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A Fractal Approach to theGlassification of Mediterranean Vegetation
Types in Remotely Sensed lmagesS.M. de Jong and P.A. Burrough
AbstractA method is presented to assess fractal dimensions from re-motely sensed images. The method is a three-dimensionolversion of the "walking dividers" method which has beenapplied to two digital images of southern France to distin-guish various types of Mediterranean \andscape units. Thefirst image is a Landsat Thematic Mapper image, while thesecond image was acquired by the airborne Geophysical En-vironmental Research Imaging Spectrometer. The methodhas been tested on some artificial images to demonstrateprocedures and results. The method can distinguish runge-Iands, maquis and closed garrigue and to a lesser extent ag-ricultural regions on the TM image. Fractal dimensions foropen garrigue and badlands are similar. However, the rcf|ec-tion properties of the land-cover units do not behave likereal fractals at the scale considered, and different methodsto compute the fractal dimension do not yield the same re-su1fs. fiesu/fs of the airborne image arc disappointing, proba-bly due to somewhat poor image quality. Finally, someadvantages and disadvantages of the method are discussed.
lntroductionMany Meditenanean regions are affected by land degrada-tion, resulting from past and present human activities. Theseactivities have caused the development of landscapes withvegetation ranging from maquis, garrigue, and rangelands tobadlands (Grenon and Batisse, 1989; Tomaselli, tg8t; LeHou6rou, 1981). Mediterranean landscapes are vulnerable toland degradation processes, and the natural conditions inmany Mediterranean areas are such that disturbed ecosys-tems do not regenerate easily. Consequently, Mediterraneanareas need to be treated with care, and methods for sustaina-ble Iand use need to be developed. In order to develop meth-ods for sustainable land use, information is needed on thepresent state of these areas, and knowledge is required onthe functioning of Mediterranean ecosystems.
As the Mediterranean regions are extended and complex,remote sensing techniques may contribute significantly todata acquisition of complex spatial patterns of vegetation(LaGro, 1991; Briggs and Nellis, 1991). However, remotesensing techniques that use only pixel-specific spectral signa-tures to distinguish vegetation types have so far not beenvery successful (Hill and M6gier, 1986; Lacaze ef o1., 1983).Pixel-per-pixel classifiers do not recognize adiacent pixels asbelonging to the same vegetation class because of the greatvariety of spatial patterns of vegetation cover and density of
Department of Physical Geography, University of Utrecht,P.O. Box 80.115, 3508 TC Utrecht, The Netherlands.
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Mediterranean landscapes. Classification results may improveif a quantitative measute of spatial heterogeneity is used asadditional information in spectral classification procedures(e.g,, Strahler, 1980; De Jong, 1993; De long and Riezebos,1s91). One of the basic assumptions of the current study isthat the various Mediterranean land-cover types show spatialpatterns of differing complexity or texture. This assumptionis supported by several other studies (Lacaze et al., 'l'g$ iBrown, 1990; Qu6zel, 1981).
The aim of this paper is to introduce and test a robustand practical method for improving the classification of im-agery when individual, but neighboring, pixels have differentspeciral signatures, and when the pattern of different signa-tures is characteristic for a given land-cover type. Such amethod should capture the local variability of reflectanceproperties. The technique must be simple and unambiguousto use and be capable of distinguishing land-cover types.
Descilbing Spatial Vadation: CV and VailogramsLocal variability in a remotely sensed image can be de-scribed by computing statistics of pixel values' e.g'' coeffi-cient of variance or autocovatiance, or by fractals. Theunderlying theory in each of these methods is that the com-puted parameters express a kind of "natural characteristic"-of
a spitially contiguous set of pixels for a given type of landconer. Although the individual pixel values may vary, thepattern is distinctive. Open types of natural vegetation suchas found in the Mediterlanean region often display such pat-terns.
The coefficient of variance (cv) gives a measure of thetotal relative variation of pixel values in an area and can becomputed quickly and easily, but it gives no informationabout spatial patterns. The same applies for many other -neighborhood operations such as diversity or variation filters:their absolute outcome is easy to compare but they do notreveal any information on spatial irregularities (Burrough,1993b, 1986; Klinkenberg, L992; Snow and Mayer, 1992; Un-win, 1989).
Spatial patterns can be described quantitatively in ̂ termsof the semivariance function, which can be computed fromtransects of data points measured on the ground or from im-ages. This technique is based on the idea that the statisticalviriation of data il a function of distance. The variogram (the
Photogrammetric Engineering & Remote Sensing,Vo l . 6 r , No. B , August 1995, pp . 1041-1053.
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graph of semivariance versus sample spacing, or lag) relatesdistances between sample points to the variance oflhe differ-ences in the data. Experimentally derived semivariances arecommonly used to fit an approved mathematical function (avariogram model) which is used for interpolation and opti-mizing sampling networks. The parameters of a fftted mbdelmay include a range (a), a nugget (c0), and a sill (c+c0). Thefo^rqr of a typical variogram is shown in Figure 1. The rangeof the variogram indicates a spatial scale ol the pattern, th-enugget is an indication of the level of spatially uncorrelatedvariation in the data, and the sill reveals the total variation.The shape of the variogram is related to the type of variationin the data (Burrough, 1gs3b, 1987; Isaaks and Srivastava,1989; McBratney and Webster, 1983; Webster, 1985; fourneland Huijbregts, 1978).
Variograms of remotely sensed measurements should beinterpreted with care, because some aspects of these vario-grams may differ from variograms resulting from ordinarysamples, In remote sensing, the support size (which is thegeostatistical term for the area or volume of material sam-pled) equals the sample spacing, i.e., reflection values are av-eraged over the "field of view" or pixel size of the measuringdevice. Furthermore, the sensor's output is always a deriva-
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tive of the complex composition of radiation from the ter-rain. Variograms of data collected by remotely senseddevices are influenced by the shape and the distribution ofelements in the image (oi the transect). Some major pointsfor variogram interpretation are (Woodco*ck ef o1., f S-BAa;Woodco*ck et al., 1.9BBb; Webster et al., 1,g9g; Curran, 19BB)
o the range is related to sizes of obiects in the terrain (e.g.,batches of shrubs);
o the shape of the variogram is related to variability in size ofobjects in the terrarn;
o the height of the variogram is influenced by the density ofcoverage of the obiects and the spectral differences betweenthe obiects;
. regularization (coarsening the spatial resolution) reduces theoverall variance of the data and blurs fine scale variation;consequently, the siII height will reduce, the range will in-crease, and the nugget wiII increase; and
o anisotropy in the image is expressed by the variation of var'-iogram parameters with the direction of the transect.
_ Variogram parameters could be useful for assessing spa-tial patterns in remotely sensed images. The nugget re.realsinformation on variability between adjacent pixels, the sill
gives information on the total variabilitv of the area consid-ered, the range presents information on spatial dependenceof reflectance, and the type of variogram model oi the shapeof the variogram reveals information on the spatial behavi^orof the data (Webster and Oliver, 1992; Ten Berge ef o1., 1983;McBratney and Webster, 19S1). If one first delineates differ-ent land-cover types by eye (or by other external criteria),variograms can be computed for each delineation separatelv.Statistical tests (e.g., ANovA) could be used to see if areas
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with app,arently similar patterns returned significantly simi-lar or different values ofthe variogram parameters. This ap-proach is only useful if an external delineation is provided.It is more_ interesting to see if an analysis of the image pat-terns could be used to distinguish different vegetation typesautomatically by using the variogram.
If one were to characterize a part of a remotely sensedimage by using variograms, the conventional approach wouldbe to take a kernel or transect of a limited size, iompute theexperimental variogram, fit a variogram model, and ihenwrite the values of the variogram parameters to the cell loca-tion at the center of the kernel or transect. Such a orocedurec-ould yield at least three new data layers per pixel, one forthe nugget, one for the range, and one for the iill. The ker-nel/transect would then be moved up one pixel and the com-putations would be repeated. The result would, in principle,be a set of data layers that showed how the patterni in theimage varied in terms of estimated varioqram piilamerers,which might reveal the differences in veletation or land-cover pattern that are being sought.
Although the variogram seems to be a robust tool, anumber of disadvantages of variograms can also be identi-f ied:
1 man] data points are required to compute a reliable vario-gram (ten lags or more are needed to fit a variogram model);consequently, an extended transect or a large kernel is re-quired to perform the compulat ion:
o it is difficult to define "best model criteria', in an automaticprocedure for estimating variogram parameters;
o different samples (i.e., sets of observationsJ from the samelandscape units can yield different estimated variograms(Webster and Oliver, 1992; Jsaaks and Srivastava, 19Sg);
I usin$ the transect method, there is no clearly defined centralpixel in which the computed variogram parimeters can bestored:
r a local estimator is required Io analyze image patterns todistinguish different land-cover types; the viribgram of atransect is a global estimator and does not give informationon local var iat ion; and
. the compglation to derive the variogram and its parameters isconsiderable.
An easier and more rapid method to assess spatial pat-terns from remotely sensed images would be useful. A fractalapproach to assess spatial patterns from images meets theneeds of such a method. This article examines the use ofmethods for assessing fractal dimensions of Mediterraneanvegetation types using digital images at two different spatialresolutions, tests the usefulness of the fractal approachfordistinguishing different types of vegetation, and compares itwith variogram methods.
FractalsFractals are a means of describing complicated, irregular fea-tures of variation (Burrough, 1993a). Several authorJ havediscussed the use of fractals to quantify "roughness,, of sev-eral types of objects (Xia, 1993; Snow ind Miyer, 1992; Klin-kenberg and Goodchild, rsgz; Moussa, 1.991; ihornes, 1990:
range distance
Figure 1. Form of a typical variogram with sil l ,nuEElet, and range.
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Burrough, 1981, 1989, 1993b; Turner et al., 1.g9g; Unwin,1989; Cull ing, 1989; Dicke and Burrough, 19BB; Mark andAronson, 19Ba). Only a limited number of studies have beencanied out so far to assess the usefulness of fractals for im-age analysis (De Jong, 1993; Vasil'yev and Tyuflin, 1992; Ar-dini ef o1., tggt; LaGro, 1991; Walsh et al. 1.991.; De Cola,1989; Jones et o1., 19Bg; Lovejoy, 1982). A fractal is an objectwhose shape is independent of the scale at which it is re-garded, also referred to as "self-similarity" (Turcotte, 1992).The fractal dimension (D) is a quantitative measure of the ir-regular features or "roughness" of phenomena (Burrough,1993a; Burrough, 1993b). The variability of many naturalphenomena is often irregular and, sometimes, it can be ap-proximated by a stochastic fractal such as the model ofBrownian motion (Mandelbrot, 1982). It is reasonable to sup-Dose that different kinds of terrain might have characteristi-ially different texture or roughness wf,ich could beexpressed in terms of different fractal dimensions (Klinken-berg, 1992; Fox and Hayes, 1985; Barenblatt et 01., 1984;Bradbury and Reichelt, 1983; Mark and Aronson, 1984).Therefore, Iocal fractal analysis of remotely sensed imagesmay reveal information on patterns of vegetation and rockoutcrops much better than pixel-per-pixel procedures.
A single-band remote sensing image can be consideredas a kind of topographical surface: rows and columns of theimage matrix represent the spatial location while the pixelvalue embodies the imaginary elevation. The "roughness"described by D is determined by the variation in observed ra-diance. Values of D for surfaces range by definition flom 2.0for completely smooth surfaces to just below 3.0 for very ir-regular surfaces (Turcotte, 1992). Overviews of availablemethods to assess D are given by Xia (1993), Klinkenbergand Goodchild (1992), and Burrough (198G).
Most methods for determining D at present only givelumped values for an entire image or an entire catchment.This lumped value is useless for detecting patterns of rough-ness over the image, and local methods to assess D are re-quired to provide a spatial map of patterns of differingcomplexity or texture. Although several authors (Xia, 1993;Lifton and Chase, 1992; Chase 1992; Turcotte, 1992; Klinken-berg arrd Goodchild, 1992; Elliot, 1989; Culling and Dat\o,1987) have shown that there is a relation between fractalsand landscape development or landscape patterns, the exactrelation is not yet fully understood. This paper examines thehypothesis that D can be used to distinguish different land-cover types.
Methods for Estimating Fractal Dimension Used.in this StudyTwo methods to determine D wete used in this study: the"variogram method" and a new local method based on the"Triangular Prism Surface Area Method" (Clarke, 1986)'
Vadogram MethodIn the variogram method, the fractal dimension (Du) is esti-mated from the best fitting line of the log-transformed semi-variance function computed from one-dimensional transectsfrom field data and from images. Transects are often used tocharacterize vegetation patterns in the field (Mueller-Dom-bois and Ellenberg, 1974; Kent and co*ker, 1992) because thetransect method is easy and quick. The slope of the best fit-ting line relates to Dr as slope : 4 - zDv (Mandelbrot,1982). The essence of a log-transformed variogram of a trueBrownian fractal is that it has no single, unique range nor asill. Such a variogram will be a straight line on double logpaper. If the contribution of noise in the data of a true fractal
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increases, it will shift the variogram upwards along the vari-ance axis, If noise is added to a variogram with a clear rangeand sill, it will reduce the distinctiveness of the range andsill, and the value of D" will inctease. The value of Du forone-dimensional transects can vary byldefinition between 1.0(completely smooth) and 2.0 (highly irregular)'
The variogram yields several kinds of information onspatial patterni. If a variogram has a well-defined range- andrill, the.t the data do not come from a real fractal. On thecontrary, if a clear range and sill is absent, then the datasetcan be tonsidered as a"candidate-fractal"'The linearity andthe slope of such a log-log variogram provide.information onspatial patterns in the data. Furthermore, the break distanceof the log-log variogram (defi.ned by Klinkenberg-{1992) asthe maximum distance to which a least-squares line can befitted with a correlation greater than 0.90) indicates the dis-tance of spatial independence of the data. Unfortunately, thedisadvantages mentioned for the common variograms arealso true if D is estimated from variograms: many data pointsare required to obtain a reliable variogram, the necessarycomputations are very laborious, and the various variogramswithin one landscape unit do not yield the same results' Theobjective of the new proposed local method to estimate D isto overcome some of these disadvantages'
Tilangulal Prism Suilace Arca MethodThe "Triangular Prism Surface Area Method" (rrsalr) is athree-dimensional geometric equivalent of the "walking di-viders" method proposed by Clarke (19s6)' This methodestimates lumped D-values from topographical surfaces or re-motely sensed images. The method takes elevation values(Digit;l Numbers) it the corners of squares, i.e., the center ofa pixel, interpolates a center value of the square by averag-ing, divides the square into four triangles, and then uses Her-on-'s formula to compute the surface areas of the imaginaryprisms resulting from raising the triangles to their given ele-vations (Figure 2). This calculation is repeated for differentsquare sizei, yielding the relationship between the total areaof the surfaco and the spacing of the squares (resolution).The computed surface area will decrease with increasingsquare siie, because peaks and bottoms will smooth out. Thecalculations stop if the size of the square is too big to fit onthe image. Surface area and spatial resolution are both logtransforired, and a linear funCtion is fitted through the calcu-Iated points. One (lumped) value of D for the-entireimage isthen estimated by the slope of the regression line' The num-ber of steps (squire sizes) to calculate the surface area de-pends on-the size of the image. The required formulae toiarry out the computation are given by Clarke (1980). The"Triangular Prisrn- surface Area Method" provided good esti-mates of D for images and for small phenomena such as par-ticles and molecules (Clarke and Schweizer, 1991)'
A local method to assess the fractal dimension (Dr) wasdeveloped by modifying the original "Trian-gular Prism Sur-face Aiea Method." A kernel of I by I pixels is moved overthe digital image (Figure 3) and, at each position of the ker-nel, D, is assesied by calculating 4 times the surface area atdifferent resolutions (squares of r by 1,2by 2, aby 4, and 8by B pixels) within the kernel. The surface area is computedin the same way as the lumped "Triangular Prism SurfaceArea Method." Resolution and calculated surface area areboth log-transformed and D. is estimated from the linearfunctioi fitted through these four points bY D" = 2 - Slope.D, is written to the center cell of the kernel in a new imagefile, the kernel is moved one pixel to the next position over
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izo
1 2 3 4 5 6columns >
Figure 2. Example of the "Triangular Prism SurfaceArea Method" (Clarke, 1986) to calculate D. Withina square of increasing size, the "surface area" ofthe image is assessed. The surface area de-creases with increasing square size, becausepeaks and and bottoms are smoothed. The regres-sion l ine of the log transformed surface area andthe log transformed square spacing yield an esti-mate of the fractal dimension.
the image, and the calculation starts again. A kernel of I by9 pixels is chosen as a compromise between computing timeand the number of points required to fit the function. Thenew proposed local method is a type of convolution opera-tion and results in a map of D, values for the entire image,which can then be used as an indicator for the spatial varia-bility of land-cover categories.
The advantages of the new local method are that it iseasy to use and quick, it renders information on spatial pat-terns within the template size, no extended transects are re-quired, and it can be used in relatively small areas. A spatialcontinuous map of D, values is produced by writing thecomputed D. value to the center pixel of the kernel. Due tothe size of the kernel (S by 0 pixels), two disadvantages ofthe new local merhod can be identified:
. the surface area is calculated within the kernel for foursquare sizes: L by 1., 2 by 2, 4by 4, and B by B pixels; conse-quently, only four points are available for the linear regres-sion of the log-transformed surface area and resolution; theleast-square fit might be strongly influenced by extreme val-ues of the computed surface area; and
o the relatively large size of the kernel causes blurring orsmoothing of the output image, a very common, unfavorableeffect of spatial filtering (Gonzalez and Wintz, 19BZ), and thesize of the kernel causes some boundary effects.
A further limitation of the method is that it is not applicableto multi-band images. Consequently, efficient data reductionmethods such as principal component analysis or ratioing
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should be applied first to the multi-band image. AIso, Xia(1993) suggests that this method is generally less reliablethan the variogram method.
Fractal Dimension of Artificial lmagesBefore the proposed "local D algorithm" was used for realdigital images, the approach was tested by applying it to arti-ficial images which are not fractals. Some typical examplesare presented in Figure 4. The images at the left side of Fig-ure 4 are artificial input images, while the images on theright side show the results of the D, algorithm. The size ofeach artificial image is 40 by 40 pixels, and the values of thedigital numbers are presented in the legend of the input im-ages. The ranges of estimated "D, values" are by definitionbetween 2.0 and 3.0 and are presented in the legend of theoutput images.
The first two images of Figure 4 show the effect on D, oftwo intersecting lines. The previously described blurring ef-fect of the Q algorithm is visible along the lines: D. valuesstart to increase at a distance of half the template size awavfrom the line. The most complex part of the input image, i.e.,the junction of the two lines, yields the largest D. values.The central-left image of Figure 4 becomes more complex; itconsists of six small flat, hom*ogeneous raised surfaces. Thesmoothing and blurring effect of the local algorithm is visiblein the output image on the right. The sections in between theflat areas yield the largest D. values, due to the position ofthe kernel over thethe kernel over the edges of one high and two low areas. Theupper part of the third example in Figure 4 was created us-upper part of the third example in Figure 4 was created us-ing a random number generator; digital numbers range from0 to 99. The lower part is flat and hom*ogeneous with digitalnumber zero. The required kernel size for the D. algorithmcauses some boundary effects. It is not possible to performcomputations close to the borders of the images. Therefore, afew rows and columns at edge of the image are dropped andfilled with zeroes. The number of rows and columni-dropped equals half the template size. This "boundary ef-fect" is clearly visible at the borders of the output image. D.values in the upper part range from 2.00 to 2.[8. Drde-creases quickly towards the lower, hom*ogeneous part of thisimage.
A general trend of D. computations is that flat hom*oge-neous areas yield low estimates of D, and, as the image's het-erogeneity increases (intersection of lines, fringes ofhom*ogeneous areas), D, increases too. The largest Q valuesare found for areas with a very high spatial variability suchas the random part of the third example of Figure 4. The Dr.method seems to perform satisfactorily in this study and dis-tinguishes areas with different variability of pixel values.This is in contrast with results reported bv Klinkenbers andgoodchild (1992) and Xia (1ss3). The former merely foundIow D values using the "walking dividers" method and con-cluded that this method has low discriminating power. Xia(1993) states that this method onlv produces reasonable re-sults when careful considerations-ii siven to the selection ofthe maximum cell size and the r-squ"ared value.
Case StudyIn the study presented here, two methods are used to esti-mate D: the first method (variogram method) is suitable todetermine D,, for one-dimensional field transects; the secondmethod (local D algorithm) yields a spatial map of estimatedD. values, where the new image equals the size of the origi-nal image minus half the kernel siie due to boundary effects.
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' Local Triangular Prism Surface Area Method '
B
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t , 2 3 4 5 6 7 8 9
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o e e 0
o o o I
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surtace area = > (8 squares)
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e
o o
surlace area = > (4 squares)
D
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I
E
Pixel
. center of pixel
O interpolated core
l-l "qu"'"
surface area = ) (1 squares)
Figure 3. The working method of the new proposed "local D algorithm'" A kernel (9 by 9 pixels) is moved
over the image, and for each kernel position, the "surface area" is computed at four different resolution
(squares). Dl is assessed from the log-transformed surface areas and resolutions and the kernel is moved
io in" n"*t plosition. The method yields a distributed map of Q values'
o o 0 o 0 o es 6 (0 e o o o ee o o e o o o o
o @ 0 o e o 0 o
e o o o e e ee o o o o o 0
o o o o o o oo o o o o o o
surface area = ) {64 squares)
The case study aimed at finding the answer of two research
questions:
o Is the Brownian fractal a useful means of describing the"roughness" or "texture" in remotely sensed imagery of Med-
iterr inean land-cover tYPes? ando How do the two method-s [variogram and local method) per-
form at distinguishing between different known types o{Mediterranean Iand-cover tYPes?
Study Areaihe suitability of the estimated fractal dimension as a tool
for separating different types of Mediterranean vegetation
-u. uir"rr"d"in a study area in the southern Arddche prov-
ince (France). A physiographic survey was carried out, re-
t"tti"g in six main iand--cover classes or mapping units (De
)ong et ol. , rggo):
(r) Badlands are strongly incised areas.-Bare, high r-efle-ctancesurfaces vary with densely vegetated areas- at gully floorsand in betw'een gully systems. Shadows play an importantrole in badlands with regard to apparent reflectance proper-
ties'(Z) Rangelands are dominated by annuals and herbaceous per-'-'
".tnials with deep root systems. Shrubs are not or are only
scarcely present in the ringelands' Rangelands often form a
rather hom*ogeneous cover over extended areas'(3) Open garrigu'e is an area of low scattered bushes, smaller in' '
nutnbJt thin in the previous class The bushes are rarely
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more than 2 metres high with bare patches of rock or stony
soil between the grasses and herbs'(+) Closed garrigue iJan open forest type of vegetation with
scattere"d buihes alterniting with bare patches' rock out-
crops, and grasses. Garrigue show distinct spatial patterns
of shrubs.f sf fr,luqltit forms the local climax vegetation and is a type 9f'
"u"inr""n mixed forest dominated by oak species' Maquis
has i dense. everg,reen vegetative cover'(o) itre ii*ttr class is"dominul"a ty }uman influences and com-'
prisu, agricultural areas and built-up areas The spatial pat-
te..t of i'his class shows spectral variation at regular
distances, i.e., Parcel size'
Two types of digital multispectral im-ages were available
for this u."u, t ru image acquired on 18 July 1991 with a
pi*"1 sir" of 30 by r0 iretrei and an airborne image acquired
[; th" Geophvsical Environmental Research (cun) Imaging^
Sil;irom;;;'o., zg l,r.t" leae with a nominal pixel size of
;6;; i0 metres (Hii l , 1ee0; De fong, 1ee2)' I igure 5 shows
tn"iv image of ihe study area wilh the s. ix land-cover types
iJu"tln"a. ihe Landsat rv image was radiometrically c.or-
.""i"J"tr"g-ihe method p.oposld by Markham and Baker
iis86t usin"g gain and offiet values to convert digital num-
i".t ittto re"flJctance. The original GER image contains 63
spectral bands. The radiometric and geometric preprocesslng
o? the airborne image was carried out by the German Aero-
tou"" n"r-.ut"h Est;blishment (Lehmani et al', 1989) and the
iJi.rt R"r"ut"h Centre [Bc) of the European Community in It-
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b10.008.757.506.255.003.752.501.250.00
2.M02.O352.O302.O252.0202.0t52.0102.O052.000
d
::::::::::::i:t::
70.oo63.75s7.5051.2545.0038.7532.5026.2520.00
2.162.142.122.ro2.O82.062.042.022.00
99.0086.6374.2561.8849.5037.r324.7512.380.00
2.452.392.342.282.232 . 1 72 . 1 12.062.00
Figure 4. The effect of the "local D algorithm" is shown on three aftificial images. tmages on the left show the inputimages, while output images are shown on the right. Q values tend to increase with thie complexity of the image.
c
f
aly (Hill, 1990). Geometric preprocessing comprised correc-tions for aircraft roll, detector ipeed, and s.anhing angles.Digital numbers were converted to reflectance faciors irsineradiometric ground measurements made during the overpa"ss
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and an atmospheric correction model developed at lnc (Hill,1990). A selection was made of cnR bands corresponding toTIr4 bands 1 to 5 and 7. The different pixel size oi th" trr"oimages makes it possible to test the new D, method on Dat_
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Figure 5. Landsat Thematic Mapper image (Band 4,5,tinblack and white) of the study area showing the six land-cover classes: (1) badlands, (2) rangelands, (3) open ga-rrigue, (4) closed garrigue, (5) maquis, and (6)agricultural areas.
and, for each variogram, breaks of slope were located visu-ally (Mark and Aronson, 1984). Straight lines were fitted upto ihe breakpoint using the csS statistic-al software package(Statsoft, rsbr), and Df, was computed from the regressioniine. This method was applied to all units except for the ag-ricultural areas. The m"ftrba is of little use for agriculturalresions. because the spatial variation is determined by thehriman induced boundaries of the parcels. The method alsofails in maquis, because maquis is hardly penetrable and thevegetation is too high for hand-held radiation devices' There-foi, variograms foimaquis were estimat4 -"fi"g data tran-sects takeri from the air6orne GER image. Table 1 presents D.,values and break distance for each land-cover unit and, pertransect, the D values and their break distance. Table 2shows the average Du value, and the average variogram-model parameteis and their cv values per lald-cover class'
From the variogram model parameters,-it can be seenthat short variogram "range distances" are found for openand closed ganigne and badlands; the largest "range dis-tances" areleteimined for rangelands and maquis. These re-sults match intuitive expectations that the spatial dimensionsof the variability of rangelands and maquis are larger thanthe variability of Uaatunas and garrigue (i'e., badlands andgarrigue have finer patterns). The Du values indicate rmg-e-landJ and maquis ai most irregular. The Du values are all farover 1.5, indicating that the vegetation index determinedfrom the radiance ireasured along the transects is highly ir-regular. Large values of Dn are-alCo reported by Burrough.(rber ; rsssi). Discrimination between land-cover categoriesusing only D' from hand-held radiometer data is poor' Aver-age b values'for the different land-cover types are close to
TneLE 1. Pen LlruCoven Untr, I NoRtrlaltzeo DtrrenelcE VEGETATIoN INDEX
Wns DErenutrurD ALoNG SEVERAL TRANSEcTs Ustuc I HnluHeuo RnotottlgreR'
Fon encu Tnntsecr rHE FRAcTAL DlMENsloN (D) Wns Covpureo UsING THE
VnntocRav METHoD. DuVlLues nlo BRenx DlsrANcES ARE PRESENTED'
Landunit
Dvvariogram
Breakdistance (m)n 2
terns of natural vegetation cover at two levels of scale' Thedifferent dates of data acquisition do not seem to havecaused any major differences in the images because the dy-namics of the (semi-)natural ecosystems are rather low. Incontrast, temporal changes of the agricultural areas can beconsiderable.
Fractal Dimensions of Ttansects by the Vailogram Method (2")The "variogram method" was used to assess D from transectsin the diffeient mapping units which were surveyed in thefield. The Du valueibbtained are useful to check whetherspatial variation estimated from field data matches that esti-mated from images. A hand-held radiometer with a field-of-view of 1 m' wai used to measure reflectance in the visibleand near infrared along various transects in the mappingunits. Each transect comprised a minimum of 175 samplepoints. A normalized difference vegetation index was com-outed from the visible and infrared measurements, and, forill transects, a semivariance function was calculated follow-ing the method described by Isaaks and_Srivastava (1989).Tlie variograms were all plotted on double-logarithm paPer,
Badlandshansectltransect2transect3transect4transect5Rangelandstransectltransect2transect3transect4Open Garriguetransectltransect2transect3Closed Garriguetransectltransect2transect3transect4transect5Maquistransectltransect2transect3transect4transectS
1 .651 .697 . 7 8T .781 .90
1 .811 .85t . 797 .77
7 . 7 87 .707 . 7 7
1 .817 .821 . 7 31 .827 . 7 0
1 .841 .961 .931 .951 .89
0.980.99o.730.890.86
0.920.910.940.94
0.920.990.94
0.90o.730.960.880.96
0.910.850.83o.820.81
74.877 .817.71.2.O39 .8
39.848.948.9t2 .o
10.048.972.O
7.O6.1o . r7 .O5.8
25.739.828.728.732.O
PEER.REVIEWED ARI IC IE
Land Cover Unit Open ClosedNumber of Badlands Rangelands Gariigue Garrigue MaquisTransects (n : 5) (n = aJ (n :-3) (n :-s) (n : s)
Tnsre 2. Prn Lln+Covrn Ururr, n VecernloN INDEX Wes DrreRvrrueD ALoNGSeveRnr TRetsecrs Ustr.tc I Hlt>HElo ReorovrreR. Fon ElcH TRANsEcr, THE
SevrvnRrnnce Futcrron Wrc Cnrcuureo, A MoDEL Was Frrreo, AND rHEFRncrnl DruelrstoN (D) WAS Corr,tputEo Usrnc rHe VnRrocnnv MErHoD.
Avenlce Drnno VnnrocRav Mooet peRnvrrrRs Anr pResEtrro wtrH THEIRCoEFFtctENr or Vrnrntce (CV).
or by the fact that the reflectance properties of the studiedsurfaces are not scale invariant.
Apart from the estimation ol Dv, a conventional statisti-cal procedure was canied out to assess the relative hom*oge-neity of the six ma-pping units. Five test plots of 10 by 10pixels were located within the core of eaih land-covei classin the rv image and in the airborne image. CVs based on atotal of 500 pixel values per spectral banl per land-coverclass were computed and are ihown in Table 3. The resultsof the TM image analysis reinforce intuitive expectations be-cause the la-rgest-Cv values are found for badlands and agri-cultural areas, while the smallest CV values are computef, forrangelands and maquis. It is notable that, in the firsf two vis-ible bands of the ru image, badlands have the largest Cv val-ues of the six land-cover types whereas agriculturil areasshow the largest cV values in the next forir rrra bands. Thiscan be explained by the abrupt changes of infrared reflec-tance between densely covered lots and bare lots. This effectis less pro-nounced in badlands because vegetation in bad-lands is often "water stressed," resulting iri smaller contrastbetween infrared and visible reflection.
The CV values computed from the cER image show a lessdistinct p-attern. The cv values are generally mich largerthan for the TM image, and the land--cover ivpu,
"urrrrot "ur-ily be separated. Vaiiability of reflectan.r *i'thin the experi-mental test plots is apparently much greater. There u." t*opossrDle explanatrons:
. there is a greater variability in the terrain at distances lessthan 30 met.res; this variability is detected by the crn pixel(1-0 by 10 m) and is smoothed within the piiel (30 by
-sO m;
of the TM scanner; and. there is more noise present in the cnn image than in the TM
image.
A visual interpretation of the GER image showed that the im-age is of somewhat poor quality and that the contribution of
Avg. D (variogr.): '1,.26
CV ( / " ) : ( 5 . 5 )
Avg. range (m): 9.1CV (%) : (s7 .1)
Avg. nugget (cO): s.LzCV (%): (64.e)
Avg. Sili-nugget (C): 1-T.TCV (%): (66.3)
1 . 8 1 1 . 7 5(1 .s ) (2 .5 )
36 .0 5 .6(63.e) (41.\)
2 .82 4 .31(55.6) (s1 .5)
9 .56 6 .19(e4.0) (64.4)
1 . .74 1 .91(3.2) (2.4)
3 .6 27 .1 ,(25 .6) (11 .1)
3 . 2 0 6 . 1 1(24.o) (26.3)
5.56 9.74(14.2) (45.4)
each other, and the CV values are relatively high. Maquis issomewhat different from the other land-cover types and hasthe largest Dr, but it is unclear whether this is i-function ofthe support size of the data source (cnn image) or of the spa-tial pattern of the maquis. A graph relating Du with break-distance of the log transformed variogramJ separares range-Iands, ofien an-d closed garrigue, and maquis (Figure 6).
-
Badlands are the most variable and are difficult io grorlp.Furthermore, the question should be answered whelheithetransects per land-cover unit represent real fractals. The li-nearity of the 1og-transformed variograms provides informa-tion on the self-similarity. Although somelog-log variogramsare linear over a certain range, most log-log iaridgramslhowclear breaks of slope. This non-fractal 6eha"vior mlght becaused by the limited number of points in the traniect (175)
c o u
.9
t s o
@ T o o
o *
* *
A . r1
ao .ar .6 1 .65 1 .7 1 .75 1 .8 1 .85 1 .9 1 .95 2
DV (variogram method)
A Badlands O Range lands I Open Garrigue <) Closed Garrigue :lr MaquisFigure 6. Graph showinglhe relation between Drand breakdistance from the log-transformed variograms for each of the five land-cover types.
1048PE&RS
PEER.REYIEWED ARI ICTE
TneLe 3. CorrHcteNr oF VAR|ANoE (CV lN PERCENT) oF rHE DlclrAL NUMBERS
or FrvE ExpeRrnenuL Prots (ru : 500 Ptxels) een Lrru>Coven Cuss ron nu
SprcrRnr Beruos or rxe Txevlrtc Mppen (TM) AND FoR THE GER-AIRBoRNElvrce (GER).
Land Cover Unit TM1 TM3 TMs TM7
variability and of D values using the GER image might be in-fluenced by noise.
Fractal Dimension 0f lmages by the Local Method (4)Before the local algorithm for D computations was- applied tothe digital images, the multi-band images were reduced tosingle-"band imiges. Spectral ratioing was preferred for datareduction for two reasons:
. ratioing of one neat infrared band and one visible band en-
hances patterns of vegetation cover. ando ratioing reduces the effect of shadows in the badlands'
The optimal bands for ratioing were determ-ined using the .correlation matrix (Pearson correlation) of the experimentaltest plots described earlier. The two bands u'ith the lowestco.t6lutio.t (Table 5) were selected for ratioing. Band 1 andBand 4 have the lowest correlation for both images' A nor-malized spectral ratio (4 - 1)l(4 + 1) was calculated for bothimages anh, after scaling, used as inputfor the D. algorithm'The-D, algorithm, applied to the TM and GsR ratio images,yielded two new images with Dr values. In contrast to thevariogram method, th; D, algorithm yields rather small Dvaluei. Figure 7 shows the result of the D, method applied tothe ratio of the ru image. Values range from 2.Oo to 2.55.The next step in this study was to determine the accuracywith which the two images reflect the six land-cover classes'Objective assessment of iccuracy of the new map is very dif-ficult because
r the spatial transition of the units, e.g., rangelands to opengarrigue, is hrzzyt
o ihe dlistinguished land-cover classes are not exactly definedin terms of cover percentage or species; and
. a map based only-on aerial photointerpretation and fieldworkof the land-corr"i types wasivailable, and the accuracy ofthis map is unknown.
The usefulness of the D, images was estimated by digitizing
polygons (minimum of aOo pixels) wjthin the center of each
i".ri].o'o"r class. For each pblygon, the average D, value and
the standard deviation were computed and are presented in
Table 6.Normalized curves of the average D. values for all six
polygons are plotted in Figures B and 9 for the GER and TM
i*ig"", respeciively. The degree of separability between^the
land'-co,rei types using D, is indicated by the amount of over-
lap betweerrthe curves. A t-test for independent samples was
Taele 5. Conneuttott MArRlx FoR rxe SElEcreo TM rr'ro GER Brt'tos. DnrlWEne GlrHEReo FRot\4 THE Ftve Exeent"a^tnr Prots tl EncH Llru>CovER
TM4
Badlands 1.O.7Rangelands 4.4Open Garrigue 6.2Closed Garrigue 6.9Maquis 2.6Agricultural 9.7
Land Cover Unit GER1
74.4 77.56 .1 7 .58 .6 r2 .59 .4 15 .13 .9 6 .9
74.2 22.r
GER2 GER3
17.2 77.56 .1 10 .38 .9 1 .2 .6
11 .0 18 .86 . 6 1 1 . 6
13 .0 22 .5
GER5 GER6
1 0 . 15 . 06 .5J . U
3 . 91 3 . 3
GER4
BadlandsRangelandsOpen GarrigueClosed GarrigueMaquisAgricultural
23 .8 18 .828.7 20.226.2 t5.432.4 22.740.7 20.92 7 . O 2 2 . 7
9.0 21.O 13.98 . 7 2 7 . 3 7 2 . 77 . 7 1 8 . 1 r 2 . 77.4 35.7 24.O5.0 33.1 20.1
r2.o 45.4 28.3
noise to the "within image variability" might be important,The image was used because the different pixel sizes of thecnn and rv image make it possible to study patterns of vege-tation cover at two levels of scale. Therefore, image qualitywas assessed by determining the signal-to-noise ratios.
Signal-toNoise EstimatesThe quality of the ru image and of the cnR image was_as-sessea by determining the signal-to-noise ratios (sun) directlyfrom the images. The nominal sNR for Ttrl measured in thelaboratory is between 2oo and 500 (USGS, 1982). Nominalvalues for the cER image are around 400 (Collins and Chang,1990). The common procedure to assess SNR from images isby selecting bright, hlgh reflectance, hom*ogeneous surfacesin the imagi (Bo-Cai Gao, 1993). The quotient of average ob-served radiance and the standard deviation yields the sNR'Bare bright soils or (empty) parking places are often suitablesurlaces.
The SNR generally decreases in shortwave infrared dueto lower radiance levels. Furthermore, the sNR determineddirectly from the images tends to be lower than laboratorymeasurements. The computed SNRs for the TM and GnR im-ages are presented in Table 4. The values for tu are mini-mum values because the number of pixels of the selectedbright surface was too small for a very accurate estimate' ThesNn of the GER image appears to be small but the quality ofthe TM image is much better, and visual interpretation of theimage confirms the somewhat poor quality of the GER image.ThJoriginal GER image looks very speckled in almost allspectrafbands due to numerous technical defects during da13acquisition (Hill, 1990). Consequently, the computations of
Tnale 4. SrcNel-roNotse RATlos FoR TM lr.ro GER. Vftues ron TM nReMrNtMA, BEcAUSE to SutrlgLe LaRce, Blne, llto Bntclr Sunreces Wene
AvATLABLE ttt tne lvnce ron nru OpttvnL SIcNAL-TGNoIsE Esrttvtnte.
7 7 . 3t7 .3I J . I
27.O26.O26.4
TM1 .I}|{z TM3 TM4 TMs 'tM7
TM1 1 .00TM2 0.99TM3 0.95TM4 0.76TMs 0.9sTM7 0.S3
GERl
1 .000.98o.820.940.95
GER2
7 .OO0 .91o .970.99
GER3
1 .000 .850.s0
1 .000 .99 1 .00
GERs GER6
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GER4
TM1, 450-520 nmTM2, 520-600 nmTM3, 630-690 nmTM4, 760-900 nmTMs, 1550-1750 nmTM7, 2080-2350 nm
GER1, 495-509 nmGER2, 557-570 nmGER3, 656-669 nmGER4,779-792 rmGERs, 1620-1740 nmGER6, 2192-2208 nm
8.5 GER1 1.0070.2 GER2 0.9817.4 GER3 0.9074.8 GER4 0.607.2 GERs 0.62
1.!.4 GER6 0.69
> 71 . .8> 60.9> 56.7> 84.7> 43.2> 34 .3
1 .000.96o.77o.72o.7s
PEER.NE
Figure 7. Result from the 4 method to compute fractaldimension applied to the ratio of the TM image. The areacovered is similar to Figure 5. e values range from darkto light from 2.OO to 2.55.
c
3
a
t€ctal dimsns.pn
- Agricultural arm ----- Opcn garrigue- - -Brdbnda -Clrerlganigre- - - - .Range lands - - -Maqu is
Figure 8. Curues of the estimated fractal dimensions(Q method) of the polygons centralized in the matrping units in the cER image. The X-axis presents thefractal dimension, while the Y-axis shows the percent-age of pixels per land+over class. An individual oeakfor a unit indicates that it is feasible to discriminatethe unit in the image based on 4.
i \ zi t'.i , ' .i t
o
'Io. xoa
fEctal dimgnsion
- Agricuhural areas --.--. Open garrigue- - - Bedbnds -Clomdganigue- - - - -R lnge l lnds - - -Mrqu is
Figure 9. Curves of the estimated fractal dimensions(Dz method) of the polygons centralized in the matrping units in the ru image. The X-axis presents thefractal dimension, while the Y-axis shows the per-centage of pixels per land-cover class. An individualpeak for a unit indicates that it is feasible to dis-criminate the unit in the image based on D..
might be elpegtg{ because estimating D" within one agricul-tural lot ry:tt Vp-ti low values, whilelstimating D, for"fringesof lots will yield high values. The curves for Uidtinas andopen garrigue coincide, indicating that they cannot be sepa-rated,using D". The curves resulting from the cEn image (Fig-ure 8) coincide to a large extent. N6 single unit can bJrecognized easily.
. tisu,ll interpretation of the "level-sliced" rM image of D"and the "level-sliced" cER image of D, confirms that tf,e ru
"
image shows the general pattern of miquis, garrigue, range-lands, and badlands much better. This is in iontiast witli ex-
carried o-gt for all six polygons and for either image. Al-though all units are significantly different at the 0l0S level,the results should be interpreted with care because the num-ber of cases is very large. Figures 8 and g show that D" val-ues in the TM image separate the six land-cover types muchbetter than does the cER image. Five peaks are diitinguishedin Figure g of the TM curves. Rangelands give a nice distinctpeak, but maquis and closed garrigue are l-ess pronounced.Agricultural areas result in very broad-shaped curves; this
TaeLr 6. AvERAGE Q eruo Tnern SrnNoano DEVIAIoN (SD) or rxe polycoNsCerurRrrzeo tN EAcH MApptNG UNtr.
GER Image Badlands Ranselands Gaorf,iesle "ff;,l,
t"n"u ttt"'!'Average D" 2.75 2.25s.D. 0.o3 0.o3n pixels 7748 7gz
2.24 2.28o.o2 0.0326S8 1108
2.22 2.27o.o2 0.o4829 1615
rM Image Badlands Rangelands ":rft"rlr" ":|?'fS"
r"o"* t*rtl'Average D, 2.23s.D. 0.05n pixels 1595
2 . too.o2t763
2 . 2 20.04t764
2 . 7 80.032992
2.14 2 .270.03 0.062218 TO527
1050
PEER.REVIEWED ARI ICTE
TneLe 7. RnnxonoeR or Esrrvnreo Fnncrnr DrvEr.,rstot'ts. Nore: RANK 1 lsTHE SMooTHEST - Svnrrest D, nruo 5 ts rHE RoucHEST.
Land cover type DL (GER) DL (TM)
BadlandsRangelandsOpen GarrigueClosed GarrigueMaquis
421.3o
pectations because the smaller pixel size of the ceR imagematches the variogram "range distance of spatial depend-ence" (Table 2) much better than does the TM pixel size.However, as described previously, cER image results may bedistorted by noise present in the image.
Discussion and ConclusionsThe research presented in this paper attempted to answertwo questions: (r) is the Brownian fractal a useful means ofdescribing the "roughness" or texture of remotely sensed im-agery of different kinds of Mediterranean vegetation, and (z)which of the two methods of estimating fractal dimensions ofthese vegetation patterns is most appropriate? Before answer-ing the first question, it was necessary to estimate fractal di-mensions by both methods.
The results show that, though both methods of estimat-ing D are feasible, they require much data and care. The var-iogram method requires large numbers of data points inorder to get information over suffrcient lags/spatial scales,and, if only a few linear transects are used, they may returnwidely differing values of Du. Other problems concern ani-sotropy of the pattern on the image and the fact that it is dif-ficult to assign the parameters of a variogram that have beenestimated over a large sample uniquely to a given pixel loca-tion for image enhancement. The local method avoids thelatter constraint of the variogram method but uses few data(a kernel of 9 by I pixels) and suffers from image blurringand boundary effects, and D, is estimated from only fourlags.
The two methods yield results that suggest that both Duand D, may be useful in the classification of the land-covertypes in the study area, though there are many instanceswhere the two methods strongly differ. The variogrammethod yields large values of Du (all > 1.7) for all land-covertypes, whereas the local estimator produces smaller values(all < 2.3). D values where the decimal component is large(> 0.5) imply a weak pattern of noisy, random variation,whereas D values where the decimal component is small (<0.3) imply smooth variation with little local noise. The abil-ity of D. to separate land-cover types clearly depends on theimagery used. The estimates of D depend on spatial resolu-tion (which varied from 1 by 1 m along the transects to 30by 30 m for the TM imagery), and it is not clear whether thedifferences in estimated D values can be wholly ascribed tothe differences in methodology or whether they can be ex-plained by the variations in the imagery of the vegetationpatterns not being self-similar and therefore not truly fractal.The only situation where data from the same source and res-olution were used by both methods is the GER data for themaquis: Du was estimated at 1.91 and D, at 2.22. This resultsuggests that the methods do indeed differ considerably, aconclusion that is further borne out not only by the negativePearson correlation between D, and D, (i.e., -0.65) but alsoby examining the rank order of estimated D values for all
PE&RS
vegetation types as estimated by both methods from all datasources (Table 7). These results suggest strongly thai the im-ages used are not true fractals. Significant differences in theeitimates of D obtained from one-dimensional and two-di-mensional methods applied to the same area have also beenfound by Klinkenberg ind Goodchild (1992) and Clarke andSchweizer (1991). Clarke and Schweizer (1991), without giv-ing an answer, have asked whether a fractal dimension esti-mated by a variogram method necessarily bears any relationto that estimated by the walking dividers method, andclearly this dependence of estimated D on method is an im-Dortant area that needs to be investiqated, as does their otherquestion as to whether the fractal diinension of a p-rofile-
Gransect) across a fractal surface necessarily has a fractal di-mension of that of the surface minus one.
The difference in estimated fractal dimension betweenDu and Dr(rrtl) in this study may also be due to smoothing oflocal variation within the 30- by 30-m pixels - in otherwords, the variation is scale dependent' This information, to-gether with the appearance of strong breaks of slope in thevariograms of the transect data, reinforce our conclusions
that the remotely sensed images of the land-cover units arenot true ftactals, though they undoubtably differ in rough-ness, This finding is consistent with the conclusions of Bur-rough (rgag; 1993a), Kl inkenberg and Goodc;hi ld (1992),
Mark and Aronson (1ss4), Xia (1993), and others that land
surfaces are only rarely self-similar, and then only withinlimited scales. The disappointing results for the airborne GERimage are most probably due to the low signal-to-noise ratioand poor image quality which caused the severe overlap be-tween the land-cover classes (Figure B).
Although D. for TM imagery does seem to reflect the dif-ferent vegetation types in the study area, it is clear that D, byitself is insufficient for the automatic classification of ru im-ages into land-cover categories. The relations between Dr andbreak distance (the range of the variogram) in Figure 6 sug-gest that information about the texture of patterns may beused to separate important vegetation classes, though moreresearch is needed to determine how this information can beunambiguously acquired and used.
AcknowledgmentsThe authors would like to thank three anonymous refereesfor providing constructive comments on an earlier draft, Dr.K.C. Clarke and Dr. Z. Xia for provision of literature, and Mr.C. Wesseling for his contributions in preparing the softwarefor the fractal analysis. The Institute for Renlote Sensing Ap-plications of the loint Research Center (Ispra, Italy) of theEuropean Community is thanked for providing the GER im-ages.
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(Received 27 Apil 1993; revised and accepted 14 January 1994; re-vised 4 April 19s4J
Physical Geography (MSc) from the UniversitPhysrcal Geograpny IMDCJ lrom tne unrversrtvof Utrecht and specialized in soil physics at the
doctorate on imaging spectroscopyAgricultural University of Wageningen. He completed hisdoctorate on imasins sDectroscopv for Iand degradation ndegradation map-
ping in 1994.
S.M. de |ongSteven M. de /ong is a research scientist andlecturer remote sensing at the University ofUtrecht in the Netherlands. He graduated in
P.A. BurroughDr. P.A. Burrough is Professor of Physical Geog-raphy (Land Resources Assessment and Geo-graphical Information Systems) at the Universityof Utrecht in the Netherlands. FIe graduated inChemistry (B.Sc. 1st class Hons.) from the Uni-ssex, England and completed his Doctorate onversity of Sussex, England and complet€d his l)octorate on
quantitative methods of soil survey at the University of Ox-fbrd in 1969. He worked on natural resources surveys in Sa-
bah, Malaysia and at the University of New South Wales,Australia before coming to the Netherlands in 1'976. From1,976-80 he was a Visiting Research Scientist, at the Stichtingvoor Bodemkartering, Wageningen, the Netherlands engagedin the development hnd implementation of computer-assistedmethods for soil, Iandscape and geological survey and evalu-ation. From 1981-1984 he was Senior lecturer at the Depart-ment of Soil Science and Geology, Agricultural University,Wageningen before being appointed Professor of Physical Ge-ogriphy it the Faculty of Geograptrical Sciences at the Uni-versity-of Utrecht in 1984. He is Chairman of a researchprogrim that covers (1) the development and application_s ofgeoitatistics; (2) the propagation of errors in geographical in-formation processing; (3) applications of geographicalinformation systems for environmental resource survey, bothwithin western countries and in developing countries; (4)problems of soil and groundwater pollution; and (5) manyispects of land use, spatial planning, environmental impact(acid rain), low-land geomorphology, Iand evaluation, etc.He is Chairman of the Netherlands Centre for GeographicalInformation Analysis and Chairman of the Steering Commit-tee of the European Geographical Information Systems Con-ferences. He was a member of the four-person team ap-pointed by DGXIII of the European Community to investigateind prepare for the setting up of a European Umbrella Or-ganisation for Geographical Information, and now repres-entsEGIS on the EUROGI Committee. His book, Principles of Ge-ographical Information Systems for Land Resources Assess-menf, was published in 1986 by Oxford University Press. Healso serves on the Editorial Boards of the lnfernational lour-nd for Geographical Information Systems, ()IS-Europe, andSoii Technology and is a former Chief Editor of Catena. Hehas served as a consultant to various International and na-tional Governmental and commercial agencies.
