Delineation of forest/nonforest land use classes using nearest neighbor methods

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1 Remote Sensing of Environment 89 (2004) Delineation of forest/nonforest land use classes using nearest neighbor methods Reija Haapanen, Alan R. Ek*, Marvin E. Bauer, Andrew O. Finley Department of Forest Resources, University of Minnesota, 115 Green Hall, 1530 Cleveland Avenue N., St. Paul, MN 55108, USA Received 6 May 2003; received in revised form 24 September 2003; accepted 9 October 2003 Abstract The k-nearest Neighbor (knn) method of forest attribute estimation and mapping has become an integral part of national forest inventory methods in Finland in the last decade. This success of knn method in facilitating multi-source inventory has encouraged trials of the method in the Great Lakes Region of the United States. Here we present results from applying the method to Landsat TM and ETM+ data and land cover data collected by the USDA Forest Service s Forest Inventory and Analysis (FIA) program. In 1999, the FIA program in the state of Minnesota moved to a new annual inventory design to reach its targeted full sampling intensity over a 5-year period. This inventory design also utilizes a new 4-subplot cluster plot configuration. Using this new plot design together with 1 year of field plot observations, the knn classification of forest/nonforest/water achieved overall accuracies ranging from 87% to 91%. Our analysis revealed several important behavioral features associated with knn classification using the new FIA sample plot design. Results demonstrate the simplicity and utility of using knn to produce FIA defined forest/nonforest/water classifications. D 2003 Elsevier Inc. All rights reserved. Keywords: Forest/nonforest; FIA; knn 1. Introduction The k-nearest Neighbor (knn) method is a nonparametric estimation approach that can be used in a wide range of estimation and classification applications. In the past decade, the knn method has been advanced for estimation of forest variables and is now operational in Finland s national forest inventory (Muinonen & Tokola, 1990; Tokola, Pitkanen, Partinen, & Muinonen, 1996; Tomppo, 1996, 1997). The method couples field-based inventory and satellite imagery data to produce continuous digital layers of measured forest or land use attributes. The knn algorithm assigns each unknown (target) pixel the field attributes of the most similar reference pixel(s) for which field data exists. The similarity is defined in terms of the feature space (e.g., Euclidean distance in spectral space). Attributes of interest are imputed to target pixels by calculating a weighted average of measurements of each of the (k) reference pixels. Class variables such as cover type or land use are * Corresponding author. Tel.: ; fax: address: aek@umn.edu (A.R. Ek). estimated as a weighted mode. These weights can be applied as some function of spectral distance between each target and reference pixel. Because forest attributes are imputed based solely on spectral similarity, the method can be used to simultaneously impute all field-measured attributes to target pixels. Holmgren and Thuresson (1998) reviewed 35 studies focusing on land classification from North America, Scandinavia, and some other temperate and boreal regions. For a dozen or more forest classes ranging from regeneration areas to mature stands, classification accuracy was consistently in the range of 65 85%, regardless of the sensor used or local climatic conditions. If water bodies and land uses other than forestry were included, the accuracy increased to above 90%. These studies also indicated that such classification could possibly be used for stratification purposes in large-scale forest inventories. The objective of this study was to evaluate the utility of the knn method for forest/nonforest/water stratification and ultimate application in developing forest area estimates for the USDA Forest Service s Forest Inventory and Analysis (FIA) program (McRoberts, Nelson, & Wendt, 2002) /$ - see front matter D 2003 Elsevier Inc. All rights reserved. doi: /j.rse

2 266 R. Haapanen et al. / Remote Sensing of Environment 89 (2004) Methods 2.1. Study area The study area covers a portion of a six-county area in Northeastern Minnesota. Most of the area is in the FIA Aspen-Birch Unit (Lake, Carlton, Cook, Koochiching, Lake, and St. Louis counties). The southwestern portion of the study area lies in the FIA Northern Pine Unit, specifically Itasca County. The study area is the most heavily forested region in the state. Lake and Cook Counties are more than 90% forested and the other counties in the area are at least 60% forested (Leatherberry, Spencer, Schmidt, & Carroll, 1990). The study area encompasses approximately 29,748 km 2 and is shown Fig. 1. For a detailed description of the study area, see Bauer et al. (1994) Field data The FIA program began fieldwork for the sixth forest inventory of Minnesota in This effort also initiated a new annual inventory or monitoring system. Under this new system, approximately one-fifth of the field plots in the State are measured each year. The new inventory protocol collected field data on the new 4-subplot cluster plot configuration (USDA Forest Service, 2000). This plot design consists of four 1/60 ha fixed-radius circular subplots linked as a cluster, with each of the three outer subplots located 36.6 m from the center subplot (Fig. 2). FIA assigns each subplot to the land use class recorded at the subplot center. The 1999 inventory sampled 1001 subplots within our study area. Four subplots were omitted from the analysis because their land use class was undetermined, thus resulting in 997 subplots and 250 cluster plots (Table 1). The resulting sampling intensity in the study area was approximately one subplot per 3000 ha. This field data was then used in subsequent knn classification Image data Fig. 2. New FIA 4-subplot cluster plot layout. Landsat 7 ETM+ satellite images were used for this analysis. The study area fell within two Landsat images in path 27, rows 26 and 27 (Fig. 1). Three dates were included in the study: a late winter image acquired on March 12, 2000; a spring image acquired on April 29, 2000; and a late spring image acquired on May 31, Fig. 1. Study area and location of FIA field plot clusters, FIA Aspen-Birch Unit and vicinity in Northeastern Minnesota.

3 R. Haapanen et al. / Remote Sensing of Environment 89 (2004) Table 1 Number of forest, nonforest, and water subplots by actual FIA land use classes, 997 subplots in total Forest Number of subplots Nonforest Number of subplots Timberland 628 Cropland without trees Pastured timberland 4 Pasture etc., without trees 8 Plantations 20 Idle farmland without trees 4 Unproductive forest land 12 Marsh without trees 55 Reserved forest land 54 Urban etc., without trees 18 Marsh with trees 12 Right of ways 17 Urban forest land 1 Urban and other with trees 6 Total Water, number of subplots The images were geo-referenced to the UTM coordinate system using the following parameters: spheroid GRS80, datum NAD83, and zone 15. The resampling method was nearest neighbor using a 30-by-30 m pixel size. The reference material for geo-referencing was road vectors from the Minnesota Department of Transportation. For parts of the image where roads were very sparse, the USGS Digital Orthophoto Quads from years 1991 to 1992 with 3-m resolution were used. The number of control points used in geo-referencing was per date in path 27, row 27 images and in the 27/26 images. The regression model used was a second-order polynomial. Table 2 displays the RMSE of the six images. The same-date images were mosaiced together. Clouds were hand digitized and a cloud mask was created. For each date, bands (1 to 5, and 7) and the high and low gain thermal bands were used in the analysis. Because panchromatic band data was not available for some of our selected dates and corresponding images, we did not explore its utility in these trials Estimation knn estimation methodology For estimation with Euclidean distances, consider the spectral distance d pi,p, which is computed in the feature space from the target pixel p to each reference pixel p i for which the ground measurement or class is known. For each pixel p, take the k-nearest field plot pixels (in the feature space) and denote the distances from the pixel p to the nearest field plot pixels by d pi,p,,...,d pk,p (d pi,p V...V d pk,p ) The estimate of the variable value for the pixel p is then Table 2 Root mean square errors (RMSE) for rectification of Landsat 7 images Path/row Date RMSE (m) 27/27 12 Mar /27 29 Apr /27 31 May /26 12 Mar /26 29 Apr /26 31 May expressed as a function of the closest units, each such unit weighted according to a distance function in a particular feature space. A commonly used function for weighting distances is:, w ðpi Þp ¼ 1 X k 1 dðp t i Þp dðp t ð1þ j Þp j¼1 where t is a distance decomposition factor, typically set to 0, 1, or 2. For estimation of class variables, such as land use, the modal land use class of the weighted k nearest neighbors serves as the estimator. For a class variable, the error rate (Err) indicates the disagreement between a predicted value ŷ and the actual response y in a dichotomous situation such as, y does or does not belong to class i, with values 0 or 1 (Efron & Tibshirani, 1993). Thus we used the overall accuracy (OA) (Congalton, 1991; Stehman, 1997) defined as: OA ¼ 1 Err ð2þ where Err ¼ Xn i¼1 ðy i ŷþ=n: ð3þ This is a special case of the mean square error for an indicator variable. These estimators were preferred over the usual Kappa estimator for reasons given by Franco-Lopez, Ek, and Bauer, (2001). Errors were estimated by leave-one-out cross-validation. This technique omits training sample units one by one and mimics the use of independent data (Gong, 1986). For each omission, we applied the knn prediction rule to the remaining sample. Subsequently, the errors from these predictions were summarized. In total, we applied the prediction rule n times and predicted the outcome for n units. Such estimates of prediction error are nearly unbiased (Efron & Tibshirani, 1993) Selection of parameters In order to obtain good class estimates with the knn method, it is important for the reference data to capture the

4 268 R. Haapanen et al. / Remote Sensing of Environment 89 (2004) range of spectral variability within a class. For continuous variable estimates, the reference data must cover the range of spectral variability across each variable of interest. Nilsson (1997) suggested that at least 500 forested field sample plots should be used for estimating volume of growing stock. However, this sample recommendation was derived for boreal forests which are relatively homogeneous in species composition in comparison to the highly mixed conifer/deciduous forest landscape of northeastern Minnesota. Given a sufficient sample size, Katila and Tomppo (2001) noted that the most important algorithm parameters are the distance metric, number of nearest neighbors, and the extent of geographic search radius. In addition, Franco- Lopez et al. (2001) recognized that varying the distance decay coefficient in the distance weighting function and optimal selection of bands can contribute to classification accuracy. Several studies have found that stratification by elevation or other factors that drive vegetative gradients can also improve classification, see Tokola and Heikkilä (1997) and Katila and Tomppo (2002). These parameters are treated below with the exception of the elevation, which tended to be of little importance in the preliminary trials, likely because the study area has little topographic variation Evaluation Behavior of the FIA 4-subplot cluster plot The close geographic relationship of subplots within each FIA cluster plot suggests that the subplot observations are not independent. Preliminary trials indicated a tendency for reference pixels to be chosen from the same plot as the target pixel. Thus, by varying maximum geographic distance constraints, we examined the likelihood and implications of a target pixel selecting nearest neighbors from its own subplot cluster Image dates and the use of thermal bands Under the constraint that a target pixel cannot select nearest neighbors from within its own subplot cluster, image dates were used independently and in combinations of March/April, April/May, and March/April/May for forest, nonforest, and water classification. To gauge the utility of the thermal bands for class discrimination, the trial was run with and without the thermal bands associated with each date. Further, we tested the effect that thermal bands have on selecting neighbors spatially adjacent to target pixels Neighbor s weighting function and number of neighbors As noted in the description of the neighbor weighting function (Eq. (1)), the distance decay parameter t, has typically been set to 0, 1 or 2. Franco-Lopez et al. (2001) noted equal weights (t=0) resulted in higher classification accuracy in some instances, notably when three or fewer neighbors were selected. Consequently, we tested both t = 0 and 2. The number of neighbors has a direct influence on root mean square error (RMSE), confusion matrices, and ultimately maps based on such predictions. Typically, the value of k employed in forest inventory studies has ranged from 1 to 15. Franco-Lopez et al. (2001) focused on k = 1 to emphasize retention of the original reference data variability. Tomppo (1996, 1997) and others have typically used k =5. Nilsson (1997) and Tokola et al. (1996) examined a range of k from 10 to 15. In this study, we examined a range of k values between 1 and 10, with the omission of k = 2. Note that when k = 2 the mode estimate is identical to that for k = Weighting of spectral bands Following Franco-Lopez et al. (2001), spectral bands which contributed the greatest to discrimination among classes were preferentially weighted through a downhill simplex optimization (Nelder & Mead, 1965). These weights were then incorporated into the classification algorithm; see Franco-Lopez et al. (2001) Limiting of maximum horizontal search radius Some limitations of the maximum search distance in geographical space for nearest neighbors seemed appropriate, if only on a phenological basis. In Finland, with the current sampling intensity of the Finnish national forest inventory, Katila and Tomppo (2001) found that a geographic search area with a radius of km was optimal for volume estimates in the mineral land map stratum. In our study, four search radii conditions were tested: 70, 90, 120 km, and no restriction. Because of the paucity of FIA field plots, a starting search radius of 70 km was chosen to ensure that sufficient reference observations were included in each nearest neighbor search. 3. Results and discussion 3.1. Behavior of the 4-subplot cluster plot Fig. 3 summarizes the behavior of the new FIA 4-subplot cluster plot for knn classification, with and without band optimization, and varying geographic search radii. This figure shows that by limiting the search radius, the probability of choosing the reference nearest neighbor from within the target s subplot cluster increases significantly. By increasing the search radius, we increase the number of reference observation considered in the search and therefore the likelihood that a target will select a reference observation outside its own subplot cluster. Band optimization, with no maximum constraints on search radius, marginally increases the preferential selection of the reference observation within each subplot cluster over that of the nonoptimized and unconstrained search (i.e., described as basic search in Fig. 3).

5 R. Haapanen et al. / Remote Sensing of Environment 89 (2004) Fig. 3. The number of subplots selecting neighbors from within their own subplot cluster versus outside this cluster for k = 1. Results for 18 bands with March/April/May image dates. Basic trial has no search radius restriction. Fig. 5. Tendency of thermal bands to guide the selection of nearest neighbor to the same subplot cluster. Basic trial using k = 1 and 18 bands (March, April, May) Image dates and the use of thermal bands Results depicted in Fig. 4 show that the selection of image dates contributes to overall classification accuracy. At k = 1, the April/May and the March/April/May band combinations produced the highest accuracies. As k increased the single 6- band April date matched or slightly surpassed the multi-date combinations ability to discriminate among forest, nonforest, and water classes. However, the differences are too small to suggest any real superiority of any particular date or combination. Although not shown in Fig. 4, the addition of the two thermal bands marginally decreased classification accuracy for single dates and combinations. Further analysis showed that the addition of the thermal bands would, if permitted, increase the tendency of the targets to select reference subplots from within its own subplot cluster (Fig. 5). We note that given the original m pixel size of thermal bands, it is possible for several subplots of the same cluster to fall in the same thermal pixel. Because of the slightly higher classification accuracy achieved through band combinations, the remainder of this analysis contrasts conditions placed on the 12-band April/ May and 18-band March/April/May band combinations Neighbor s weighting function and number of neighbors The effect of weighting the Euclidian feature space distance of neighbors is shown in Fig. 6. Varying the distance decay parameter had little influence on overall Fig. 4. Overall accuracy of forest/nonforest/water classification for single date images compared with various combinations of dates and for different numbers of neighbors. Selection of nearest neighbors prohibited within the same 4-subplot cluster plot. Fig. 6. Overall accuracies of land use classification with different weighting functions and k values. Note that 12 bands refer to the combination of April and May images, while 18 bands refer to the March, April and May images. Selection of nearest neighbors prohibited within the same 4-subplot cluster plot.

6 270 R. Haapanen et al. / Remote Sensing of Environment 89 (2004) Table 3 Error matrix for 18-band data set, with inverse squared weighting, k = 1, and no distance search constraints Class Nonforest Forest Water User s accuracy Nonforest Forest Water Producer s accuracy Overall Accuracy = 0.88 accuracy. Due to the cluster plot design, the overall accuracy typically improved from k=1 to k=4 and then dropped slightly and then improved again to k=8. Table 3 shows the error matrix and the user s and producer s accuracy for the 18-band data set, using inverse squared weighting, and k = 1. As seen throughout the trials, the major source of classification error is confusion between the forest and nonforest classes. However, we also note that overall accuracy is a measure of classification performance and might not produce the optimal map or classification of forest area or nonforest area. Although the use of subplot references within the same cluster as the target was prohibited, it was possible for one entire subplot cluster of four subplots (i.e., available neighbors) to be spectrally close to the subplot being processed. Conversely, if reference selection within the same subplot cluster was allowed, a squared distance decomposition parameter produced higher classification accuracy when k was set larger than Weighting of spectral bands When the use of subplots from the same cluster was prohibited and the maximum horizontal search radius was set at 120 km, the classification accuracies for both date sets increased by only 2% through band weight optimization (Fig. 7). Because the calculation of weights through the simplex algorithm is a computationally time consuming process, the marginal gain in accuracy might not be worth the effort. Fig. 8. The effect of different limiting horizontal search radii to overall accuracy for k = 1, 3, Note the weights are inversely proportional to the squared distance. Selection of nearest neighbors prohibited within the same 4-subplot cluster plot Limiting of maximum horizontal search radius The effect of limiting the maximum horizontal search radius was tested with search distances of 70, 90, and 120 km. The results for the 12-band data set of April/May dates are presented in Fig. 8. A 120-km radius produced the highest overall classification accuracy. The same was true for the March/April/May date combination. For the 12-band data set, the 70 and 90 km radii performed slightly worse than no search restrictions. For the 18-band data set, only the 90-km radius performed worse than no radius, but differences were small. Limiting the maximum search radius might become effective as more dates are included. Clearly more dates would allow more phenological differences to emerge. Although limiting search radius showed only marginal influence on our ability to discriminate between forest and nonforest classes, we believe that distance constraints can prove to be more effective when estimating multiple forest type classes or continuous measures such as growing stock volume or basal area. 4. Conclusions Fig. 7. The effect of weighting of spectral bands (optimization) on overall accuracy for k = 1, 3, 4, 5, and 10. Selection of nearest neighbors prohibited within the same 4-subplot cluster plot. Within the trials, overall accuracy was only marginally influenced by number of neighbors considered (k), the distance decay parameter (t), preferential weighting of bands, and band combinations. We suggest the influence of these parameters greatly depends on the choice of image dates and associated data. If this analysis was repeated with image dates that span the full seasonal variation in vegetation, these parameters could exhibit greater influence on classification accuracy. From an inventory operations standpoint, we were pleased to see high classification accuracy for several individual image dates, i.e., there appears to be flexibility in the choice of dates. Additional

7 R. Haapanen et al. / Remote Sensing of Environment 89 (2004) trials with a wider range of dates may capture more temporal and spatial variation in vegetation and improve accuracy further. Finally, trials showed that specific nearest neighbor search constraints should be used when FIA 4-subplot cluster plots serve as reference observations in knn classification. Specifically, high correlation among subplots in a cluster will cause preferential selection and hence artificially inflate classification accuracy in the validation stage. This can, and should, be avoided by constraining the nearest neighbor search to the region outside of the target subplot s cluster plot. The results presented in this paper suggests the knn method offers a very feasible approach for forest/nonforest mapping. Acknowledgements This research was supported by the College of Natural Resources and the Minnesota Agricultural Experiment Station, University of Minnesota, St. Paul, the McIntire- Stennis Cooperative Forest Research Program, the USDA Forest Service, NCASI, and NASA. The authors gratefully acknowledge the assistance of the staff of the USDA North Central Research Station FIA unit, especially Dr. Mark H. Hansen and Dr. Ronald E. McRoberts. Additionally, we thank Dr. Erkki Tomppo of the Finnish Forest Research Institute, Helsinki, Finland for several helpful suggestions in support of this work. References Bauer, M. E., Burk, T. E., Ek, A. R., Coppin, P. R., Lime, S. D., Walsh, T. A., Walters, D. K., Befort, W., & Heinzen, D. F. (1994). Satellite inventory of Minnesota s forest resources. Photogrammetric Engineering and Remote Sensing, 60 (3), Congalton, R. G. (1991). A review of assessing the accuracy of classifications of remotely sensed data. 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