VARIOGRAM-DERIVED MEASURES OF TEXTURAL IMAGE

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VARIOGRAM-DERIVED MEASURES OF TEXTURAL IMAGE CLASSIFICATION Application 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. CLARKE Department of Geography and National Center for Geographic Information and Analysis University of California, 3510 Phelps Hall, Santa Barbara, CA 931064060, 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 digital remote sensing third order image characteristics are considered a nuisance, while potentially useful spatial 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 image classification: variogram-derived texture has been recently proved to increase the accuracy. The objective of this study was to assess the potential of variogram-derived texture measures applied to classification of high ground resolution imagery. The study was conducted using ADAR images acquired over the Santa Monica Mountains, dominated by chaparral vegetation. Textural parameters were derived from a moving geographic window (of a size determined by the range), as opposed to the commonly applied geometric window of a fixed size. Binary decision tree was used to assess the potential of texture derived from variograms, cross variograms and pseudo-cross variograms, to discriminate between land cover classes. Finally, images were classified using the most significant texture 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 not change, while significant increase was reported for highly textured classes. Further methods of improving 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.

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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 texture and structure are as important as tone in traditional visual photointerpretation. Parallel to advances in spectral image classification techniques, research has been undertaken, albeit by a limited number of researchers, on incorporating texture and contextual information in image classification. A growing number of high ground resolution satellite sensors is operating 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 texture measures applied to classification of high ground resolution imagery. The method was applied to a chaparral environment, which has a much finer texture than forest. The technique employed was a combination of the approaches used to date, with a few improvements. The following section describes variogram applications in classification of remotely sensed images.

1.1. VARIOGRAM APPLICATIONS IN IMAGE CLASSIFICATION Geostatistics is currently a well-understood and frequently applied image processing technique: it has been shown (Woodcock 1988a, 1988b) that range is directly related to the texture and/or objects size, while sill is proportional to global object (class) variance, although it is also affected by external factors, such as sensor gain, image noise, atmospheric conditions etc.. An increasing interest in applications of variogram-derived texture has been noted in image classification. Two approaches to texture derivation from the variogram have been suggested and proved to increase image classification accuracy: semivariogram textural classifier algorithm STC (Miranda et al. 1992, 1996) and modeling the variogram ( Ramstein and Raffy, 1989). In STC, semivariances for the first consecutive lags are used directly as additional input layers to image classification, while in the second technique variogram model coefficients are used. However, both techniques have a significant shortcoming: variogram computation is based on a moving kernel of a fixed size, where window size is chosen experimentally in the preprocessing phase and depends highly on the particular data used in a study. There is a trade-off between application of too large and too small a window. The first approach leads to straddling class boundaries and encompassing several classes in the same variogram. On the other hand, several authors reported 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). Although the first few lags may be a good approximation of variogram shape, and hence theoretical variogram model type, their application seems to give an incomplete picture, since, in many cases, the sill is not achieved. Since variogram range measures texture coarseness and has been proven to be an important discriminant of forest stands, vegetation types and land cover classes. Range is also directly related to the size of objects: for small patches (in dispersed landscapes) range is shorter. Hence it is inappropriate to measure all the classes and objects with the same measure. Furthermore, Berberoglu et al. (2000) pointed out that 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 consecutive lags is a gradually smoother edge detector. Franklin and McDermid (1993) and Franklin et al. (1996) proposed an alternative technique: a geographic window, where dimensions of a moving kernel are customized and are determined by variogram range. The technique proved to be promising and has been applied to derive texture measures like the co-occurrence matrix for image classification as 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 a moving geographic window, the size of which was determined locally by a range. Next, a set of parameters was derived from the variogram and their discriminative potential was assessed using a binary decision tree constructed from combined and separate spectral and textural bands. The final image classification (minimum distance algorithm) was based on the original spectral bands and a few texture parameters, which best 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 an Airborne Data Acquisition and Registration Systems 5500. ADAR systems capture data with 4 digital cameras operating in the spectral range of 400 to 1000 nm. Green, red and 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 range extending 73 km west of Los Angeles and rising from sea level to 949 m elevation within a few kilometers. The primary vegetation type in this area is chaparral (hard chaparral dominated by Ceanothus, Adenostoma, Arctostaphylos and Quercus species and soft chaparral dominated by Artemisia, Eriogonum and Salvia species). Coastal scrubs, salt marshes, grasslands, oak and riparian habitats add to the full vegetation composition. The vegetation pattern is complex, responding not only to many environmental factors but 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 species composition and age, leading to a diversified and complicated structure of individual vegetation stands. Exploratory data analysis and parameter assessment were based on the study area covering the 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 Canyon dominated 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. Hard chaparral dominated by Ceanothus spp (mainly C. megacarpus) 5. Oak woodland dominated by Quercus agrifolia 6. Bare rocks

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Figure 2. Textures of studied classes. Each ADAR image in IR, R, G false color composi- image represents area of 100 x100 m, corretion: chaparral-dominated upper part of Zuma sponding to the distance of 40 lags assumed as the maximum range of the experimental Canyon. Image covers 15,625 ha. variogram. Upper row (from left): rock/road, grassland, soft chaparral; lower row: chamise chaparral, ceanothus chaparral and oak woodland. Figure 1. Subset of Santa Monica Mountains

In the Santa Monica Mountains grasslands form small communities located in welldrained areas at all elevations. Native perennial needlegrasses, introduced annual grasses, as well as some herbs make up the community. Plant cover is typically dense and homogenous, resulting in a smooth texture (Figure 2). Soft chaparral is the coastal sage scrub community found on the lower, gentle slopes in the vicinity of the ocean. It is generally found at lower elevations than hard chaparral, however it frequently reseeds burned chaparral areas, eventually giving way to chaparral. It is hence often adjacent to hard chaparral forming a mosaic. It is dominated by sagebrush species (Artemisia californica), sage species (Salvia apiana, S. leucophylla, S. mellifera) and buckwheat species (Eriogonum fasciculatum, E. cinereum). Shrubs do not grow closely together hence its texture has often a speckled pattern (Figure 2). California chaparral is composed mainly of evergreen shrubs that are adapted to fire and drought. It grows on poor, rocky soils in a Mediterranean climate. Most chaparral stands appear at higher elevations. Chamise chaparral (Adenostoma fasciculatum) is a dominant chaparral community in California and often forms nearly pure stands on south and west facing slopes and ridges. Ceanothus chaparral is dominated by various species of California lilac (Ceanothus). 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 on slopes and ridges throughout the mountains. It grows also near most intermittent streams, while larger streams support Riparian Woodlands. Oak forest creates dense overstory created by only one dominant tree: Quercus agrifolia, which has large tree crowns and hence the community texture is coarse.

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GEOSTATISTICS 3. Methods

Experimental variograms, cross variograms and pseudo-cross variograms between 3 bands 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 a range is not achieved during the calculation, the range is set at the maximum allowable lag (lag=40). A set of indices was calculated for each central pixel within a moving window of a changeable size (Table 1). TABLE 1. List of calculated variogram-derived measures

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To evaluate the discriminative power of the above texture indices, five sets of training samples were extracted from 128 x 128 window size (102400 sq. m). Due to the large number of derived parameters a first screening of parameters was carried out through principal components and correlation analysis. The final choice of the parameters was based on the analysis of variogram derivatives' performance evaluated through binary decision tree classification. Trees were constructed using: a) original spectral bands, b) measures of spatial variability and c) both sets of parameters. Indices used in tree construction 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 on remotely sensed data as well as the fact that neither spectral nor textural information used in this study had a normal distribution final image classification was performed using the minimum distance method. Classification accuracy was evaluated using stratified random sampling and was based on 300 points, where visual photointerpretation and field survey 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 proper identification of the selected classes: only the bare rocks class has distinct spectral signature (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 the vegetation communities are structured, complex composition of species.

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3. Spectral signatures of the selected land cover classes.

Spatial information might be of particular benefit for mapping classes characterized by complex spatial pattern represented by heterogeneous spectral response, especially if within-class variance is higher than interclass variance. Variograms derived from training samples show better differentiation for the selected classes than spectral signatures (Figure 4). Although Ramstein and Raffy (1989) showed that land cover classes can be well differentiated 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. Furthermore, for a particular class, range seems to be more stable for all bands, while sill varies, allowing additionally multivariate analysis (Figure 3).

Spatial signatures (variograms) of the classes (bands from left: G, R and IR). Semivariances shown in a log scale. Figure 4.

4.2. EVALUATION OF VARIOGRAM-DERIVED MEASURES

Decision split rules are highly dependent on the input data, hence each decision binary tree, derived from a different set of training samples was based on different values of parameters. However, parameters actually used in the construction of trees for all 5 training samples were similar: 4 of 5 decision split rules are based on spatial information. Generalizing, the first splitting rule distinguishes between classes of low and high pseudo-cross variogram between green and infrared bands, which is the main division between green vegetation and non-photosynthesizing classes. Soft chaparral and grassland communities fell into this class due to the fact that the image was captured in the dry season, when both communities were already senesced and little vegetative matter was present. Higher response in the green band discriminates grasslands from soft chaparral. Bare rocks were grouped together with green vegetation, due to high reflectance in all bands. However they are clearly distinguished from green matter by high redgreen pseudo-cross variance at a range, due to much higher reflectance in visible bands than vegetation. Oak woodlands are distinct from hard chaparral communities by very high red/infrared pseudo-cross variance at a range. Finally, Ceanothus chaparral has lower cross variogram sill for red and infrared bands, than Chamise chaparral. The following parameters proved to have the highest discriminative power, and were chosen for the final classification of the whole image: - sills of variogram and cross variogram, - 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.

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Variogram derivatives were calculated for 3 bands and multivariate derivatives for all 3 combinations of bands: altogether 21 texture measures and 3 spectral bands were used in final classification. Notably, parameters derived from consecutive lags (raw semivariances, cross variances or pseudo-cross variances, differences between variances at consecutive lags, slope of the variogram) did not classify as a significant discriminant measure: direct semivariances 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 a range 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 sill and range information. 4.3. IMAGE CLASSIFICATION: ASSESSMENT OF VARIOGRAM-DERIVED MEASURES PERFORMANCE

The overall accuracy using both spectral and textural information outperformed perpixel 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 has been noted for: - grasslands and soft chaparral (both classes were senescent at image acquisition time and characterized by similar spectral response but different texture: grasslands are more homogenous) - Chamise and Ceanothus chaparral with soft chaparral (this occurred mainly in shadowed areas, where the reflectance of Chamise and Ceanothus was low and close to that of soft chaparral. The only discriminant in this case appeared to be texture). - Ceanothus and oak woodland (both classes have high green biomass which responds to low red and high infrared reflectance. Oak woodland has coarse texture, while Ceanothus 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 following classes: grasslands and rocks/roads; and Ceanothus chaparral and oak woodland. The first of the above is due to similar reflectance of dry grasslands and rocks and high spatial homogeneity of both classes. Confusion between hard chaparral classes decreased in 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 the shaded 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 can be however easily distinguished by spatial signatures (Figure 5), as variogram measures are based on differences between pixels values, as opposed to absolute values of spectral response. Confusion of shaded Ceanothus with soft chaparral amounted to 38% in spectral classification, and only to 6% when textural information was added (the overall class error decreased from 46.2% to 25.5%).

Figure 5. Spectral (left) and spatial signatures (right) of 3 classes. Univariate variogramderivatives

are shown for green band, while multivariate between green and red bands. (Parameters listed on the right figure: v1_1 - variogram sill, vl 2 -- mean semivariance, vl 3 - sum of absolute differences between 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-cross semivariance at range. Finally textural classification produces less dispersed classes. This is an advantage for vegetation community classification as opposed to species mapping. Applied method avoids classifying single, shaded pixels, as they do contribute to the texture and are a part of the vegetation community structure. 5. Discussion

The results are encouraging: classification based on variogram-based measures proved to increase overall and class-specific classification accuracy. It has been shown that measures incorporating variogram parameters are more robust than raw variances calculated at consecutive lags. Furthermore it has been shown that discrimination between classes in shade is possible 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 of detail on maps for cartometric applications (Clarke and Schweizer 1991), remotely sensed imagery is not a data model and registers real world objects which are too complex to be self-similar at all scales (De Cola 1993). At larger scales there is much undesirable detail present: for instance the shadows of particular bushes or trees. In per-pixel classification this is regarded as noise, however, if spatial variability is taken into account in the analysis, shade may be an important component of texture.

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The technique does have the potential for providing improved discrimination of vegetation classes, especially between pairs off classes, which have similar spectral response but contrasting spatial structure (for instance grasslands and soft chaparral). However some confusion between vegetation classes is still present. In highly diversified landscapes with respect to species composition and age, like the present study, accuracy could be significantly increased if vegetation classes were divided into subclasses of different age and structure. Further abatement of error could be obtained if other classification techniques were employed. Binary decision tree classification performed on training samples has shown that some classes were discriminated using solely spectral information, some just spatial information, and others both. It is expected then, that knowledge-based classifiers would perform better than minimum distance classifiers, since decision 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 not require a priori knowledge of statistical distribution of data. The decision rules are not fixed by a deterministic rule applied to the training signatures (as opposed to employment of hard rules by expert systems), but are determined iteratively by minimizing classification error. Other advantages of neural networks, like the possibility of including a large number of diverse variables, have been widely emphasized in the literature. This hypothesis will be tested in the future. Acknowledgements

The authors are grateful to Dr. Dar Roberts and the Advanced Remote Sensing Group of Geography Department, University of California - Santa Barbara, for providing vegetation reference data as well as expertise in remote sensing techniques for mapping chaparral vegetation. We acknowledge Pacific Meridian Resources for permission to use ADAR images. Additionally Anna Jakomulska wishes to express her gratitude to NCGIA for providing excellent computing facilities, and an especially hospitable and creative environment. Funding for this work was provided by the Fulbright Commission, by a Fulbright award to the first author. References Berberoglu S., Lloyd C. D., Atkinson P. M., Curran P. J., 2000, The integration of spectral and textural information using neural networks for land cover mapping in the Mediterranean, Computers & Geosciences, 26,385-396 Carr J. R., 1998, The semivariogram in comparison of the co-occurrence matrix for classification of image texture, IEEE Transactions on Geoscience and Remote Sensing, 36 (6) Chica-Olmo M., Abarca-Hernandez F., 2000, Computing geostatistical image texture for remotely sensed data classification, Computers & Geosciences, 26, 373-383 Clarke K. C. and Schweizer D. M., 1991, Measuring the Fractal Dimension of Natural Surfaces Using a Robust Fractal Estimator, Cartography and Geographic Information Systems, Vol. 18, No. 1, pp. 37-47 De Cola L., 1993, Multifractals in Image Processing and Process Imaging, In: Lam N. N.-S., Fractals in Geography, Prentice Hall Franklin S. E., McDermid G. J., 1993, Empirical relations between digital SPOT HRV and CASI spectral response and lodgepole pine (Pinus contorta) forest stand parameters, Int. J. Remote Sensing, Vol. 14, No. 12, 2331-2348 Franklin S. E., Wulder M. A., Lavigne M. B., 1996, Automated derivation of geographic window sizes for use in remote sensing digital image texture analysis, Computers & Geosciences, Vol. 22, No. 6, 665-673

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Gardner M., 1997, Mapping Chaparral with AVIRIS using Advanced Remote Sensing Techniques, Unpublished Masters Thesis, University of California Santa Barbara, pp.58 Miranda F. P., Macdonald J. A., Can J. R., 1992, Application of the semivariogram textural classifier (STC) for vegetation discrimination using SIR-B data of Borneo, International Journal of Remote Sensing, Vol. 13, No. 12, 2349-2354 Miranda F. P., Fonseca L. E. N., Can J. R., Raranik J. V., 1996, Analysis of JERS-1 (Fuyo-1) SAR data for vegetation discrimination in northwestern Brazil using the semivariogram textural classifier (STC), International Journal of Remote Sensing, Vol. 17, No. 17, 3523-3529 Ramstein G. and Raffy M., 1989, Analysis of the structure of radiometric remotely-sensed images. International Journal of Remote Sensing, 10, 1049-1073 Roberts D.A., Gardner M.E., Church R., Ustin S.L., Scheer G., and Green R.O., 1998, Mapping Chaparral in the Santa Monica Mountains Using Multiple Endmember Spectral Mixture Models, Remote Sensing of Environment St-Onge B. A., Cavayas F., 1995, Estimating Forest stand Structure from High Resolution Imagery using the Directional variogram, International Journal of Remote Sensing, Vol. 16, No. 11, 1999-2021 Wallace C. S. A., Watts J. M., Yool S. R., 2000, Characterizing the spatial structure of vegetation communi ties in the Mojave Desert using geostatistical techniques, Computers & Geosciences 26 (2000) 397-410 Woodcock C. E. et al., 1988a, The use of variograms in remote sensing: I real digital images, Remote Sensing of Environment 25:323-348 Woodcock C. E. et al., 1988b, The use of variograms in remote sensing: II real digital images, Remote Sensing of Environment 25:349-379 Wulder M. A., Lavigne M. B., LeDrew E. F., Franklin S. E., 1997, Comparison of texture algorithms in the statistical estimation of LAI: first-order, second-order, and semivariance moment texture (SMT), Canadian Remote Sensing Society Annual Conference, GER'97, Geomatics in the Era of Radarsat, May 24-30, 1997, Ottawa, Canada

geoENV III GEOSTATISTICS FOR ENVIRONMENTAL APPLICATIONS Proceedings of the Third European Conference on Geostatistics for Environmental Applications held in Avignon, France, November 22-24, 2000

Edited by

PASCAL MONESTIEZ Institut National de la Recherche Agronomique, Avignon, France

DENIS ALLARD Institut National de la Recherche Agronomique, Avignon, France and

ROLAND FROIDEVAUX FSS Consultants SA, Geneva, Switzerland

KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

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