VARIOGRAM-DERIVED MEASURES OF TEXTURAL IMAGECLASSIFICATIONApplication to large-scale vegetation mapping

A. JAKOMULSKA

University of Warsaw, Faculty of Geography and Regional Studies,

Remote Sensing of Environment Laboratory, ul. Krakowskie Przedmiescie 30,00-927 Warsaw, Poland

AND

K. C. CLARKEDepartment of Geography and National Center for Geographic Information andAnalysis University of California, 3510 Phelps Hall, Santa Barbara, CA 93106-4060, USA

Abstract. Traditional elements of image interpretation include characteristics of first order (tone/color), second order (spatial arrangement: size, shape and pattern) and third order (height, shadow). In digitalremote sensing third order image characteristics are considered a nuisance, while potentially usefulspatial information has been usually ignored, due to lack of methodology and computational limitations.However few researchers have undertaken integration of spatial and spectral information for imageclassification: variogram-derived texture has been recently proved to increase the accuracy. Theobjective of this study was to assess the potential of variogram-derived texture measures applied toclassification of high ground resolution imagery. The study was conducted using ADAR imagesacquired over the Santa Monica Mountains, dominated by chaparral vegetation. Textural parameterswere derived from a moving geographic window (of a size determined by the range), as opposed tothe commonly applied geometric window of a fixed size. Binary decision tree was used to assess thepotential of texture derived from variograms, cross variograms and pseudo-cross variograms, todiscriminate between land cover classes. Finally, images were classified using the most significanttexture measures and the accuracy was compared with the accuracy of standard per-pixel classification.Overall classification accuracy increased by as much as 15%. Accuracy of homogeneous classes did notchange, while significant increase was reported for highly textured classes. Further methods ofimproving accuracy using variogram-derived texture were discussed.

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P. Monestiez et al. (eds.), geoENV III - Geostatistics for Environmental Applications, 345-355.© 2001 Kluwer Academic Publishers Printed in the Netherlands.

346 A. JAKOMULSKA AND K. C. CLARKE

1. Introduction

Digital classification of remotely sensed images is commonly performed on a per-pixel basis,ignoring spatial characteristics and the arrangement of imaged objects, whereas both textureand structure are as important as tone in traditional visual photointerpretation. Parallel toadvances in spectral image classification techniques, research has been undertaken, albeitby a limited number of researchers, on incorporating texture and contextual information inimage classification. A growing number of high ground resolution satellite sensors isoperating or scheduled for launch within the next years (e.g. OrbView-3 and OrbView-4,SPOT 5), and these systems provide extra incentives for further research in this direction.

The objective of this study was to assess the potential of variogram-derived texturemeasures applied to classification of high ground resolution imagery. The method was appliedto a chaparral environment, which has a much finer texture than forest. The techniqueemployed was a combination of the approaches used to date, with a few improvements.The following section describes variogram applications in classification ofremotely sensed images.

1.1. VARIOGRAM APPLICATIONS IN IMAGE CLASSIFICATION

Geostatistics is currently a well-understood and frequently applied image processingtechnique: it has been shown (Woodcock 1988a, 1988b) that range is directly related to thetexture and/or objects size, while sill is proportional to global object (class) variance, althoughit is also affected by external factors, such as sensor gain, image noise, atmospheric conditionsetc.. An increasing interest in applications of variogram-derived texture has been noted inimage classification. Two approaches to texture derivation from the variogram have beensuggested and proved to increase image classification accuracy: semivariogram texturalclassifier algorithm STC (Miranda et al. 1992, 1996) and modeling the variogram (Ramstein and Raffy, 1989). In STC, semivariances for the first consecutive lags areused directly as additional input layers to image classification, while in the second techniquevariogram model coefficients are used. However, both techniques have a significantshortcoming: variogram computation is based on a moving kernel of a fixed size, wherewindow size is chosen experimentally in the preprocessing phase and depends highly onthe particular data used in a study. There is a trade-off between application of too large andtoo small a window. The first approach leads to straddling class boundaries andencompassing several classes in the same variogram. On the other hand, several authorsreported applications, where variograms were derived from small moving windows (e.g.:Chica-Olmo and Abarca-Hernandez 2000 used only the first lag of the variogram). Althoughthe first few lags may be a good approximation of variogram shape, and hence theoreticalvariogram model type, their application seems to give an incomplete picture, since, in manycases, the sill is not achieved. Since variogram range measures texture coarseness and hasbeen proven to be an important discriminant of forest stands, vegetation types and landcover classes. Range is also directly related to the size of objects: for small patches (indispersed landscapes) range is shorter. Hence it is inappropriate to measure all the classesand objects with the same measure. Furthermore, Berberoglu et al. (2000) pointed outthat variograms for short lags measure field edges, rather than within-field variability. In

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fact, semivariance for the first lag is a strong edge detector, and semivariance at con-secutive lags is a gradually smoother edge detector.

Franklin and McDermid (1993) and Franklin et al. (1996) proposed an alternativetechnique: a geographic window, where dimensions of a moving kernel are customized andare determined by variogram range. The technique proved to be promising and has beenapplied to derive texture measures like the co-occurrence matrix for image classificationas well as first and second order texture and semivariance moment texture (nugget,range, sill, slope, mean semivariance) for LAI estimation (Wulder et al. 1997).

In this study experimental variograms were derived for each image pixel from amoving geographic window, the size of which was determined locally by arange. Next, a set of parameters was derived from the variogram and their discriminativepotential was assessed using a binary decision tree constructed from combined and separatespectral and textural bands. The final image classification (minimum distancealgorithm) was based on the original spectral bands and a few texture parameters, whichbest exploited the differences between classes tested.

2. Study Area and Data

The analysis was performed on high ground resolution (2.5 m) image registered by anAirborne Data Acquisition and Registration Systems 5500. ADAR systems capturedata with 4 digital cameras operating in the spectral range of 400 to 1000 nm. Green, redand infrared bands were chosen for analysis. Images were acquired in late summer (08.29.1998) over the Santa Monica Mountains in Southern California, a rugged mountain rangeextending 73 km west of Los Angeles and rising from sea level to 949 m elevation within afew kilometers. The primary vegetation type in this area is chaparral (hard chaparraldominated by Ceanothus, Adenostoma, Arctostaphylos and Quercus species and softchaparral dominated by Artemisia, Eriogonum and Salvia species). Coastal scrubs, saltmarshes, grasslands, oak and riparian habitats add to the full vegetation composition.The vegetation pattern is complex, responding not only to many environmental factorsbut also to a variable fire history. Fire results in a mosaic of successional stages of species (Roberts et al. 1998), hence vegetation communities are diversified with respect to speciescomposition and age, leading to a diversified and complicated structure of individualvegetation stands.

Exploratory data analysis and parameter assessment were based on the study area coveringthe central part of the Santa Monica Mountains (between 118° 52' 53" and 118° 45' 03" W;and 34° 11' 22" and 33° 59' 56" N). Classification was performed on a subset of a 1.25 x 1.25 km2 area (Figure 1), encompassing the upper part of the eastern slopes of Zuma Canyondominated by hard chaparral. The following classes were analysed: (Figure 2):1. Grasslands

2. Soft chaparral dominated by Ashy-Leaf Buckwheat (Eriogonum cinereum) 3.Hard chaparral dominated by Chamise (Adenostoma fasciculatum) 4. Hardchaparral dominated by Ceanothus spp (mainly C. megacarpus) 5. Oakwoodland dominated by Quercus agrifolia6. Bare rocks

348 A. JAKOMULSKA AND K..C. CLARKE

Figure 1. Subset of Santa Monica MountainsADAR image in IR, R, G false color composi-tion: chaparral-dominated upper part of ZumaCanyon. Image covers 15,625 ha.

Figure 2. Textures of studied classes. Eachimage represents area of 100 x100 m, corre-sponding to the distance of 40 lags assumed asthe maximum range of the experimentalvariogram. Upper row (from left): rock/road,grassland, soft chaparral; lower row: chamisechaparral, ceanothus chaparral and oak wood-land.

In the Santa Monica Mountains grasslands form small communities located in well-drained areas at all elevations. Native perennial needlegrasses, introduced annualgrasses, as well as some herbs make up the community. Plant cover is typically denseand homogenous, resulting in a smooth texture (Figure 2). Soft chaparral is the coastalsage scrub community found on the lower, gentle slopes in the vicinity of the ocean. Itis generally found at lower elevations than hard chaparral, however it frequently reseedsburned chaparral areas, eventually giving way to chaparral. It is hence often adjacent tohard chaparral forming a mosaic. It is dominated by sagebrush species (Artemisia cali-fornica), sage species (Salvia apiana, S. leucophylla, S. mellifera) and buckwheat species(Eriogonum fasciculatum, E. cinereum). Shrubs do not grow closely together hence itstexture has often a speckled pattern (Figure 2). California chaparral is composedmainly of evergreen shrubs that are adapted to fire and drought. It grows on poor, rockysoils in a Mediterranean climate. Most chaparral stands appear at higher elevations.Chamise chaparral (Adenostoma fasciculatum) is a dominant chaparral community inCalifornia and often forms nearly pure stands on south and west facing slopes andridges. Ceanothus chaparral is dominated by various species of California lilac (Cean-othus). It has lower plant density than Chamise but more complete, often unpenetrable,crown cover, hence its texture is smoother than the texture of Chamise chaparral.Southern Oak Woodland is dominated by Coast Live Oaks. Oak groves are found onslopes and ridges throughout the mountains. It grows also near most intermittentstreams, while larger streams support Riparian Woodlands. Oak forest creates denseoverstory created by only one dominant tree: Quercus agrifolia, which has large treecrowns and hence the community texture is coarse.

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3. Methods

Experimental variograms, cross variograms and pseudo-cross variograms between 3bands were calculated for each image pixel, using a program written in the C language.The source code of the program is available to interested researchers from the authors.To determine variogram range for each pixel, variances were obtained for up to 40 lags (100 meters) on a per-pixel basis. A bounded semivariogram model is assumed: if arange is not achieved during the calculation, the range is set at the maximum allowablelag (lag=40). A set of indices was calculated for each central pixel within a movingwindow of a changeable size (Table 1).

TABLE 1. List of calculated variogram-derived measures

6 A. JAKOMULSKA AND K..C. CLARKE

To evaluate the discriminative power of the above texture indices, five sets oftraining samples were extracted from 128 x 128 window size (102400 sq. m). Due to thelarge number of derived parameters a first screening of parameters was carried out throughprincipal components and correlation analysis. The final choice of the parameterswas based on the analysis of variogram derivatives' performance evaluated through binarydecision tree classification. Trees were constructed using: a) original spectral bands, b)measures of spatial variability and c) both sets of parameters. Indices used in treeconstruction for the training samples were used as input for the final image classification.Due to non-linear relation of variogram derived texture measures and objects registered onremotely sensed data as well as the fact that neither spectral nor textural information used inthis study had a normal distribution final image classification was performed using theminimum distance method. Classification accuracy was evaluated using stratified randomsampling and was based on 300 points, where visual photointerpretation and fieldsurvey provided ground truth data.

4. Results

4.1. CHARACTERIZATION OF SPECTRAL AND TEXTURAL PROPERTIES

ADAR sensors register radiances in quite broad spectral bands, which do not allow a properidentification of the selected classes: only the bare rocks class has distinct spectralsignature (Figure 3). Spectral signatures derived from hyperspectral imagery (like AVIRIS)are much more distinct, facilitating detailed species mapping (Gardner 1997, Roberts et al.1998). However, vegetation communities mapping is a different approach, since thevegetation communities are structured, complex composition of species.

Figure 3. Spectral signatures of the selected land cover classes.

Spatial information might be of particular benefit for mapping classes characterized bycomplex spatial pattern represented by heterogeneous spectral response, especially ifwithin-class variance is higher than interclass variance. Variograms derived from trainingsamples show better differentiation for the selected classes than spectral signatures (Figure4). Although Ramstein and Raffy (1989) showed that land cover classes can be welldifferentiated by range only (assuming an exponential variogram model), both the

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present study and other reports (St-Onge and Cavayas, 1995; Wallace et al., 2000)show, that both parameters are distinctive for different vegetation communities. Fur-thermore, for a particular class, range seems to be more stable for all bands, while sillvaries, allowing additionally multivariate analysis (Figure 3).

Figure 4. Spatial signatures (variograms) of the classes (bands from left: G, R and IR). Semivari-ances shown in a log scale.4.2. EVALUATION OF VARIOGRAM-DERIVED MEASURESDecision split rules are highly dependent on the input data, hence each decision binarytree, derived from a different set of training samples was based on different values ofparameters. However, parameters actually used in the construction of trees for all 5training samples were similar: 4 of 5 decision split rules are based on spatial informa-tion. Generalizing, the first splitting rule distinguishes between classes of low and highpseudo-cross variogram between green and infrared bands, which is the main divisionbetween green vegetation and non-photosynthesizing classes. Soft chaparral and grass-land communities fell into this class due to the fact that the image was captured in thedry season, when both communities were already senesced and little vegetative matterwas present. Higher response in the green band discriminates grasslands from soft chap-arral. Bare rocks were grouped together with green vegetation, due to high reflectancein all bands. However they are clearly distinguished from green matter by high red-green pseudo-cross variance at a range, due to much higher reflectance in visible bandsthan vegetation. Oak woodlands are distinct from hard chaparral communities by veryhigh red/infrared pseudo-cross variance at a range. Finally, Ceanothus chaparral haslower cross variogram sill for red and infrared bands, than Chamise chaparral.

The following parameters proved to have the highest discriminative power, andwere chosen for the final classification of the whole image: - sills of variogram and crossvariogram,- mean semivariance and cross semivariance,- sum of absolute differences between spherical variogram model and semivariances at

consecutive lags up to a range,- pseudo-cross variance at lag 0 and at a range.

352 A. JAKOMULSKA AND K..C. CLARKE

Variogram derivatives were calculated for 3 bands and multivariate derivatives for all3 combinations of bands: altogether 21 texture measures and 3 spectral bands were usedin final classification.

Notably, parameters derived from consecutive lags (raw semivariances, cross vari-ances or pseudo-cross variances, differences between variances at consecutive lags, slopeof the variogram) did not classify as a significant discriminant measure: directsemivariances at lags are not as stable, as the global parameters based on a range.With the exception of pseudo-cross variance at lag=O, all texture indices are derived at arange or involve computation based on consecutive variances up to a range.Mean values of variances and cross variances calculated up to a range incorporate both silland range information.4.3. IMAGE CLASSIFICATION: ASSESSMENT OF VARIOGRAM-DERIVED

MEASURES PERFORMANCEThe overall accuracy using both spectral and textural information outperformed per-pixel classification and was 82% and 69.5% (respectively). Per-class accuracy is shown in(Table 2). Significant decrease in class confusion comparing to spectral classification hasbeen noted for:- grasslands and soft chaparral (both classes were senescent at image acquisition time

and characterized by similar spectral response but different texture: grasslands aremore homogenous)

- Chamise and Ceanothus chaparral with soft chaparral (this occurred mainly in shad-owed areas, where the reflectance of Chamise and Ceanothus was low andclose to that of soft chaparral. The only discriminant in this case appeared to betexture).

- Ceanothus and oak woodland (both classes have high green biomass which responds tolow red and high infrared reflectance. Oak woodland has coarse texture, whileCeanothus is more homogenous).

In two cases accuracy decreased by several percent: Chamise chaparral (users only)and oak woodland (both users and producers). In spite of the overall increase of accuracy,some confusion still occurs in spectral-textural classification between the followingclasses: grasslands and rocks/roads; and Ceanothus chaparral and oak woodland. The firstof the above is due to similar reflectance of dry grasslands and rocks and highspatial homogeneity of both classes. Confusion between hard chaparral classes decreasedin comparison with per-pixel classification, however it still poses a problem in

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terms of proper vegetation identification. Ceanothus chaparral was partially shaded,hence an additional signature was derived for the classification. Spectral signature of theshaded Ceanothus chaparral is however much closer to the signature of soft chaparral (Figure 5),.and its proper identification appears to be problematic. The three classes canbe however easily distinguished by spatial signatures (Figure 5), as variogram measuresare based on differences between pixels values, as opposed to absolute values of spec-tral response. Confusion of shaded Ceanothus with soft chaparral amounted to 38% inspectral classification, and only to 6% when textural information was added (the overallclass error decreased from 46.2% to 25.5%).

Figure 5. Spectral (left) and spatial signatures (right) of 3 classes. Univariate variogramderivativesare shown for green band, while multivariate between green and red bands. (Parameters listed on theright figure: v1_1 - variogram sill, vl 2 -- mean semivariance, vl 3 - sum of absolute differencesbetween spherical variogram model and semivariances, c12_1 - sill of a cross variogram, c12 2 -mean cross semivariance, c12 4 - pseudo-cross semivariance at lag=O, c 125 - pseudo-crosssemivariance at range.

Finally textural classification produces less dispersed classes. This is an advantagefor vegetation community classification as opposed to species mapping. Appliedmethod avoids classifying single, shaded pixels, as they do contribute to the texture andare a part of the vegetation community structure.

5. Discussion

The results are encouraging: classification based on variogram-based measures provedto increase overall and class-specific classification accuracy. It has been shown thatmeasures incorporating variogram parameters are more robust than raw variances calcu-lated at consecutive lags.

Furthermore it has been shown that discrimination between classes in shade is pos-sible if textural parameters are used. With the increasing ground resolution of imagery,there is more detail observable. However, as opposed to a desirable increase of level ofdetail on maps for cartometric applications (Clarke and Schweizer 1991), remotelysensed imagery is not a data model and registers real world objects which are too com-plex to be self-similar at all scales (De Cola 1993). At larger scales there is much unde-sirable detail present: for instance the shadows of particular bushes or trees. In per-pixelclassification this is regarded as noise, however, if spatial variability is taken into ac-count in the analysis, shade may be an important component of texture.

10 A. JAKOMULSKA AND K.-C. CLARKE

The technique does have the potential for providing improved discrimination ofvegetation classes, especially between pairs off classes, which have similar spectral re-sponse but contrasting spatial structure (for instance grasslands and soft chaparral).However some confusion between vegetation classes is still present. In highly diversifiedlandscapes with respect to species composition and age, like the presentstudy, accuracy could be significantly increased if vegetation classes were dividedinto subclasses of different age and structure. Further abatement of error could be obtainedif other classification techniques were employed. Binary decision tree classification per-formed on training samples has shown that some classes were discriminated using solelyspectral information, some just spatial information, and others both. It is expected then, thatknowledge-based classifiers would perform better than minimum distance classifiers, sincedecision rules can be designed to include only textural or only spectral information.A better solution could be the application of artificial neural networks, since they do notrequire a priori knowledge of statistical distribution of data. The decision rules are notfixed by a deterministic rule applied to the training signatures (as opposed toemployment of hard rules by expert systems), but are determined iteratively byminimizing classification error. Other advantages of neural networks, like the possibilityof including a large number of diverse variables, have been widely emphasized in theliterature. This hypothesis will be tested in the future.Acknowledgements

The authors are grateful to Dr. Dar Roberts and the Advanced Remote Sensing Group ofGeography Department, University of California - Santa Barbara, for providing vegeta-tion reference data as well as expertise in remote sensing techniques formapping chaparral vegetation. We acknowledge Pacific Meridian Resources forpermission to use ADAR images. Additionally Anna Jakomulska wishes to express hergratitude to NCGIA for providing excellent computing facilities, and an especiallyhospitable and creative environment. Funding for this work was provided by theFulbright Commission, by a Fulbright award to the first author.

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geoENV III -GEOSTATISTICS FOR

ENVIRONMENTALAPPLICATIONS

Proceedings of the Third European Conference on Geostatisticsfor Environmental Applications held in

Avignon, France, November 22-24, 2000

Edited by

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Avignon, France

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