climatic variables, etc., iIi:iy pro\itle ;i tim\

tool fbr gaining ;I greater untlerstancling of‘ lantlscq~e processes front pattern. Furthrr explanation falls b(Jvond the SCOpc’ of tlliS ~u~ticle, thOUgl1 tlleW &lS ill’? ill1 iSSUC

of current research (Niemann and Hay, 1996 ). Each pixel in the ctrricir,cr datasct (Fig. 8) represents

a unique variance value obtained when a series of’thrrslr-

old heuristics are met. As indicated, these heluistics arc‘ based OII the shape of vaJiamce trrcwures plotted over changing kernel size; consequently, each pixel is also re- lated to a uniquely calculatrd spatial extent which defines the maximlm~ scale of an imag-object it is ;UI H-resoh- tion member of’, Iu this dramatically textured image (Fig. X), dark DNs represent spatial extents of low spectral variance (i.e., relative homogrneit),). whilr bright DNs represent areas of high spectral variance (i.ca.. relative heterogeneity). This dataset provides ;LJI c~xcellent visual

measure of how well the object-specific algorithm oper- ates to delineate objects. Essentially it p~rforiirs as an edge detector, where image-objects (dark pixel groups) reside within edges (bright pixels). Visual analysis of this scene reveals a large amount of IIC~G infbrmation, partic- ularly of phvsical boundaries, or ecotonrs that were not immediately obvious within the original imagery, but are confirmed by ground surveys and aerial photography. Based on the well-defined edge effects that appear in this image, we feel highly confident in the ability of this technique to define image-objects that mode1 realworld scene components.

RMSE and Visual Interpretation

The root mean square error (Algorithm 1) represents the average difference in DNs per class between the cor- rected 10 m dataset (R,) and an upscaled dataset (R,,) generated by one of the five resampling algorithms. Once the 1 .ii m. :3 III. and Fi ni data wer(x ~~ps~.aletl to ;I

Spatial Thresholds, Image-0hjcxt.s. and Ifpsding 11

Figure 6. This four image collage represents the area data through four scales of imagery. Each of the unique tones models (both numerically and thematically) the relationship between every pixel and the spatial or struc- tural extent of the image-object it is presently a member of. Eventually it may be possible to link these maps to physiological processes active in the landscape, or to use them in establishing the spatial extents at which specific ecosystem models and data are required. Illustrated in the right image and at the top left are the ~5 m data. Belo\n~ it are the 3 m, 5 m, and 10 m datasets representing the area \?rithin the highlighted polygon.

10 m spatial resolution, 50 samples (N,,s) per six forest classes were evaluated for each algorithm (five total), for each scale of imagery (for a total of 6000 samples). Sam- ples were selected away from class boundaries, and at a minimum distance of 20 m (2 pixels) apart from each other within the original and upscaled 10 m datasets:

Based on the initial premise that the upscaled image

with the lowest RMSE is the most accurate upscaling routine of those tested, RMSE results (Table 2) indicate that the variance-weighted technique (SUP) is the most accurate upscaling algorithm of those tested, as it pro- duces an upscaled image with the lowest RMSE in 10 out of 18 classes over all forest types and ranges of scale tested. In the eight times it did not obtain the lowest RMSE, it produced six values with the second lowest. Simple nonoverlapping averaging provided the second most accurate class results, with the lowest error values

Figu ro 7. This collage illustrates cac11 of’ the fblm scidcs of )WUT~ data, wl~c~t~ cdl pixel wprtwnts a~ a\(~ag( spectral valw of all pixels within the uniqw ~~mcirnum spatial extent (or zone of’ influence) of’ the inlagc-objwt it resides in. For comparative purposes, each subirnage represents the sww location as tlw arc~a data set [Fig. 5). Illustrated in the right image and at the top left are the I..5 111 data. Below it ;uc the 3 m. 5 m, ant1 IO III datasets respectively.

7 out of 18 times. Although the RMSE values appear exceptionally high, they are a valid measure when con- sidered that the data are 16-bit spectral values. There are also the possibilities of class samples at a particular scalp being misregistered at another scale due to roll error, image smear (see Image Acquisition subsection), and ge- ometric error.

Regarding image smear, it is interesting to note that visual analysis of the variance and area datasets indicate that the variance-weighted algorithm considers areas of

image smear-usually a composite of several tree crowns, which appear through different scales and forest classes over the study area-as a single image-object, just as a human interpreter would. From an evaluation perspec- tive, this results in different window sizes, variance and area measures, weighting functions, and RMSE values being generated over these smeared areas, from what would be the case if crowns were individually assessed. This characteristic was only noted as we attempted to understand why several RMSE results for SIJI’ indicated

Spatial Thresholds, knage-Objects, and Upscaling 13

Figure 8. This image illustrates the spectral oariance dataset which is produced from a contextual analysis over increasing spatial extents until a threshold heuristic is met. Bright areas represent locations of high vari- ability (i.e., edges), while dark areas represent more homogeneous locations. Multiscale images are included to visually illustrate changing information content as data are generalized due to a coarsening of the sensors spa- tial resolution. Illustrated in the right image and at the top left are the 1.5 m data. Below it are the 3 m, 5 m, and 10 m datasets.

substantially different values from those of AVG. By rec- ognizing how the algorithm interpreted the “smeared” objects over sampled classes, we consider these unchar- acteristic RMSE values (i.e., Table 2: intersection of Class 4, and 5-10 SUP) as further support for how well the object-specific approach works.

When the upscaled images (Fig. 9) are visually com- pared to the original data collected at 10 m, greater land- scape structure are apparent in the resampled images-

though this may be difficult to assess on the printed medium. In several cases this structure is noise gener- ated as a function of the algorithm used (i.e., NN). In other cases, these spatial structures represent actual scene components, and may be explained by the relation- ship between the sensor’s ground resolution and the size of the scene objects. Slater (1980) indicates that if scene- objects are less than one quarter the ground resolution of the remote-sensing system, they are imaged at the size

14 II/l!/ d /II

l’dde 2. Hoot Mean Squxe Error I-lcsdts -..- _____ _._.._-.

AlgOrifhltI c1ms 1 Clns.v 2 ClN.(..). 3 Clnss 1 Clnss 5 Ckss 6

I .5-IO cx: 6 13.67 HOI .02 ““3.7% I I 1-u I 413.0:3 5:10.24 1 .s-10 13IL 559.99 7x.21 “08.52 IO46.7-l :3t#io9 ,512..&3 I .5-IO NN 583X3 75i.5 I 223.70 I I Iv.89 1 44fili 3:34. I6 I .5-IO AVC: 325.56 556.64 1.58.*57 859.61 318.01 3356.82 I ..5-IO SUP :394. I9 520.49 152.94 W9.93 :360.4-I 271.92

:3-IO <x: 424.21 (i:37.74 199.22 9m.7:3 4x7.05 .54 I .SY :3-10 BIL 364.40 6ol.:3H “93.73 %36.40 432.80 .X9.:33 :3-10 NN :37:3.zl 6i48.3.5 ‘305.87 9K3.48 440.05 539.8 I 3-10 A\‘(’ J X3.06 493.62 68 1.44 756.19 49S.G 446.12 :3hlo SUP 309.19 446.00 261.37 S9h.46 499.41 3:37..jT

S-IO cc 4i4. I I 508. 1; 2:34.li1 96.5.0.5 41s.:3:3 .3X.35 5-10 BIL 428.31 445.42 220.0.5 cl;. I7 :3c%.4:3 :350.‘# 5-10 NN 44s.43 *527.x 229.66 939.54 4 IO.53 :399.1(i 5- 10 AVC: 400.77 *502.x:3 209.25 784.19 43;x3 42:3.:32

5-10 SUP 394.23 466.:32 21:3.7; 1012.69 356.00 312.58

Bold figures represent the lowest KMSE value, thus the most appropriatt~ qscding algorithrrr

of the point-spread function of the system. Since this function describes how a point of light is spread by lense aberrations-which in modern lenses tends to be very small-their influence is essentially negligible. Similarly, Marr (1982) states that the features of an object that are much smaller than the primitives used to describe it (i.e., the resolution cell of the sensor) are not just inaccessible, they are completely omitted from the description. There- fore, determining the most accurate upscaling routine based on the lowest RMSE value (as we have done) may not be suitable for evaluating this type of data, as up- scaled datasets incorporate fine object detail from their H-resolution parent images which does not exist (or is sufficiently negligible) within the original L-resolution image. Thus they can never be the same.

Understanding this perspective is important as it im- plies that traditional evaluation techniques that compare the original (i.e., 10 m data) with the model (i.e., 1.5-10

m upscaled data) may not be acceptable for assessing up- scaled information, as original scale data are potentially less representative of the realworld scene than the model it evaluates. So upon what criteria can an evaluation be made? Determining and validating the most appropriate upscaling technique is not trivial, and new criteria will need to be established.

Visual analysis of the upscaled and original images (Fig. 9) and an understanding of the relationship be- tween IFOV and scene-objects suggest that, with a theo- retically sound resampling routine such as the variance- weighted algorithm, an upscaled image is more represen- tative of the scene it models than an image captured at the same upscaled resolution, as an upscaled image in- corporates information that the sensor filters out, or is “blind to” in the original L-resolution image. Conse- quently, it may be more appropriate to focus fllture sen- sor development towards collecting data at the finest spa-

tial resolution possible (i.e., the EarthWatch Early Bird system with 3 m panchromatic planned for late Decem- ber 1996, and the submeter QuickBird platform sched- uled for late 1997) and algorithm development focused on upscaling routines, rather than collecting a host of dif- ferent spatial resolution data each with their own sensor specific challenges. Obviously there are numerous detec- tion, retrieval, storage, and analysis considerations that require attention before this occurs, but this is where we believe the future lies.

Different Optimal Spatial Resolutions

for Different Objects

Just as the lenses of our eyes change shape to “optimally” resolve different sized, shaped, and spatially arranged ob- jects within a scene, no single spatial resolution of digital imagery provides an optimal (i.e., perfect, or exact) reso- lution for examining the varying sized, shaped, and spa- tially arranged image-objects it models. Rather, different optimal spatial resolutions exist for different object char- acteristics, suggesting the need for a multiscale approach for detection and analysis (Marceau et al., 19941); Hay et al., 1994; 1996). Here the term optiwul is used ideally, with reference to many suitable scales from which to choose. It is not used in the sense of selecting the most satisfidctory from a limited set of potentially inappropri- ate scales.

From a spectral classification perspective-where low within-class variance is desired, as it tends to result in a higher classification accuracy when using traditional classifiers-the spatial resolution that provides the mini- mum variance may be considered as optimal (Marceau et al., 1994b). By using this theory as a guide, an analysis of each of the six forest classes through the four cor- rected wavelengths (Fig. 10) confirms that no single spa- tial resolution of imagery can satisfy this criteria for all

Figure 9. This collage illustrates the visible differences between the original 10 m CASI imagery, and the datnsets gen- erated by resampling from 1.5 m to 10 m. Viewing from top left to bottom right, the illustrations are: 10 m original CASI imagery, 1.5-10 m cubic convolution (CC), l.ij-10 m bilinear interpolation (BIL), 1.5-10 m nearest neighbor (NN), 1.5-10 m nonoverlapping averaging (AVG), and 1.5-10 m \,ariance-weighted upscaling (SUP).

classes. In class 1, the minimum variance is reached with

a spatial resolution of 10 m. In classes 2, 3, and 5, mini- mum variance is obtained with the 1.5 m dataset, and, in classes 4 and 6, the 3 m data provides the lowest mea- sure of variance.

From an information perspective-where high within- class variance is sought--there is also no single scale of imagery which provides a ubiquitous optimal spatial reso- lution for all forest classes. Classes 1 and 6 illustrate a measure of maximum variance in the I.5 m dataset, class 2 at a spatial resolution of 10 m, classes 3 and 5 at 3 m, and class 4 at 5 m.

It is also interesting to note (Fig. 10) that the finest spatial resolution imagery does not always produce the largest measure of class variance, for example, low reso- lution 5 m data provides the greatest within-class vari-

ance in class 4, rather than high resolution I.5 m data, and may be explained in the following manner. Mini- mum variance primarily results from two conditions: When pixels are L-resolution, thus the signal from many objects are integrated producing a smoothed response, or, when the signal is H-resolution, thus many pixels rep- resent the same object with a greater likelihood of closer pixels having a similar spectral value. But when the pixel size is nearly the same size as the scene objects, that is, 3 m data in classes 3 and 5, the 5 m data in class 4, the 1.5 m data in class 6, and the 10 m data in class 2 (Fig- ure 2), variance tends to be higher as the potential for a pixel to directly sample a single object (i.e., tree crown) is reduced. Instead, the pixel possesses the probability of representing the object, background, or combination of the two. resulting in increased spectral variance.

Variance of Six Forest Classes, Through Four Scales of Imagery.

--V--1Om

1 2 3 4 5 6 Forest Classes

Figuw 10. This graph plots variance change in six forest cl&es through four scales of corrected imagery. A sample size of 50 pixels per class, per wavelength were selected (1200 total). Note that no single scale is optimal for all classes over all scales.

Class variance is a function of the size, shape, spatial

arrangement, and spectral characteristics of the objects

within the class, in relation to the spatial resolution of

the sensor. While this theoretically sounds concise, the

heterogeneity of varying sized objedts within a single class can result in a host of difficult-to-predict outcomes. For

example, in class 1 the 1.5 m data should result in a low

variance measure due to a high correlation of Kresolu-

tion samples; instead, it produces the highest variance without being the same size as the objects. This may occur

because the crown density is relatively low: thus the op- portunity to sample a greater number of pixels with both

similar tree, and background (shadow) values increases, resulting in an increased variance between the t\~o.

Algorithm Caveats

Of the algorithms tested, it is apparent that NN, HII,. and CC are unsuited for upscaling remotely sensed data for several fundamental reasons. None of these tech-

niques take into consideration the influence of neigh-

boring pixels outside the upscaling kernel, and, in cases where upscaling requires a window size greater than

5x.5, they generate an upscaled value from a sample which may not accurately represent the area they model. For example, within a 5x5 kernel. NN only samples a single pixel, BIL samples 5 pixels, and CC samples Ii out of 25 pixels. When these pixels are considered as ac- tual landscape samples ranging in nominal area from 1 m’ to 1 km” (i.e., CASI to AVHRR), their nonrepresen- tative influence on the upscaled image and/or their sub- sequent effect in ecosystem models could be dramatic. Also, if the upscale kernel size were increased beyond *5x5. these algorithms would still sample the same mlm-

In norlo~erlapping a\waging, all pixels \vitliirr tl1Y

upscaling kerncll are evaluatr~d. resulting ill a more rqm-

sentatiw dataset than thcl prr\ious threrb algorithms. The

greatest concern with this algorithm is tllat a\-cq$:ing iis-

SUIWS that the larger scale svstem behaves like the aver-

age smaller scale svsteln, wh~cl~. as ilhlstratcd. bv the cliI_

ferences in area tl~resliolds o\.er varying K&S (see Fig.

(i). is not a valid assuniption. Over small spatial clutr7rts

this techniqur, is certainh, convr~riicnt, arrcl ill ItIan!’ (‘a’;(‘~

Inay provide a suitabk~ model ii.cl.. as iisecl to gcm~ratt~

the 1ncw1 dataset), b1It o\yLr large extents this assumption

is not valid. Furtller discussion rrgarding t11(, c*a\,rats iI\-

valved in a\.eraging autl scalr ma\ bo found in O’Nr~ill

(198X) allt1 Beven ( 1995). In the \-~~ri~urcc,-u;c,ighte(l tr%clI-

niclue all pixels within a uscxr-defined upscalr~ kc~rnel ;lr(’

evaluatc>d as ~~11 as 110~’ these pixels-1.cpl-f~srlitiIig parts

of objects outside the arbitrary 1q)scaliilg prrimrter-

influence tliosr ins&>.

CONCLUSION

In an attempt to define and validate the most appropriate

upscaling technique to represent a rcinotel), sensed sig-

nal at various scale changes, we have examined how a

660 nni signal of six forest stands var> through four dif-

ferent (same-sensor) scales of imagery, md fiw rcsan- pling algorithms. From this studs the following COIIC~U- sions cm 1)~ dnmm:

just as a ~ibiquitous IiteraIy definition of‘ scalp

does uot exist, neither do& a singlra o/M&

scak that is capable of accurately describing the

rrrultisizt,d, sliape(l, and spatiallv distributed ob-

jects within a rrnlotel\- scmsetl scf3Ic”. \\‘(a suggest that 1,~ sampling ima&-objects uridr~r iteratively

growing object-specific kmiels, uniquc~ optimal

scalrs aid iriforniation ciui br d&c~d for them.

The, spatial extent (or object influence) of uniltisc& image-objects can I)(> tlefinrd 1)). the,

similarity measures of the elements (piurls) that constitute theill. These spatial measurc5 (*ail then be effectively used to represeritati\.c,l!; rlpscale data. This novel approach also provides a junc-

tlire whereby pin ant1 extent may be iteratively recalcldatcd to dt~trrmiiie the next scalr~(s) of’ ink age-01$3zts within ;i datwwt (i.c., malysis wing the mean dataset). As the grain (spatial resolution) of an image b(>- comes coarser, while the spatial extent \Cwed I-C’-

mains constant, tlic, sc~ene tends to I~O\YL to\varcls

a level of reduced variance as scene components become finer portions of the next level of larger, more dominant landscape objects (see Fig. 6).

l Providing that an appropriate resampling algo- rithm is applied, an upscaled image represents a mart‘ accurate model of a scene than an image obtained at the upscaled resolution. This occurs because upscaled images incorporate H-resolu- tion detail that does not exist in the coarser scale image due to the relationship between sen- sor IFOV and scene component size. This sug- gests that while the RMSE is a suitable tech- nique for evaluating a data model against the original data, it may not be suitable for assessing the most appropriate upscaling routine as we ha\~, clone, as the model (i.e., upscaled image) can never be the same as the original data against which it is evaluated. These ideas also suggest that uew evaluation criteria need to be established to verify the appropriateness of up- scaled data and that future platform and algo- rithm development should focus on H-resolution spatial data and upscaling techniques.

l Nearcast neighbor, bilinear interpolation, and cu- bic convolution resampling algorithms are not silitable for resampling remotely sensed data to a coarser spatial resolution (i.e., upscaling), espe- cially when the upscale factor is greater than 5 This is important to recognize, as these algo- rithms continue to be built into commercial re- mote sensing image analysis packages and inap- propriately find their way into upscaling analysis.

l Nonoverlapping averaging appears a simple method for approximating the spectral response in an upscalrd image, though caution should be used as averaging assumes that the larger-scale system beha\,es like the average smaller scale sys- tein. \\‘hen. in reality, different structuring pro- cesses occur ill the landscape at different (often unique) scalt%s in a nonlinear fiishion, as illus- trated by observing th(> changing spatial extents defined in the area datasets (Fig. 6).

l A new \-arialIce-weightc~d upscaling technique has been described that produces a generalized spectral response more similar to the original coarser resolution signal than the response pro- duced by nearest neighbor, bilinear interpolation, cubic convolution, and nonoverlapping averaging. This techniqlie also introduces an object-specific approach to upscaling, with the ability to gener- ate additional datwsets (from a single chaiinel in- put) which lnay be beneficial as logic channels in traditional classification strategies, and as guides and input for developing a hierarchy of linked scale-specific models.

l Large volumes of high resolution multiscale data offer challenges to the user that are more time- consuming, complex, and computationally inten- sive than single scene analysis. Each scale of data essentially provides the analysts with a new single-scene project to understand and integrate with the other scales. Multiscale analvsis is not trivial.

This article is part of a research agenda directed to- wards utilizing multiscale remotely sensed iniagey to quantitatively identify the spatial extent of critical land- scape thresholds as it is hypothesized that they define specific regions of scale dependence at which unique scale-limited models are needed (Holling, 1992). As illus- trated in this article, these threshold qualities may also be used as upscaling inputs, potentially capable of pro- viding the ke!. for translating results obtained from a model at one scale, to the parameter set of a model op- erating at the next scale (Wickland, 1989). Further re- search will be directed towards refining the heuristics used: f&wing the mean dataset throllgh a hierarchy of scale changes: examining multispectral scale changes rather than a single band scale change; and determining if and lrow datasets produced from these object-specific thresholds relate to landscape processes.

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