The Effect of Training Strategies on Supervised Classification at Different Spatial Resolutions

Transcription

1 The Effect of Training Strategies on Supervised Classification at Different Spatial Resolutions DongMel Chen and Douglas Stow Abstract Three different training strategies often used for supervised classification-single pixel, seed, and block or polygon training-are compared in this paper. The range parameter of semi-variograms obtained from sample image subsets of each land-uselland-cover class was used to measure the autocorrelation level during training set selection. Eight training sets with different sizes were generated and then applied to image subsets with three multispectral bands and variance texture images in the classification of six land-use classes. The classification results using these training sets were compared at five resolution levels and were based on six Color Infrared Digital Orthophoto Quarter Quadrangle (DOQQ) subsets of different urban land types in urban and rural fringe areas of the San Diego metropolitan area. The performance of different training strategies is shown to be influenced by the training size, the image resolution, and the degree of autocorrelation inherent within each class. Training approaches had more impact on classification results at fine resolution levels than at coarse resolutions. For spectrally homogeneous classes, a spatially independent, single-pixel training approach is preferred. But for spatially heterogeneous classes, small block training has the advantage of readily capturing spectral and spatial information and reduces the amount of interaction time for the analyst. Introduction Digital classification of multispectral airborne and satellite remotely sensed data can be an effective means for generating land-uselland-cover maps. There are two general steps in a typical computer-assisted supervised land-uselland-cover classification process when applying a supervised strategy. In the first phase, training pixels are selected and associated statistics are generated. The second phase involves the assignment of each image pixel to a class according to the training statistics, by using a classification algorithm. Most attention has been given to the second phase of developing new algorithms to increase the classification accuracy by incorporating spatial1 contextual information (Wharton, 1982; Gong and Howard,. 1990b; Barnsley and Barr, 1996; Flygare, 1997; Sharma and Sarkar, 1998), image segmentation (Cross and Mason, 1988; Woodcock and Harward, 1992), or using knowledge-based classification and expert systems (Knontoes and Rokos, 1996), DM. Chen was with the Environmental Systems Research Institute, Inc., 380 New York Street, Redlands, CA ; he is presently with the Department of Geography, Queen's University, Kingston, Ontario K7L 3N6, Canada (chendm@post.queensu.ca). D. Stow is with the Department of Geography, San Diego State University, San Diego, CA Fuzzy set (Fisher andpathirana, 1990; Foody, 1999), and neural nets (Civco, 1993). Relatively little attention has been devoted to the selection of training data. An important assumption made in image classification is that the training data represent the classes of interest. In any supervised classification, the aim of the training stage is to derive a representative sample of the spectral signatures of each class. The quality of training data can significantly influence the performance of an algorithm and, thus, the classification accuracy. The accuracy of the decision rules in the next stage may depend on the accuracy of the standard deviation measure derived from training site statistics. This is particularly true for maximum-likelihood and other classifiers that are based on parametric statistics. Inappropriate placement or too few training pixels in a training site produces statistics unrepresentative of the land-uselland-cover classes of interest. Previous studies have shown that different training strategies can result in very different accuracy estimates for the final classification ( Hixson et al., 1980; Campbell, 1981; Chuvieco and Congalton, 1988; Gong and Howarth,lggoa). Therefore, several authors have emphasized the importance of the training stage for achieving reliable classification results ( Hixson eta]., 1980: Story and Campbell, 1986; Chuvieco and Congalton, 1988; Foody eta]., 1995; Foody, 1999). Ideally, training data should be based on in situ data collected in advance of image classification. However, given the vast time and labor cost and problems in achieving the desired accuracy of calibration, it is common and reasonable to derive training data directly from the image using a priori knowledge of the scene. Several spatial sampling objects are used to select training data in traditional supervised training from images: (1) single pixel, (2) polygons or blocks of pixels, and (3) similar contiguous pixels through seeding (Jensen, 1996). When selecting a training strategy, a range of factors should be considered, such as the number of pixels used in training, the effect of spatial autocorrelation, intra-image variance, time and labor costs, and the functionality of current processing systems (Campbell, 1996; Jensen, 1996). It is often impractical to collect training data that satisfy all of these requirements. Spatial autocorrelation existing among pixels which are contiguous or close together is an important consideration when selecting a training strategy. According to Campbell (1981) and Labovitz and Masuoka (1984), training data collected from autocorrelated data tend to have reduced variance, Photogrammetric Engineering & Remote Sensing Vol. 68, No. 11, November 2002, pp IO2I6811-ll55$3.00/0 O 2002 American Society for Photogrammetry and Remote Sensing PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING Novprnher

2 which makes the training signatures for each class biased and less representative. The ideal way is to select training data within a region using every nth pixel or some other sampling criteria to derive non-autocorrelated (i.e., spatially independent) training data. This conclusion is also supported by Gong and Howarth (1990a) after comparing the classification accuracy of single-pixel training and block training on land-cover classification using SPOT HRV images. However, it is important to recognize that the previous studies were conducted on spectral-based classification with an image spatial resolution coarser than 20 m with low inter-class variation. They do not take into account the spatial and structural information inherent in each class. This may not be a major issue for low-resolution image data in which the spatial resolution is coarser than the spatial unit of a discernable land-uselland-cover class (Strahler et al., 1986). But with the greater heterogeneity of high-resolution images, spatial autocorrelation properties may be a characteristic for defining a class. It is uncertain whether non-autocorrelated training data still lead to more accurate results. The objective of this study is to evaluate some of the strategies for selecting training data and to determine their influence on classification results for different, high spatial resolution images. This paper is limited to investigation of single-pixel training (sp), seed training (ST), and block training with spatial distance limitation (BT). Each strategy was applied to two feature combinations at five different spatial resolutions (2 m, 4 m, 8 m, 12 m, and 16 m). The semi-variograrn was estimated to characterize the degree of autocorrelation in each class. The overall and individual Kappa coefficients were employed to assess the accuracy of the different training strategies. training strategies. Figure 1 shows these six subsets at a 2-m spatial resolution and specifies the size of each subset. In addition to the original three bands of the CN DOQQ images, a texture band derived as the variance of a 5 by 5 moving window from the near-infrared band was incorporated into the analysis. Two feature combinations were used, the original three spectral bands and the original three bands plus the NIR texture band. The rationale for this selection is that the three bands form the basic data set and the combination of a variance image with the three bands incorporates spatial structural information (i.e., texture) into the classification. Seml-Varlogram for Measurement of Spatial Autocorrelatlon Because spatial autocorrelation may be a consideration in selecting training data, it is useful to quantitatively measure the degree of autocorrelation to guide the selection of non-autocorrelated or autocorrelated data. Semi-variance analysis is the most commonly used approach to establishing the spatial characteristics of images (Atkinson, 1997). The more detailed theoretical and mathematical exploration of semi-variograms can be found in Curran (1988), Jupp et al. (1989a; 1989b), and Cressie (1993). The formula of semi-variogram is briefly described below. Research Design Data Set and Classiflcatlon Scheme Data selected for this study consisted of digital multispectral imagery extracted from us~s color infrared (CIR) Digital Orthophoto Quarter Quadrangles (DOQQ'). Color infrared aerial uhotoarauhs acauired on September, 1996 were scanned and LbjecYted to photogrammet& processing by the USG~. The imaees -~ were radiometricallv balanced and aeoreferenced to - State Plane Coordinates by commercial service provider, in the process of producing &I image mosaic covering San Diego Countv. The resultant mosaic has a fine spatial resolution of 1 meter kith three spectral bands (green, red, and near infrared (NIR)). The area selected for this study is the urban and rural fringe areas of the Del Mar quadrangle of San Diego. 'TO evaluate the effect if training strategies at different spatial resolutions, the original l-m ~OQQimages were aggregated into five spatial resolutions (2 m, 4 m, 8 m, 12 m, and 16 m). The reason for not using the 1-m spatial resolution is that the finest spatial resolution currently available for multispectral satellite images is 2.4 m. A simple averaging method was utilized for aggregation. Six general land-uselland-cover categories encountered in this area were used in image classification, including singlefamily residential, multi-family residential, industry, irrigated grass, cleared land, and undeveloped land. Features associated with transportation land use are linear and generally require different pattern recognition algorithms for identification. Therefore, transportation is not used in this study. In order to avoid the influence of boundary and mixed land-usellandcover pixels on classification accuracy and for the convenience of training data selection and reference data identification, six subsets, each representing one type of land-uselland-cover, were chosen for analysis. In this way, training and reference data from each subset were correctly identified so that differences in classification accuracies were only influenced by (a) (9 Figure 1. Six 2m image subsets (NIR band) used in testing different train~ng strategies. Image dimensions in pixels. (a) Undeveloped Land (UL) (140 by 130). (b) Multi-Family (MF) (184 by 160). (c) Irrigated Grassland (GL) (180 by 190). (d) Cleared Land (CL) (220 by 224). (e) Industry (IN) (224 by 224). (f) Single-Family (SF) (230 by 220) Novembrr ZOO? 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3 'C '$ 0.4 w r W r W W r ( O K m * m T % Lag (pixels) Figure 2. The semi-variogram calculated from the NIR band at 2-m spatial resolution images for six classes used in this study (SF = Single-Family, MF = Multi-Family, IN = Industry, GL = Irrigated Grassland, CL = Cleared Land, UL = Undeveloped Land). The semi-variogram is a graph of the semi-variance of values given for pixels separated by different distances. The semivariance represents the average of the squared difference in values separated by a specific lag distance. The formula of the semi-variogram is where n is the number of pixel pairs separated at distance h, and X(1) and X(i + h) are the pixel values at i and i + h, respectively. The semi-variance is often normalized by the global variance (Cressie, 1993). The semi-variance may be fitted with a model (such as linear, exponential, spherical, or Guassian). Typically, the range and sill are two parameters of semi-variograms used to describe a data set. The semi-variance is zero when the lag is zero. As distance increases, the difference between pixel pairs generally becomes larger. At some distance, the semi-variogram usually develops a flat region called the sill. The distance (or lag) at which the sill is reached is called the range. The range is the limit to spatial autocorrelation and generally indicates the distance over which values sampled from a spatial process are similar. In other words, the range can be used to determine whether two pixels are likely to be spatial autocorrelated or not. If the distance between two pixels is greater than the range, they are likely to be independent samples. Otherwise, they may be autocorrelated. The semi-variogram of the six subset images was calculated and plotted (see Figure 2). The ranges of each subset were determined by fitting to the spherical, exponential, and Gaussian models. The range obtained from the model with the best fit was used in the selection of training data and is listed in Table 1. Training Strategies Three training strategies were tested in this study. The first strategy was carried out using single-pixel training (SP). For each class, the training data were selected as individual pixels, but the closest distance between training pixels was required to be at least greater than the range obtained from the corresponding semi-variogram, in order to avoid spatial autocorrelation. Considering the time that an analyst must devote and while large training sizes may not be realistic for single-pixel training, three sample sizes-approximately 100,50, and 25 pixels for each class-were selected to evaluate the influence of training size. These single training pixels were distributed throughout the whole subset and selected to be as evenly distributed spatially as possible. The second strategy involved the selection of contiguous pixels or blocks with similar spectral values kom representative locations across each subset. This was generated by the region growing tool in IMAGINE by locating seed pixels across the image. The region growing tool evaluates neighboring pixel values using spatial andlor spectral criteria and finds pixels with characteristics similar to the original seed pixel (ERDAS, 1997). This is a very effective way of selecting homogeneous training data and is referred to as seeding block training (ST). Two numbers of evenly distributed seeds (15 and 25 seeds) for each subset were applied. The third set of training data was selected by visually identifying and digitizing polygons or blocks of pixels. Because sizes of training blocks are important (Campbell, 1996), two sets of training data with different sizes were used. The first one is referred to as big polygon or block training (PT), in which a single large polygon or block was selected to represent each class. The second training data set for this approach was collected by selecting several small polygons or blocks for each class (BT). As a general rule, the length and width of small blocks for each class were close to the range obtained from the semi-variogram, so that each block was sufficiently big to represent spectral and spatial properties of each class. Thus, the heterogeneity or autocorrelation within each class was included in training data. The distance separating any two polygons was at least that of the range, so the pixels in one block were likely to be autocorrelated, but may not be correlated with those in another block. For this strategy, two training sizes with 15 and 25 small blocks each were used in order to compare with the first and second strategies under the same number of training units. The number of training pixels at the 2-m spatial resolution is shown in Table 1. For each strategy, the same training areas were used at the five different spatial resolutions so that the change of classification accuracy can be examined at varying spatial resolutions with the same training locations. TABLE 1. THE NUMBER OF TRAINING PIXELS USED FOR EACH CLASS AT A 2-M RESOLUTION Single-Pixel Training (SP) Seeding Training (ST) Block Training [BT) Polvgon - - Training - Class SP1 SP2 SP3 ST1 (15) ST2 (25) (PT) BT1 (15) BT2 (25) SF MF IN GL UL CL (SF: Single-family, MF: Multi-family, IN: Industry, GL: Irrigated grassland, CL: Cleared land, UL: Undeveloped land) PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING November

4 Parametric statistics for the eight training sets were generated for two feature combinations at five different spatial resolutions, resulting in 40 sets of training statistics. Transformed divergence (TD) values were calculated to indicate the separability between two training class signatures Uensen, 1996). For comparison of sets of training statistics, average TD values were calculated for each set. Classlflcatlon Method The Gaussian maximum-likelihood (GML) classifier was used as the classification rule. The GML classifier requires training data to be normally distributed, and such a distribution is not guaranteed for both the spectral and spatial features used in this study. The maximum-likelihood decision rule was used because it is by far the most common classification rule used for supervised classification of multispectral image data (Richards, 1986). In order to determine the accuracy of each classification, the classified images were compared with the reference data at each spatial resolution selected from the same six image subsets. The pixels in six subsets except those used for training data were used as the reference data in accuracy assessment. For this study, the overall and individual Kappa coefficients (Jensen, 1996) were calculated and used in the comparison. Results and Analysis SemCVarlagram Semi-variograms of six subsets were derived for each spectral band image at a 2-m spatial resolution. The range is assumed to be the same at all five resolutions for each subset. Because the semi-variances of the three spectral bands are highly correlated (the correlation coefficients are greater than 0.99 for all subsets), only the standardized semi-variance calculated from the NIR band is plotted in Figure 2 for each class. The spherical, exponential, and Gaussian models were fitted to the semi-variance for each class. The range obtained from the model with the best fit was selected. From Figure 2 it can be seen that semi-variance values increase as the spatial lag becomes larger. The rate of increase of semi-variance prior to reaching the sill is influenced by the spatial structure of material components associated with each class. The more heterogeneous the landscape, the more rapidly the semi-variance reaches the sill and, thus, the smaller the range. Comparing the slopes of semi-variance curves of different classes at different lags shows the relative scales over which pixels are autocorrelated. At small lags (less than 4 pixels) semi-variances of all classes increase rapidly, but the curves of single family and multi family have the steepest slopes, followed by those of undeveloped land and irrigated grassland. The relatively higher autocorrelation for undeveloped land and irrigated grassland is due to vegetation patches within these two classes. As the lag distance increases, the rate of semi-variance increase is reduced for the irrigated grassland and undeveloped land, corresponding to their more homoge- neous surfaces. The semi-variance of cleared land is the smallest, reflecting its relatively homogeneous characteristic. Containing relative large buildings and parking lots, the semivariance of the industry subset is lower than that of the undeveloped land and irrigated grassland at small lags, but gradually reaches and exceeds them at large lags. An examination of the curves of semi-variograms obtained from each class suggests that semi-variogram quantifies the degree of autocorrelation inherent in each land-use class at different lags. Transformed Divergence (TD) of Training Sets Table 2 shows the TD values obtained for different sets of training data at five spatial resolutions. Among the three strategies, the seed training produced the largest TD values while block training generated the lowest TD values. This is particularly the case at finer spatial resolutions. This result is not surprising because seed training with spectral criteria selects spectrally similar pixels and block training may include heterogeneous pixels with low spectral separability. When the same combination of features was compared, a greater number of training pixels yielded lower values than did fewer numbers. It is also apparent that inclusion of variance (texture) channels substantively increased TD values at all spatial resolutions. All TD values were greater than 1990 when variance image was added, except for the three training sets generated from block training at a 2-m resolution (the TD saturates at a value of 2000, meaning complete separability). This indicated that the inclusion of spatial information pertaining to the texture of an image increased the class separability. Overall Kappa Coefficients The overall Kappa coefficients of classification results are summarized in Table 3, for five spatial resolutions. From Table 3 it can be seen that, for all training data sets, overall classification accuracy increased for coarser image resolution, whether or not the variance images were combined with the spectral bands. It also shows increased accuracy when the variance image is included as one of the features in the classification except for the big polygon training set at a 16-m resolution. The results for the training sets obtained by the seed training approach show the poorest accuracy compared with those obtained by the single-pixel training and block training with few exceptions. Considering the highest TD values obtained from seed training, it appeared that the TD values were not a reliable predicator of classification accuracy. This may be caused by the non-normality in the data. The last row of Table 3 shows that single-pixel training with the largest training set resulted in the highest average Kappa coefficients among all the training sets, while the twoblock training sets show the second and third best performances. But when examined at each individual resolution level, the single-pixel training set with the largest training size achieved the highest overall Kappa coefficient only at 2 m and 12 m. However, the best performance at other resolutions was obtained from block training sets, when only the three spectral TABLE 2. AVERAGE TRANSFORMED DIVERGENCE (TD) VALUES FOR DIFFERENT TRAINING SETS AT FIVE RESOLUTIONS Three Spectral Bands Three Spectral Bands + Variance Band SP1 SP2 SP3 ST1 ST2 PT BT2 BT1 SP1 SP2 SP3 ST1 ST2 PT BT2 BT1 2m m m m m (SP: Single-pixel Training; ST: Seeding Training; BT: Block Training; PT: Polygon Training) 1158 November 2002 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

5 TABLE 3. OVERALL KAPPA COEFFICIENTS OF CLASS~RCAT~ON RESULTS USING DIFFERENT TRAJNING SETS AT FIVE RESOLUTIONS Three Bands Three Bands + Variance Band SPl SP2 SP3 ST1 ST2 PT BT2 BT1 SP1 SP2 SP3 ST1 ST2 PT BT2 BT1-2m m m m m Average (SP: Single-pixel Training; ST: Seeding Training; BT: Block Training; PT: Polygon Training) bands were used. When the variance image was added, the single-pixel training set with the largest training size yielded the best results with one exception at a 2-m resolution. Comparing accuracy results for the three training sets obtained by single-pixel training, the highest overall accuracy resulted from the largest training size at all resolutions except at 12 m, while the lowest accuracy occurred for the product derived from the smallest training size (25 pixels for each class). This suggests that the training size can have an important impact on the classification performance when the single-pixel training approach is used. Training sizes of 25 pixels for each class were apparently too small to extract the representative statistics, especially at finer resolutions. But differences between the overall Kappa coefficients were not so apparent among the training sets with the block and polygon training. The training set with 15 training blocks lead to an average Kappa coefficient very similar to that generated from 25 training blocks. Selecting training sets with different sizes can vary considerably in the amount of time required for analyst interaction with the image. The analyst spends similar amounts of time to locate 25 single pixels as to locate 25 seeds or blocks, although the latter involves parameters controlling the blocks and takes longer machine time. With a similar cost of analyst interaction time (in this case, 25 training units for each class), the block training always showed the best classification accuracy. Also, differences between single-pixel training and block training with the same training units were much smaller at coarser resolution levels (12 m and 16 m) than at finer resolution levels (2 m and 4 m). Conditional Kappa Coefficients Figures 3 and 4 graphically present the conditional Kappa coefficients calculated from classification results with and without the variance band, respectively. For each class, the Kappa values obtained from five resolution levels are plotted against Figure 3. Individual Kappa coefficients (K) obtained from different training sets for each class at five resolution levels when only three spectral bands were used. The definition of each training type is same as shown in Table 1.

6 5;;EE:iK"a (el (9 Figure 4. Individual Kappa coefficients (K) obtained from different training sets for each class at five resolution levels when the variance images were combined with three spectral bands. The definition of each training type is same as shown in Table 1. training sets. This enables examination of how the individual Kappa value changed with different training sets for each landuse class. An obvious trend that can be observed from Figures 3 and 4 is that, for each class, the average conditional Kappa value increases when the resolution becomes coarser. All classes reach their maximum Kappa values at the coarsest resolutions of 12 m or 16 m. The fine resolutions achieved lower classification accuracy results when the maximum-likelihood classifier was applied. However, it should also be noted that in this study only six single-class subsets were used and no boundary effects or mixed land-uselland-cover situations were considered. When a larger area with multiple classes is used, the greater likelihood of mixed pixels for coarse spatial resolution imagery may reduce the classification accuracy. The magnitude of conditional Kappa values for each class is different for different training sets and resolution levels. For highly heterogeneous land-use classes such as single-family, multi-family, and industry, the conditional Kappa values exhibit a relatively large range (see Figures 3a, 3c, and 3d). On the other hand, for spectrally homogeneous classes such as cleared land and grass land (Figures 3b and 3fl, the differences in Kappa values are relatively small among the five resolution levels. By comparing the change in magnitudes of Kappa values at each resolution, it is apparent that differences in Kappa values generated from different training sets are greater at fine resolutions of 2 m and 4 m and smaller at coarse resolutions for all classes except for multi-family. This shows that different training strategies had more influence on classification accuracy at fine resolutions than at coarse resolutions. Comparing individual Kappa values of products derived from the three training sets obtained by single-pixel training, the highest value did not always correspond to the largest training size at all resolutions, as was the case for the overall Kappa values. At coarse resolution levels of 12 m and 16 m, differences between Kappa values generated by the three single-pixel training sets are minimal except for highly heterogeneous classes with relatively larger building structures such as multifamily and industrial land. In fact, these differences were negligible when texture was incorporated. For single family, multiple family, and industry land-use types, the largest training size yielded the largest Kappa value. For undeveloped land, the highest classification accuracy was achieved with the intermediate size training set (50 pixels for each class), while the largest Kappa values for cleared land and grass land resulted from the smailest size single-pixel training Hets. This result suggests that the training " sam~le size is im~ortant in su~ervised classifi- L cation when a single-pixel training strategy is applied. The number of pixels needed to extract training statistics varied for different classes with different spatial structures. For spectrally homogenous classes, a small number of training pixels are sufficient for generating reliable training statistics for use in classification. But for spatially heterogeneous classes, a relatively large number of pixels was required in order to extract representative training statistics. The finer the spatial resolution, the more training pixels are required. Considering the large amount of analyst interaction time required locating a large number of pixels, a small-block training approach is recommended for fine resolution images with heterogeneous classes November 2002 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

7 Summary In this paper, we compared three different training strategies often used for supervised classification. Tests were run on multispectral images of five resolution levels, derived from six CIR DOQQ subsets of different urban land-uselland-cover types within an urban and rural fringe study area scene in the San Diego metropolitan area. Single-pixel training, seed training, and block or polygon training methods were tested. The ranges obtained from semi-variograms for each land type were used to minimize spatial autocorrelation and sampling effort when selecting training pixels. Eight training sets with different training sizes were generated and then applied to both three multispectral band images and variance images in the classification of six land-use classes. A maximum-likelihood classifier was used in the classification. The averaged transformed divergence (TD) was calculated for each training set. The classification results were evaluated using the overall and conditional Kappa values. Some of the major findings from this research are as follows: Different training strategies may produce different classification results. The training size, the image resolution, and the degree of autocorrelation inherited in each class influenced the performance of different training strategies. However, the differences in classification accuracy were greater between different spatial resolutions than between training strategies. The size of the training set was important in influencing supervised classification results when the single-pixel training strategy was applied. The number of pixels needed to extract training statistics varied for different classes with different spatial structures. For spectrally homogeneous classes, a small number of training pixels may be sufficient. But for spatially heterogeneous classes, a relatively large number of pixels are likely to be required in order to extract representative training statistics. Single-pixel training may be implemented to avoid spatial autocorrelation effects, but it did not always lead to more accurate classification results than other training approaches involving contiguous pixel selection. For spectrally homogeneous classes, the single-pixel training approach may be preferred. But for spatially heterogeneous classes, small-block training has the advantage of easily capturing spectral and spatial information and saves the analyst interaction time. Different training approaches had more impact on classification results at fine resolution levels than at coarse resolutions. The differences among overall classification accuracies for different spatial resolutions were smaller than those among individual classification accuracies. The finer the spatial resolution of an image, the more training pixels were required. Using a variance texture image as an additional band increased the classification accuracy for all classes and tended to reduce the differences of classification results caused by training strategies at all resolution levels when the maximum-likelihood classifier was used. Acknowledgments The authors would like to thank the three anonymous reviewers for their insightful comments and suggestions. References Atkinson, P.M., Selecting the spatial resolution of airborne MSS imagery for small-scale agricultural mapping, International Journal of Remote Sensing, 18(9): Barnsley, M.J., and S.L. 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Smith, On the nature of models in remote sensing, Remote Sensing of Environment, 20: Wharton, S.W., A context-based land-use classification algorithm for high-resolution remotely sensed data, Journal of Applied Photographic Engineering, 8(1): Woodcock, C., and V.J. Harward, Nested-hierarchical scene models and image segmentation, International Journal of Remote Sensing, 13(16): (Received 21 August 2001; revised and accepted 28 March 2002) 1 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING November ZOO2 1161