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The impact of relative radiometric calibration on the accuracy of kNN-predictions of forest attributes
Remote Sensing of Environment 110 (2007) 431 – 437 www.elsevier.com/locate/rse
The impact of relative radiometric calibration on the accuracy of kNN-predictions of forest attributes Tatjana Koukal ⁎, Franz Suppan, Werner Schneider Institute of Surveying, Remote Sensing and Land Information, Department of Landscape, Spatial and Infrastructure Sciences, University of Natural Resources and Applied Life Sciences, Vienna, Austria Received 12 August 2005; received in revised form 18 August 2006; accepted 27 August 2006
Abstract The k-nearest-neighbour (kNN) algorithm is widely applied for the estimation of forest attributes using remote sensing data. It requires a large amount of reference data to achieve satisfactory results. Usually, the number of available reference plots for the kNN-prediction is limited by the size of the area covered by a terrestrial reference inventory and remotely sensed imagery collected from one overflight. The applicability of kNN could be enhanced if adjacent images of different acquisition dates could be used in the same estimation procedure. Relative radiometric calibration is a prerequisite for this. This study focuses on two empirical calibration methods. They are tested on adjacent LANDSAT TM scenes in Austria. The first, quite conventional one is based on radiometric control points in the overlap area of two images and on the determination of transformation parameters by linear regression. The other, recently developed method exploits the kNN-cross-validation procedure. Performance and applicability of both methods as well as the impact of phenology are discussed. © 2007 Elsevier Inc. All rights reserved. Keywords: Scene-to-scene radiometric normalisation; k-nearest-neighbour method; Cross-validation; Forest inventory; Phenology
1. Introduction In forestry, the k-nearest-neighbour (kNN) algorithm is often used to combine two data sources: field data obtained at sample plots and remote sensing data. Forest variables are estimated from the remotely sensed spectral information using the terrestrial sample plots as a reference, e.g. for the purpose of national forest inventories (Koukal, 2004; Tomppo, 1991). The typical problem setting is as follows: Detailed forest variables are collected on the ground at sample plots. For reasons of economic efficiency, the density of the sample points has to be rather low. Therefore the production of large-scale maps from the terrestrial inventory results is not feasible, and the estimates of forest variables for small areas are imprecise. The result can be improved by augmenting the terrestrial inventory data with remotely sensed image data. With the kNNmethod, forest variables can be estimated for every location (for every pixel of the remotely sensed images) between the ⁎ Corresponding author. E-mail address: [email protected] (T. Koukal). 0034-4257/$ - see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2006.08.016
terrestrial sample plots, resulting in forest maps and smaller error margins in the forest variable estimation in small areas (Franco-Lopez et al., 2001; Katila & Tomppo, 2001). The basic idea of the kNN-method (Cover & Hart, 1967; Dasarathy, 1991) is to compare every pixel, for which the forest variables have to be estimated (“unknown pixel”), with pixels of known forest variables (pixels coinciding with terrestrial plots, called “plot pixels”). The k plot pixels that are most similar in their spectral characteristics to the unknown pixel are selected, and the mean value of the forest variables of these k selected plot pixels is taken as the estimate for the unknown pixel. In the case of a categorical forest variable, the most frequent class among the k selected plot pixels is assigned to the unknown pixel (Fazakas et al., 1999; Kilkki & Päivinen, 1987; McRoberts et al., 2002). The kNN-method is a non-parametric approach making no assumptions on the distribution of pixels in feature space as a function of forest variables. For every forest variable value (e.g. for every forest cover type), an adequate number of plot pixels must be available in order to find similar ones. These plot pixels must lie on the same image as the unknown pixel, otherwise the
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spectral similarity is disturbed by external factors such as sun elevation and atmospheric conditions. This is one of the severest drawbacks in practical applications. This problem particularly occurs in countries that are elongated in east–west direction as scenes from neighbouring image acquisition paths are usually acquired on different dates. As a consequence, the individual images should have an extent as large as possible (e.g. LANDSAT with 185 km by 170 km is more favourable than SPOT or ASTER with 60 km by 60 km), and every image to be used in the kNN-method should be covered by the terrestrial inventory area to an extent as large as possible (Fig. 1). To improve the success of forest inventories using the kNNmethod, adjacent scenes of different acquisition dates could be used in the same estimation procedure assuming relative radiometric calibration was carried out previously (Elvidge et al., 1995; Hall et al., 1991; Over et al., 2003; Schott et al., 1988). Radiometric differences of test areas with identical forest attributes but sampled at different locations and at different times originate mainly from atmospheric effects (absorption, scattering), varying sun-target-satellite geometry (bi-directional reflectance effects), and phenology. Radiometric calibration aims at minimising all these effects except phenology. It is an important technique in applications that are based on multi-date satellite imagery, e.g. change detection (e.g. Du et al., 2002). In relative radiometric calibration of images, one of the images has to be declared as the “reference image”, and the other images are called “subject images”. The aim of calibration is to transform the subject images in such a way that they have pixel digital number (DN) values as if they were acquired on the same date as the reference image. This study focuses on two empirical methods of relative radiometric calibration. They are tested on adjacent LANDSAT
TM scenes in the eastern, flat regions of Austria. One aim of this study was to investigate the extent to which phenology (i.e. the development of vegetation during a year mainly driven by the climate) limits the application of relative calibration methods. Therefore, subject images from different phenological stages were chosen (spring, mid-summer and late-summer), whereas the reference image was taken in mid-summer. 2. Data Four LANDSAT TM images of three adjacent scenes (path/ row) were used in the study. One of them served as reference image (190/26–27, Aug. 1994) and the others as subject images (190/27, Sept. 1991; 189/27, Aug. 1992; 189/27, June 1996). Overlapping occurred between the subject and reference images. All images were acquired within or close to the field inventory period from 1992 to 1996 of the Austrian forest inventory (AFI). The AFI is based on a systematic sampling grid of width 3.89 km. At each grid point that lies within forest, a cluster of four permanent sample plots is established (cluster sampling design). The plots are located in the corners of a square with a side length of 200 m. The plots are either relascope (i.e. Bitterlich) plots or fixed area plots depending on the forest attribute to be measured. The fixed area plots are circular with a radius of 9.77 m (i.e. an area of 300 m2). Inventory data have been collected since the early 1960s. The spectral information for a sample plot was taken from the pixel with centre closest to the sample plot centre. Altogether, 1629 sample plots were covered by the images employed in this study. 3. Methodology 3.1. Model of relative radiometric calibration
Fig. 1. Scene coverage (LANDSAT TM) and distribution of the Austrian forest inventory (AFI) field plots in the eastern part of Austria. The scene 189/27 is required to obtain a full coverage of the territory. However, this scene is covered by the terrestrial inventory only to a small extent leading to a shortage of reference data in the kNN-process.
Relative radiometric calibration investigates the relationship between the pixel DN values of the same area remotely sensed on two images at different dates. It is based on the assumption that the reflectance values at any location on the ground remain unchanged between the two acquisition dates. The relationship between the pixel DN value at any acquisition date and the surface reflectance is a non-linear one, due to backscattering in the atmosphere of radiation reflected by the surface (see e.g. Sandmeier, 1995; Steinwendner et al., 2001). Therefore, the relationship between corresponding pixel values from two images can also be non-linear. An analysis was performed using the computer simulation code 6S (Vermote et al., 1997). Image acquisition with LANDSAT TM at a geographical latitude of 48° (corresponding to the test images in Austria) with mid-latitude summer atmospheric conditions and a continental aerosol model with a horizontal visibility between 8 km and 23 km at acquisition dates between June 1 and August 30 was assumed. The simulations revealed that the maximum deviation (which occurred in TM band 4) from a linear relationship of the pixel values of vegetation between any two simulated acquisition cases is less
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than half a pixel DN and therefore well below the noise level. Therefore, the effects of non-linearity are ignored. The pixel values of the corresponding areas remotely sensed at different times are assumed to be linearly dependent (Schott et al., 1988). There are two transformation parameters for each band that have to be estimated: slope and intercept. Two methods for the determination of optimal transformation parameters were tested. The conventional method is based on a number of radiometric tie points in the overlap area of the adjacent scenes (Section 3.2). The transformation equations are set up for every spectral band by linear regression. This was compared to a new empirical method for the determination of optimal transformation parameters (Section 3.3). The proposed method exploits the cross-validation procedure that is often used in combination with the kNN-algorithm. Finally, the calibration methods were evaluated by conducting a kNNclassification (Section 3.4). 3.2. Estimating radiometric calibration parameters by regression of pixel values in the overlap area The traditional approach uses a set of target objects in the overlap area of the adjacent scenes from different dates. Objects have to be selected that can be assumed to have the same reflectance on both dates (Schott et al., 1988). They are used as radiometric control points. The mean pixel values of these objects are extracted from both images band-by-band, and the transformation equations are set up for each band by linear regression. 3.3. Estimating radiometric calibration parameters within the kNN-calibration process The kNN-method for estimating forest variables from satellite imagery requires a certain set of parameters, such as the value of k (number of nearest-neighbours), the similarity measure, and the weights for each spectral band. Optimal values for these kNN-parameters are determined in the kNNcalibration process. In this process, the kNN-parameters are chosen in such a way that the subsequent kNN-classification (kNN-estimation) yields optimal results as measured by some loss function, e.g. a minimum prediction error (Franco-Lopez et al., 2001; Katila & Tomppo, 2001). The prediction error for a given set of kNN-parameters is estimated by cross-validation. Cross-validation is a common method for estimating the expected prediction error of a model or of a classifier such as kNN. It uses part of the available reference data to train the classifier and a different part to test it (Efron & Tibshirani, 1993). The reference data is partitioned into M sub-samples. There are M runs. In each run, one sub-sample serves as the testing set and all other sub-samples are used for training. In the case of kNN, this principle is implemented in the following way: In order to classify a pixel belonging to the testing set, its k most similar plot pixels (neighbours) are selected from the training set. The pixel to be classified is assigned to the class that is most frequent among the k neighbours. Then the correctness of the classification is checked. This procedure is
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repeated for each pixel within the testing sets resulting in a mean prediction error estimated for the whole data set. Special forms of the cross-validation procedure are the twogroups-method and the leave-one-out cross-validation. In the two-groups-method, the reference data are split into a group of training data and a group of testing data, which then remain unchanged for the whole validation process. In the leave-oneout-method, the testing set consists of the one single pixel classified at the moment, and the training set consists of all other reference data. The leave-one-out method is especially suited for rather small reference data sets, because the maximum amount of training data is available for the classification (estimation) of every pixel. Cross-validation was investigated to determine not only the optimal values for the kNN-parameters, but also the optimal values for the radiometric calibration parameters at the same time. A linear transformation equation was set up for each band. Arbitrary initial values were assigned to the transformation parameters. The pixel values of the testing plots were transformed according to the resulting transformation equations. Different combinations of slope and intercept were tested to determine the combination that minimises the prediction error. It was estimated by the two-groups cross-validation method with one group represented by the sample plots on the reference image (training set), and the second group represented by the sample plots on the subject image (testing set). This forced the algorithm to “compare” plots from the two different images and avoided the situation that the kNN-classification (kNN-estimation) is only based on nearest-neighbours found on the same image as the pixel to be classified. The determination of optimal transformation parameters is a rather complex optimisation problem, because there may be interactions between the parameters of different bands. In principle, the parameters of all bands have to be optimised simultaneously. In the study, the transformation parameters were optimised band-by-band, starting with the band that is expected to show the biggest difference between the reference image and the subject image. 3.4. Comparison of four approaches In order to demonstrate and to analyse the effect of enlarging the set of training data for a kNN-classification by adding radiometrically calibrated adjacent images, a kNN-classification into forest cover types (1… deciduous forest, 2… mixed forest dominated by deciduous trees, 3… mixed forest dominated by coniferous trees, 4… coniferous forest) and a kNN-classification into classes of total volume per hectare (1…b = 140 m3/ha, 2… 141 to 280 m3/ha, 3… 281 to 430 m3/ha, 4…N430 m3/ha) were performed. The similarities between training plots and testing plots were measured by the Euclidean distance measure using all LANDSAT TM bands (except the thermal band) equally weighted. The number of nearest-neighbours (k), was set to 3 as identified as optimal in preceding investigations. The prediction accuracy was estimated by cross-validation. An error matrix (Congalton & Green, 1999) was compiled for
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each run, where for each class the number of correctly classified sample plots as well as the number and the kind of misclassifications were summarised. Accuracy measures such as overall accuracy, Kappa, and producer's accuracies were computed. The testing plots were classified following four approaches: A Only sample plots from the subject image are used. This approach represents the case in which the image covers only a small number of sample plots. It can be assumed that the sample size is critically low, i.e. below the minimum number required for a satisfactory classification result. The prediction accuracy is estimated by leave-one-out cross-validation as the sample may be too small to get reliable estimates when splitting the sample into two exclusive data sets (Efron & Tibshirani, 1993). B The testing plots are classified using sample plots from another image (reference image). There is no scene-to-scene calibration. So the classification accuracy may be poor due to spectral mismatches. C The testing plots are classified using sample plots from another image (reference image). The subject image is calibrated using transformation parameters derived by linear regression. D The testing plots are classified using sample plots from another image (reference image). The subject image is calibrated using transformation parameters derived by kNN-cross-validation. In the approaches (B), (C), and (D), the prediction accuracy is estimated by the two-groups cross-validation method. 4. Results 4.1. Transformation parameters from linear regression The regression models were developed with 20 target objects in the overlap area of two images belonging to 4 land cover types: water and rock (regarded as being approximately constant reflectors over time) as well as deciduous forest and coniferous forest (which may change due to environmental stresses and plant phenology). The objects' mean pixel values extracted from the reference image band-by-band were regressed against the mean pixel values extracted from the subject images, resulting in a regression model for each band. The relationship between the same objects found in the reference image and in the subject image makes it possible to investigate effects of phenology. If the regression models for vegetation objects and non-vegetation objects differ significantly, one might conclude that the spectral characteristics of phenological stages at both times of acquisition were not the same. This was the case for two of three subject images: 190/27, Sept. 1991 and 189/27, June 1996. In Fig. 2, two examples are given: the spectral characteristics of the phenological stages found in Aug. 1994 and in June 1996 differ (Fig. 2a), whereas there are no differences between the images from Aug. 1994 and Aug. 1992 (Fig. 2b) that have a common slope and intercept for both invariant reference objects and vegetation objects.
Fig. 2. a. Mean pixel values (LANDSAT TM, band 4) of target objects in the overlapping area of the reference image (190/26–27, Aug. 1994) and the subject image (189/27, June 1996). The regression lines derived for vegetation objects and for non-vegetation objects differ due to phenology. b. Mean pixel values (LANDSAT TM, band 4) of target objects in the overlapping area of the reference image (190/26–27, Aug. 1994) and the subject image (189/27, June 1996). The regression lines derived for vegetation objects and for nonvegetation objects do not differ significantly.
As the study focuses on vegetation, more precisely on forest cover, it may be sufficient to use the transformation equations based on vegetation objects only. Therefore, further investigations focusing on forest were carried out. Additional target objects, comprising the land cover types water, coniferous forest, dry grassland, and deciduous forest were selected and the pixel values were visualized in scatter plots. As demonstrated in Fig. 3, the class of coniferous forest is homogenous, whereas the class of deciduous forest is a conglomerate of various types (see
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Table 1 Transformation parameters used to calibrate the image 189/27 from Aug 1992 Transformation parameters derived by linear regression
Fig. 3. Scatter plot of various land cover types (LANDSAT TM, band 4) with ellipses representing the standard deviation. The means of some land cover types deviate significantly from the global regression line.
ellipses representing standard deviation), the mean values of which deviate from a global linear relationship. Hence, a global regression model which neglects the influence of forest types is slightly biased for these forest types. This effect of land cover types was investigated for band 4 using a general linear model (GLM), where the land cover type membership (categorical variable) was added as an additional independent variable. In a GLM, the effect of groups (here land cover types) is incorporated by a parameter ci, which is the deviation of the mean of group i from the global regression model. A t-test was performed in order to test, if ci deviates from 0 significantly. In the current problem, nine land cover types were taken into account: water (1), grassland (2), coniferous forest (3), and 6 different types of deciduous forest (4–9). For five out of six types of deciduous forest, ci deviates from 0 significantly ( p b 0.001) and for the land cover types (1), (2), and (3) it does not. The procedure of fitting the model was done stepwise by pooling together all land cover types with a non-significant ci and by adjusting the means for the remaining land cover types one by one. The derived linear model (R2 = 0.98) shows a high level of significance ( p b 0.001). According to these results, only the subject image from Aug. 1992 acquired in the same month as the reference image was used for further analysis. The transformation parameters that were used to calibrate this image are summarised in Table 1.
Transformation parameters derived by kNN-cross-validation
Band
Slope
Intercept
R2
Slope
Intercept
1 2 3 4 5 7
0.712 0.903 0.876 1.046 1.016 0.906
7.1 −0.9 −2.0 −3.1 −4.9 −1.9
0.970 0.980 0.992 0.987 0.990 0.991
0.7 1.1 1.2 1.0 1.1 0.9
8 −3 −4 0 −7 1
The combination that resulted in the highest classification accuracy as measured by Kappa (Section 4.3) was selected. In addition, the parameter k was varied in order to explore the relationship between the size of k (which determines the degree to which sparsely represented categories are suppressed) and the transformation parameter estimates. Varying k had some influence on the transformation parameters. However, the classification accuracy dropped quickly when deviating from the value k = 3. Therefore, k was kept constant at this optimal value. The optimisation procedure was started with band 1, which is affected most by atmospheric path radiance. While varying the regression parameters for band 1, they were not changed for the other bands. Then the procedure was continued for band 2, where band 1 was transformed using the derived regression parameters, and where the regression parameters for the other bands were kept unchanged. This procedure was repeated for each band. Fig. 4 shows the variation of Kappa in dependence of the transformation parameters slope and intercept for band 3. The derived transformation parameters for all bands are summarised in Table 1. As explained in Section 4.1, only the image 189/27 from Aug 1992 was calibrated.
4.2. Transformation parameters from kNN-cross-validation For each band (except the thermal band) different combinations of slope and intercept were tested. The values of the slope parameter ranged from 0.2 to 1.7 (increment: 0.1). The values of the intercept parameter ranged from − 15 to + 15 (increment: 1).
Fig. 4. Transformation parameters derived by kNN-cross-validation: variation of Kappa in dependence of slope and intercept shown for band 3. The optimal Kappa (0.502) was achieved with a slope of 1.2 and an intercept of − 4.
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Table 2 Forest cover type classification using the kNN-method (1— deciduous forest, 2— mixed forest dominated by deciduous trees, 3— mixed forest dominated by coniferous trees, 4— coniferous forest)
A B C D
Number of images
Calibration
PA1 n = 88
PA2 n = 21
PA3 n = 30
PA4 n = 62
OA
Kappa
Var(Kappa)
One Two Two Two
– Without Regression method kNN-cross-validation method
0.818 0.750 0.898 0.830
0.095 0.095 0.048 0.095
0.300 0.167 0.233 0.433
0.661 0.740 0.730 0.758
0.617 0.592 0.657 0.672
0.424 0.385 0.469 0.505
0.002 0.002 0.002 0.002
Classification accuracy (based on 201 testing plots) with and without calibration: producer's accuracies (PA) of class 1–4, overall accuracy (OA), Kappa, and variance of Kappa.
4.3. kNN-classification The accuracy of the classification results obtained with the approaches (A), (B), (C) and (D) as described in Section 3.4 are summarised in Table 2. Generally, the accuracy of the forest cover type classification was quite low. This was true especially for the mixed classes (2) and (3). According to the error matrices, there was confusion with the pure classes (1) and (4). Scatter diagrams showed that the mixed classes and the associated pure classes had very similar spectral signatures. The spectral separability in the data set is characterised by a Jeffries–Matusita distance (Richards & Jia, 2006) ranging from 0.49 to 1.54. Both methods of calibration (Table 2, row C and D) increased the total classification accuracy. There was improvement compared with the one-image-case (A) and compared with the two-image-case without calibration (B). The kNN-classification benefited from the increased number of sample plots taken from the adjacent scene due to calibration. The results achieved with the kNN-cross-validation method were slightly better than those achieved with the regression method. The classification into classes of total volume per hectare gave similar results with slightly lower accuracy levels. 5. Conclusions The study focuses on a problem that arises, when the kNNmethod is applied to a national forest inventory on an operational basis in order to produce forest maps for the whole territory. It is nearly unavoidable that there are areas where the location of satellite image scenes is unfavourable in relation to the national territory, resulting in the need for sharing field observations across images. An absolute radiometric calibration of all images covering the territory might be more efficient to handle this problem than an image-to-image approach. However, reference data that are needed for an absolute radiometric calibration are usually not available. In relative radiometric calibration, the reference data can be taken from the images themselves. In this study, a new method of relative radiometric calibration (kNN-cross-validation method) has been proposed and compared to a conventional method (regression method). Both methods are based on linear regression. Attention has to be paid to phenology. The images have to show similar phenological stages for all forest types. If there are forest types
with different phenological trends, the calibration is biased for at least some forest types. The regression method is straightforward. However, target objects from the overlap area for determining the transformation parameters have to be selected. Therefore, the method can only be applied to adjacent, overlapping scenes. Furthermore, there is often a lack of appropriate (invariant) objects, e.g. clear water, rock, which may restrict the applicability of this method. In the kNN-cross-validation method, the images to be calibrated need not overlap, and no radiometric control points (invariant objects) have to be selected. Only spectral information of field sample plots is needed to determine the transformation parameters. The optimal transformation parameters for each spectral band were determined by stepwise modification of slope and intercept. The procedure can be easily automated but does not offer the possibility of selecting the parameters simultaneously for all spectral bands. This is a quite complex problem and requires the implementation of an algorithm for global nonlinear optimisation. Algorithms that are commonly employed for this kind of problem are genetic algorithms (Goldberg, 1989) and simulated annealing (Kirkpatrick et al., 1983). Tomppo (2004) reports that the accuracy of kNN-estimates is noticeably increased, when the vector for weighting bands in the Euclidean distance computation is determined by means of a genetic algorithm. Global optimisation can be integrated in the kNN-cross-validation method very easily and may improve the performance of the method. The kNN-cross-validation method is a promising alternative to the conventional regression method. In addition to applications in forestry, it might also be applied in general land cover classifications. In particular, the classification accuracy of land cover classes with a low frequency may benefit from the simultaneous use of training data from more than one image. Acknowledgements The work with the kNN-method was initiated in a project financed by the Austrian Federal Ministry of Agriculture, Forestry, Environment and Water Management. The authors wish to thank the Institute of Forest Inventory at the Austrian Federal Office and Research Centre for Forests (BFW) for providing the field data of the Austrian Forest Inventory and for the support in data handling and interpretation. Moreover, the Global Land Cover Facility (GLCF) is acknowledged for
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providing free access to LANDSAT TM data used in the study. We extend our appreciation to Gregor Laaha from the Institute of Applied Statistics and Computing at the University of Natural Resources and Applied Life Sciences (BOKU), Vienna, for his assistance in statistical data analysis. Finally, the authors would like to thank three anonymous reviewers for constructive comments and suggestions. References Congalton, R. G., & Green, K. (1999). Assessing the accuracy of remotely sensed data: principles and practices. Boca Raton, Florida: Lewis Publishers. Cover, T. M., & Hart, P. E. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1), 21−27. Du, Y., Teillet, P. M., & Cihlar, J. (2002). Radiometric normalization of multitemporal high-resolution satellite images with quality control for land cover change detection. Remote Sensing of Environment, 82, 123−134. Dasarathy, B. V. (1991). Nearest neighbor norms: NN pattern classification techniques. Los Alamitos: IEEE Computer Society Press. Efron, B., & Tibshirani, R. (1993). An introduction to the bootstrap. Monographs on statistics and applied probability, vol. 57. New York: Chapman & Hall. Elvidge, C. D., Yuan, D., Weerackoon, R. D., & Lunetta, R. S. (1995). Relative radiometric normalization of Landsat Multispectral Scanner (MSS) data using an automatic scattergram-controlled regression. Photogrammetric Engineering and Remote Sensing, 10, 1255−1260. Fazakas, Z., Nilsson, M., & Olsson, H. (1999). Regional forest biomass and wood volume estimation using satellite data and ancillary data. Agricultural and Forest Meteorology, 98–99, 417−425. Franco-Lopez, H., Ek, A. R., & Bauer, M. E. (2001). Estimation and mapping of forest stand density, volume and cover type using the k-nearest neighbors method. Remote Sensing of Environment, 77, 251−274. Goldberg, D. (1989). Genetic algorithms in search, optimization, and machine learning. : Addison-Wesley. Hall, F. G., Strebel, D. E., Nickeson, J. E., & Goetz, S. J. (1991). Radiometric rectification: Toward a common radiometric response among multidate, multisensor images. Remote Sensing of Environment, 35, 11−27. Katila, M., & Tomppo, E. (2001). Selecting estimation parameters for the Finnish multisource national forest inventory. Remote Sensing of Environment, 76, 16−32.
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Kilkki, P., & Päivinen, R. (1987). Reference sample plots to combine field measurements and satellite data in forest inventory. Remote sensing-aided forest inventorySeminars organised by SNS and Taksaattoriklubi, Hyytiälä, Finland. (pp. 209−212). Kirkpatrick, S., Gelatt, C. D., & Vecci, M. P. (1983). Optimization by simulated annealing. Science, 220(4458), 671−680. Koukal, T. (2004). Nonparametric Assessment of Forest Attributes by Combination of Field Data of the Austrian Forest Inventory and Remote Sensing Data. Dissertation. University of Natural Resources and Applied Life Sciences, Vienna. McRoberts, R. E., Nelson, M. D., & Wendt, D. G. (2002). Stratified estimation of forest area using satellite imagery, inventory data and the k-nearest neighbors technique. Remote Sensing of Environment, 82, 457−468. Over, M., Schöttker, B., Braun, M., & Menz, G. (2003). Relative radiometric normalisation of multitemporal Landsat data— A comparison of different approaches. In T. I. Stein (Ed.), Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Toulouse, France. Richards, J. A., & Jia, X. (2006). Remote sensing digital image analysis. New York: Springer. Sandmeier, S. (1995). A Physically-Based Radiometric Correction Model— Correction of Atmospheric and Illumination Effects in Optical Satellite Data of Rugged Terrain. : Department of Geography, University of Zurich. Schott, J. R., Salvaggio, C., & Volchok, W. J. (1988). Radiometric scene normalization using pseudoinvariant features. Remote Sensing of Environment, 26, 1−16. Steinwendner, J., Schneider, W., & Bartl, R. (2001). Image understanding methods for remote sensing. In W. G. Kropatsch, & H. Bischof (Eds.), Digital image analysis— selected techniques and applications (pp. 337−366). New York: Springer. Tomppo, E. (1991). Satellite image-based national forest inventory of Finland. International Archives of Photogrammetry and Remote Sensing, 28, 419−424. Tomppo, E. (2004). Using coarse scale forest variables as ancillary information and weighting of variables in k-NN estimation: A genetic algorithm approach. Remote Sensing of Environment, 92, 1−20. Vermote, E., Tanré, D., Deuze, J.L., Herman, M. and Morcrette, J.J. (1997). Second simulation of the satellite signal in the solar spectrum (6S): user's guide. Technical Report Version 2, Dept. of Geography, Univ. of Maryland, NASA-Goddard Space Flight Center - Code 923, Greenbelt, MD 207771, USA.
The impact of relative radiometric calibration on the accuracy of kNN-predictions of forest attributes Tatjana Koukal ⁎, Franz Suppan, Werner Schneider Institute of Surveying, Remote Sensing and Land Information, Department of Landscape, Spatial and Infrastructure Sciences, University of Natural Resources and Applied Life Sciences, Vienna, Austria Received 12 August 2005; received in revised form 18 August 2006; accepted 27 August 2006
Abstract The k-nearest-neighbour (kNN) algorithm is widely applied for the estimation of forest attributes using remote sensing data. It requires a large amount of reference data to achieve satisfactory results. Usually, the number of available reference plots for the kNN-prediction is limited by the size of the area covered by a terrestrial reference inventory and remotely sensed imagery collected from one overflight. The applicability of kNN could be enhanced if adjacent images of different acquisition dates could be used in the same estimation procedure. Relative radiometric calibration is a prerequisite for this. This study focuses on two empirical calibration methods. They are tested on adjacent LANDSAT TM scenes in Austria. The first, quite conventional one is based on radiometric control points in the overlap area of two images and on the determination of transformation parameters by linear regression. The other, recently developed method exploits the kNN-cross-validation procedure. Performance and applicability of both methods as well as the impact of phenology are discussed. © 2007 Elsevier Inc. All rights reserved. Keywords: Scene-to-scene radiometric normalisation; k-nearest-neighbour method; Cross-validation; Forest inventory; Phenology
1. Introduction In forestry, the k-nearest-neighbour (kNN) algorithm is often used to combine two data sources: field data obtained at sample plots and remote sensing data. Forest variables are estimated from the remotely sensed spectral information using the terrestrial sample plots as a reference, e.g. for the purpose of national forest inventories (Koukal, 2004; Tomppo, 1991). The typical problem setting is as follows: Detailed forest variables are collected on the ground at sample plots. For reasons of economic efficiency, the density of the sample points has to be rather low. Therefore the production of large-scale maps from the terrestrial inventory results is not feasible, and the estimates of forest variables for small areas are imprecise. The result can be improved by augmenting the terrestrial inventory data with remotely sensed image data. With the kNNmethod, forest variables can be estimated for every location (for every pixel of the remotely sensed images) between the ⁎ Corresponding author. E-mail address: [email protected] (T. Koukal). 0034-4257/$ - see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2006.08.016
terrestrial sample plots, resulting in forest maps and smaller error margins in the forest variable estimation in small areas (Franco-Lopez et al., 2001; Katila & Tomppo, 2001). The basic idea of the kNN-method (Cover & Hart, 1967; Dasarathy, 1991) is to compare every pixel, for which the forest variables have to be estimated (“unknown pixel”), with pixels of known forest variables (pixels coinciding with terrestrial plots, called “plot pixels”). The k plot pixels that are most similar in their spectral characteristics to the unknown pixel are selected, and the mean value of the forest variables of these k selected plot pixels is taken as the estimate for the unknown pixel. In the case of a categorical forest variable, the most frequent class among the k selected plot pixels is assigned to the unknown pixel (Fazakas et al., 1999; Kilkki & Päivinen, 1987; McRoberts et al., 2002). The kNN-method is a non-parametric approach making no assumptions on the distribution of pixels in feature space as a function of forest variables. For every forest variable value (e.g. for every forest cover type), an adequate number of plot pixels must be available in order to find similar ones. These plot pixels must lie on the same image as the unknown pixel, otherwise the
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spectral similarity is disturbed by external factors such as sun elevation and atmospheric conditions. This is one of the severest drawbacks in practical applications. This problem particularly occurs in countries that are elongated in east–west direction as scenes from neighbouring image acquisition paths are usually acquired on different dates. As a consequence, the individual images should have an extent as large as possible (e.g. LANDSAT with 185 km by 170 km is more favourable than SPOT or ASTER with 60 km by 60 km), and every image to be used in the kNN-method should be covered by the terrestrial inventory area to an extent as large as possible (Fig. 1). To improve the success of forest inventories using the kNNmethod, adjacent scenes of different acquisition dates could be used in the same estimation procedure assuming relative radiometric calibration was carried out previously (Elvidge et al., 1995; Hall et al., 1991; Over et al., 2003; Schott et al., 1988). Radiometric differences of test areas with identical forest attributes but sampled at different locations and at different times originate mainly from atmospheric effects (absorption, scattering), varying sun-target-satellite geometry (bi-directional reflectance effects), and phenology. Radiometric calibration aims at minimising all these effects except phenology. It is an important technique in applications that are based on multi-date satellite imagery, e.g. change detection (e.g. Du et al., 2002). In relative radiometric calibration of images, one of the images has to be declared as the “reference image”, and the other images are called “subject images”. The aim of calibration is to transform the subject images in such a way that they have pixel digital number (DN) values as if they were acquired on the same date as the reference image. This study focuses on two empirical methods of relative radiometric calibration. They are tested on adjacent LANDSAT
TM scenes in the eastern, flat regions of Austria. One aim of this study was to investigate the extent to which phenology (i.e. the development of vegetation during a year mainly driven by the climate) limits the application of relative calibration methods. Therefore, subject images from different phenological stages were chosen (spring, mid-summer and late-summer), whereas the reference image was taken in mid-summer. 2. Data Four LANDSAT TM images of three adjacent scenes (path/ row) were used in the study. One of them served as reference image (190/26–27, Aug. 1994) and the others as subject images (190/27, Sept. 1991; 189/27, Aug. 1992; 189/27, June 1996). Overlapping occurred between the subject and reference images. All images were acquired within or close to the field inventory period from 1992 to 1996 of the Austrian forest inventory (AFI). The AFI is based on a systematic sampling grid of width 3.89 km. At each grid point that lies within forest, a cluster of four permanent sample plots is established (cluster sampling design). The plots are located in the corners of a square with a side length of 200 m. The plots are either relascope (i.e. Bitterlich) plots or fixed area plots depending on the forest attribute to be measured. The fixed area plots are circular with a radius of 9.77 m (i.e. an area of 300 m2). Inventory data have been collected since the early 1960s. The spectral information for a sample plot was taken from the pixel with centre closest to the sample plot centre. Altogether, 1629 sample plots were covered by the images employed in this study. 3. Methodology 3.1. Model of relative radiometric calibration
Fig. 1. Scene coverage (LANDSAT TM) and distribution of the Austrian forest inventory (AFI) field plots in the eastern part of Austria. The scene 189/27 is required to obtain a full coverage of the territory. However, this scene is covered by the terrestrial inventory only to a small extent leading to a shortage of reference data in the kNN-process.
Relative radiometric calibration investigates the relationship between the pixel DN values of the same area remotely sensed on two images at different dates. It is based on the assumption that the reflectance values at any location on the ground remain unchanged between the two acquisition dates. The relationship between the pixel DN value at any acquisition date and the surface reflectance is a non-linear one, due to backscattering in the atmosphere of radiation reflected by the surface (see e.g. Sandmeier, 1995; Steinwendner et al., 2001). Therefore, the relationship between corresponding pixel values from two images can also be non-linear. An analysis was performed using the computer simulation code 6S (Vermote et al., 1997). Image acquisition with LANDSAT TM at a geographical latitude of 48° (corresponding to the test images in Austria) with mid-latitude summer atmospheric conditions and a continental aerosol model with a horizontal visibility between 8 km and 23 km at acquisition dates between June 1 and August 30 was assumed. The simulations revealed that the maximum deviation (which occurred in TM band 4) from a linear relationship of the pixel values of vegetation between any two simulated acquisition cases is less
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than half a pixel DN and therefore well below the noise level. Therefore, the effects of non-linearity are ignored. The pixel values of the corresponding areas remotely sensed at different times are assumed to be linearly dependent (Schott et al., 1988). There are two transformation parameters for each band that have to be estimated: slope and intercept. Two methods for the determination of optimal transformation parameters were tested. The conventional method is based on a number of radiometric tie points in the overlap area of the adjacent scenes (Section 3.2). The transformation equations are set up for every spectral band by linear regression. This was compared to a new empirical method for the determination of optimal transformation parameters (Section 3.3). The proposed method exploits the cross-validation procedure that is often used in combination with the kNN-algorithm. Finally, the calibration methods were evaluated by conducting a kNNclassification (Section 3.4). 3.2. Estimating radiometric calibration parameters by regression of pixel values in the overlap area The traditional approach uses a set of target objects in the overlap area of the adjacent scenes from different dates. Objects have to be selected that can be assumed to have the same reflectance on both dates (Schott et al., 1988). They are used as radiometric control points. The mean pixel values of these objects are extracted from both images band-by-band, and the transformation equations are set up for each band by linear regression. 3.3. Estimating radiometric calibration parameters within the kNN-calibration process The kNN-method for estimating forest variables from satellite imagery requires a certain set of parameters, such as the value of k (number of nearest-neighbours), the similarity measure, and the weights for each spectral band. Optimal values for these kNN-parameters are determined in the kNNcalibration process. In this process, the kNN-parameters are chosen in such a way that the subsequent kNN-classification (kNN-estimation) yields optimal results as measured by some loss function, e.g. a minimum prediction error (Franco-Lopez et al., 2001; Katila & Tomppo, 2001). The prediction error for a given set of kNN-parameters is estimated by cross-validation. Cross-validation is a common method for estimating the expected prediction error of a model or of a classifier such as kNN. It uses part of the available reference data to train the classifier and a different part to test it (Efron & Tibshirani, 1993). The reference data is partitioned into M sub-samples. There are M runs. In each run, one sub-sample serves as the testing set and all other sub-samples are used for training. In the case of kNN, this principle is implemented in the following way: In order to classify a pixel belonging to the testing set, its k most similar plot pixels (neighbours) are selected from the training set. The pixel to be classified is assigned to the class that is most frequent among the k neighbours. Then the correctness of the classification is checked. This procedure is
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repeated for each pixel within the testing sets resulting in a mean prediction error estimated for the whole data set. Special forms of the cross-validation procedure are the twogroups-method and the leave-one-out cross-validation. In the two-groups-method, the reference data are split into a group of training data and a group of testing data, which then remain unchanged for the whole validation process. In the leave-oneout-method, the testing set consists of the one single pixel classified at the moment, and the training set consists of all other reference data. The leave-one-out method is especially suited for rather small reference data sets, because the maximum amount of training data is available for the classification (estimation) of every pixel. Cross-validation was investigated to determine not only the optimal values for the kNN-parameters, but also the optimal values for the radiometric calibration parameters at the same time. A linear transformation equation was set up for each band. Arbitrary initial values were assigned to the transformation parameters. The pixel values of the testing plots were transformed according to the resulting transformation equations. Different combinations of slope and intercept were tested to determine the combination that minimises the prediction error. It was estimated by the two-groups cross-validation method with one group represented by the sample plots on the reference image (training set), and the second group represented by the sample plots on the subject image (testing set). This forced the algorithm to “compare” plots from the two different images and avoided the situation that the kNN-classification (kNN-estimation) is only based on nearest-neighbours found on the same image as the pixel to be classified. The determination of optimal transformation parameters is a rather complex optimisation problem, because there may be interactions between the parameters of different bands. In principle, the parameters of all bands have to be optimised simultaneously. In the study, the transformation parameters were optimised band-by-band, starting with the band that is expected to show the biggest difference between the reference image and the subject image. 3.4. Comparison of four approaches In order to demonstrate and to analyse the effect of enlarging the set of training data for a kNN-classification by adding radiometrically calibrated adjacent images, a kNN-classification into forest cover types (1… deciduous forest, 2… mixed forest dominated by deciduous trees, 3… mixed forest dominated by coniferous trees, 4… coniferous forest) and a kNN-classification into classes of total volume per hectare (1…b = 140 m3/ha, 2… 141 to 280 m3/ha, 3… 281 to 430 m3/ha, 4…N430 m3/ha) were performed. The similarities between training plots and testing plots were measured by the Euclidean distance measure using all LANDSAT TM bands (except the thermal band) equally weighted. The number of nearest-neighbours (k), was set to 3 as identified as optimal in preceding investigations. The prediction accuracy was estimated by cross-validation. An error matrix (Congalton & Green, 1999) was compiled for
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each run, where for each class the number of correctly classified sample plots as well as the number and the kind of misclassifications were summarised. Accuracy measures such as overall accuracy, Kappa, and producer's accuracies were computed. The testing plots were classified following four approaches: A Only sample plots from the subject image are used. This approach represents the case in which the image covers only a small number of sample plots. It can be assumed that the sample size is critically low, i.e. below the minimum number required for a satisfactory classification result. The prediction accuracy is estimated by leave-one-out cross-validation as the sample may be too small to get reliable estimates when splitting the sample into two exclusive data sets (Efron & Tibshirani, 1993). B The testing plots are classified using sample plots from another image (reference image). There is no scene-to-scene calibration. So the classification accuracy may be poor due to spectral mismatches. C The testing plots are classified using sample plots from another image (reference image). The subject image is calibrated using transformation parameters derived by linear regression. D The testing plots are classified using sample plots from another image (reference image). The subject image is calibrated using transformation parameters derived by kNN-cross-validation. In the approaches (B), (C), and (D), the prediction accuracy is estimated by the two-groups cross-validation method. 4. Results 4.1. Transformation parameters from linear regression The regression models were developed with 20 target objects in the overlap area of two images belonging to 4 land cover types: water and rock (regarded as being approximately constant reflectors over time) as well as deciduous forest and coniferous forest (which may change due to environmental stresses and plant phenology). The objects' mean pixel values extracted from the reference image band-by-band were regressed against the mean pixel values extracted from the subject images, resulting in a regression model for each band. The relationship between the same objects found in the reference image and in the subject image makes it possible to investigate effects of phenology. If the regression models for vegetation objects and non-vegetation objects differ significantly, one might conclude that the spectral characteristics of phenological stages at both times of acquisition were not the same. This was the case for two of three subject images: 190/27, Sept. 1991 and 189/27, June 1996. In Fig. 2, two examples are given: the spectral characteristics of the phenological stages found in Aug. 1994 and in June 1996 differ (Fig. 2a), whereas there are no differences between the images from Aug. 1994 and Aug. 1992 (Fig. 2b) that have a common slope and intercept for both invariant reference objects and vegetation objects.
Fig. 2. a. Mean pixel values (LANDSAT TM, band 4) of target objects in the overlapping area of the reference image (190/26–27, Aug. 1994) and the subject image (189/27, June 1996). The regression lines derived for vegetation objects and for non-vegetation objects differ due to phenology. b. Mean pixel values (LANDSAT TM, band 4) of target objects in the overlapping area of the reference image (190/26–27, Aug. 1994) and the subject image (189/27, June 1996). The regression lines derived for vegetation objects and for nonvegetation objects do not differ significantly.
As the study focuses on vegetation, more precisely on forest cover, it may be sufficient to use the transformation equations based on vegetation objects only. Therefore, further investigations focusing on forest were carried out. Additional target objects, comprising the land cover types water, coniferous forest, dry grassland, and deciduous forest were selected and the pixel values were visualized in scatter plots. As demonstrated in Fig. 3, the class of coniferous forest is homogenous, whereas the class of deciduous forest is a conglomerate of various types (see
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Table 1 Transformation parameters used to calibrate the image 189/27 from Aug 1992 Transformation parameters derived by linear regression
Fig. 3. Scatter plot of various land cover types (LANDSAT TM, band 4) with ellipses representing the standard deviation. The means of some land cover types deviate significantly from the global regression line.
ellipses representing standard deviation), the mean values of which deviate from a global linear relationship. Hence, a global regression model which neglects the influence of forest types is slightly biased for these forest types. This effect of land cover types was investigated for band 4 using a general linear model (GLM), where the land cover type membership (categorical variable) was added as an additional independent variable. In a GLM, the effect of groups (here land cover types) is incorporated by a parameter ci, which is the deviation of the mean of group i from the global regression model. A t-test was performed in order to test, if ci deviates from 0 significantly. In the current problem, nine land cover types were taken into account: water (1), grassland (2), coniferous forest (3), and 6 different types of deciduous forest (4–9). For five out of six types of deciduous forest, ci deviates from 0 significantly ( p b 0.001) and for the land cover types (1), (2), and (3) it does not. The procedure of fitting the model was done stepwise by pooling together all land cover types with a non-significant ci and by adjusting the means for the remaining land cover types one by one. The derived linear model (R2 = 0.98) shows a high level of significance ( p b 0.001). According to these results, only the subject image from Aug. 1992 acquired in the same month as the reference image was used for further analysis. The transformation parameters that were used to calibrate this image are summarised in Table 1.
Transformation parameters derived by kNN-cross-validation
Band
Slope
Intercept
R2
Slope
Intercept
1 2 3 4 5 7
0.712 0.903 0.876 1.046 1.016 0.906
7.1 −0.9 −2.0 −3.1 −4.9 −1.9
0.970 0.980 0.992 0.987 0.990 0.991
0.7 1.1 1.2 1.0 1.1 0.9
8 −3 −4 0 −7 1
The combination that resulted in the highest classification accuracy as measured by Kappa (Section 4.3) was selected. In addition, the parameter k was varied in order to explore the relationship between the size of k (which determines the degree to which sparsely represented categories are suppressed) and the transformation parameter estimates. Varying k had some influence on the transformation parameters. However, the classification accuracy dropped quickly when deviating from the value k = 3. Therefore, k was kept constant at this optimal value. The optimisation procedure was started with band 1, which is affected most by atmospheric path radiance. While varying the regression parameters for band 1, they were not changed for the other bands. Then the procedure was continued for band 2, where band 1 was transformed using the derived regression parameters, and where the regression parameters for the other bands were kept unchanged. This procedure was repeated for each band. Fig. 4 shows the variation of Kappa in dependence of the transformation parameters slope and intercept for band 3. The derived transformation parameters for all bands are summarised in Table 1. As explained in Section 4.1, only the image 189/27 from Aug 1992 was calibrated.
4.2. Transformation parameters from kNN-cross-validation For each band (except the thermal band) different combinations of slope and intercept were tested. The values of the slope parameter ranged from 0.2 to 1.7 (increment: 0.1). The values of the intercept parameter ranged from − 15 to + 15 (increment: 1).
Fig. 4. Transformation parameters derived by kNN-cross-validation: variation of Kappa in dependence of slope and intercept shown for band 3. The optimal Kappa (0.502) was achieved with a slope of 1.2 and an intercept of − 4.
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Table 2 Forest cover type classification using the kNN-method (1— deciduous forest, 2— mixed forest dominated by deciduous trees, 3— mixed forest dominated by coniferous trees, 4— coniferous forest)
A B C D
Number of images
Calibration
PA1 n = 88
PA2 n = 21
PA3 n = 30
PA4 n = 62
OA
Kappa
Var(Kappa)
One Two Two Two
– Without Regression method kNN-cross-validation method
0.818 0.750 0.898 0.830
0.095 0.095 0.048 0.095
0.300 0.167 0.233 0.433
0.661 0.740 0.730 0.758
0.617 0.592 0.657 0.672
0.424 0.385 0.469 0.505
0.002 0.002 0.002 0.002
Classification accuracy (based on 201 testing plots) with and without calibration: producer's accuracies (PA) of class 1–4, overall accuracy (OA), Kappa, and variance of Kappa.
4.3. kNN-classification The accuracy of the classification results obtained with the approaches (A), (B), (C) and (D) as described in Section 3.4 are summarised in Table 2. Generally, the accuracy of the forest cover type classification was quite low. This was true especially for the mixed classes (2) and (3). According to the error matrices, there was confusion with the pure classes (1) and (4). Scatter diagrams showed that the mixed classes and the associated pure classes had very similar spectral signatures. The spectral separability in the data set is characterised by a Jeffries–Matusita distance (Richards & Jia, 2006) ranging from 0.49 to 1.54. Both methods of calibration (Table 2, row C and D) increased the total classification accuracy. There was improvement compared with the one-image-case (A) and compared with the two-image-case without calibration (B). The kNN-classification benefited from the increased number of sample plots taken from the adjacent scene due to calibration. The results achieved with the kNN-cross-validation method were slightly better than those achieved with the regression method. The classification into classes of total volume per hectare gave similar results with slightly lower accuracy levels. 5. Conclusions The study focuses on a problem that arises, when the kNNmethod is applied to a national forest inventory on an operational basis in order to produce forest maps for the whole territory. It is nearly unavoidable that there are areas where the location of satellite image scenes is unfavourable in relation to the national territory, resulting in the need for sharing field observations across images. An absolute radiometric calibration of all images covering the territory might be more efficient to handle this problem than an image-to-image approach. However, reference data that are needed for an absolute radiometric calibration are usually not available. In relative radiometric calibration, the reference data can be taken from the images themselves. In this study, a new method of relative radiometric calibration (kNN-cross-validation method) has been proposed and compared to a conventional method (regression method). Both methods are based on linear regression. Attention has to be paid to phenology. The images have to show similar phenological stages for all forest types. If there are forest types
with different phenological trends, the calibration is biased for at least some forest types. The regression method is straightforward. However, target objects from the overlap area for determining the transformation parameters have to be selected. Therefore, the method can only be applied to adjacent, overlapping scenes. Furthermore, there is often a lack of appropriate (invariant) objects, e.g. clear water, rock, which may restrict the applicability of this method. In the kNN-cross-validation method, the images to be calibrated need not overlap, and no radiometric control points (invariant objects) have to be selected. Only spectral information of field sample plots is needed to determine the transformation parameters. The optimal transformation parameters for each spectral band were determined by stepwise modification of slope and intercept. The procedure can be easily automated but does not offer the possibility of selecting the parameters simultaneously for all spectral bands. This is a quite complex problem and requires the implementation of an algorithm for global nonlinear optimisation. Algorithms that are commonly employed for this kind of problem are genetic algorithms (Goldberg, 1989) and simulated annealing (Kirkpatrick et al., 1983). Tomppo (2004) reports that the accuracy of kNN-estimates is noticeably increased, when the vector for weighting bands in the Euclidean distance computation is determined by means of a genetic algorithm. Global optimisation can be integrated in the kNN-cross-validation method very easily and may improve the performance of the method. The kNN-cross-validation method is a promising alternative to the conventional regression method. In addition to applications in forestry, it might also be applied in general land cover classifications. In particular, the classification accuracy of land cover classes with a low frequency may benefit from the simultaneous use of training data from more than one image. Acknowledgements The work with the kNN-method was initiated in a project financed by the Austrian Federal Ministry of Agriculture, Forestry, Environment and Water Management. The authors wish to thank the Institute of Forest Inventory at the Austrian Federal Office and Research Centre for Forests (BFW) for providing the field data of the Austrian Forest Inventory and for the support in data handling and interpretation. Moreover, the Global Land Cover Facility (GLCF) is acknowledged for
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providing free access to LANDSAT TM data used in the study. We extend our appreciation to Gregor Laaha from the Institute of Applied Statistics and Computing at the University of Natural Resources and Applied Life Sciences (BOKU), Vienna, for his assistance in statistical data analysis. Finally, the authors would like to thank three anonymous reviewers for constructive comments and suggestions. References Congalton, R. G., & Green, K. (1999). Assessing the accuracy of remotely sensed data: principles and practices. Boca Raton, Florida: Lewis Publishers. Cover, T. M., & Hart, P. E. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1), 21−27. Du, Y., Teillet, P. M., & Cihlar, J. (2002). Radiometric normalization of multitemporal high-resolution satellite images with quality control for land cover change detection. Remote Sensing of Environment, 82, 123−134. Dasarathy, B. V. (1991). Nearest neighbor norms: NN pattern classification techniques. Los Alamitos: IEEE Computer Society Press. Efron, B., & Tibshirani, R. (1993). An introduction to the bootstrap. Monographs on statistics and applied probability, vol. 57. New York: Chapman & Hall. Elvidge, C. D., Yuan, D., Weerackoon, R. D., & Lunetta, R. S. (1995). Relative radiometric normalization of Landsat Multispectral Scanner (MSS) data using an automatic scattergram-controlled regression. Photogrammetric Engineering and Remote Sensing, 10, 1255−1260. Fazakas, Z., Nilsson, M., & Olsson, H. (1999). Regional forest biomass and wood volume estimation using satellite data and ancillary data. Agricultural and Forest Meteorology, 98–99, 417−425. Franco-Lopez, H., Ek, A. R., & Bauer, M. E. (2001). Estimation and mapping of forest stand density, volume and cover type using the k-nearest neighbors method. Remote Sensing of Environment, 77, 251−274. Goldberg, D. (1989). Genetic algorithms in search, optimization, and machine learning. : Addison-Wesley. Hall, F. G., Strebel, D. E., Nickeson, J. E., & Goetz, S. J. (1991). Radiometric rectification: Toward a common radiometric response among multidate, multisensor images. Remote Sensing of Environment, 35, 11−27. Katila, M., & Tomppo, E. (2001). Selecting estimation parameters for the Finnish multisource national forest inventory. Remote Sensing of Environment, 76, 16−32.
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Kilkki, P., & Päivinen, R. (1987). Reference sample plots to combine field measurements and satellite data in forest inventory. Remote sensing-aided forest inventorySeminars organised by SNS and Taksaattoriklubi, Hyytiälä, Finland. (pp. 209−212). Kirkpatrick, S., Gelatt, C. D., & Vecci, M. P. (1983). Optimization by simulated annealing. Science, 220(4458), 671−680. Koukal, T. (2004). Nonparametric Assessment of Forest Attributes by Combination of Field Data of the Austrian Forest Inventory and Remote Sensing Data. Dissertation. University of Natural Resources and Applied Life Sciences, Vienna. McRoberts, R. E., Nelson, M. D., & Wendt, D. G. (2002). Stratified estimation of forest area using satellite imagery, inventory data and the k-nearest neighbors technique. Remote Sensing of Environment, 82, 457−468. Over, M., Schöttker, B., Braun, M., & Menz, G. (2003). Relative radiometric normalisation of multitemporal Landsat data— A comparison of different approaches. In T. I. Stein (Ed.), Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Toulouse, France. Richards, J. A., & Jia, X. (2006). Remote sensing digital image analysis. New York: Springer. Sandmeier, S. (1995). A Physically-Based Radiometric Correction Model— Correction of Atmospheric and Illumination Effects in Optical Satellite Data of Rugged Terrain. : Department of Geography, University of Zurich. Schott, J. R., Salvaggio, C., & Volchok, W. J. (1988). Radiometric scene normalization using pseudoinvariant features. Remote Sensing of Environment, 26, 1−16. Steinwendner, J., Schneider, W., & Bartl, R. (2001). Image understanding methods for remote sensing. In W. G. Kropatsch, & H. Bischof (Eds.), Digital image analysis— selected techniques and applications (pp. 337−366). New York: Springer. Tomppo, E. (1991). Satellite image-based national forest inventory of Finland. International Archives of Photogrammetry and Remote Sensing, 28, 419−424. Tomppo, E. (2004). Using coarse scale forest variables as ancillary information and weighting of variables in k-NN estimation: A genetic algorithm approach. Remote Sensing of Environment, 92, 1−20. Vermote, E., Tanré, D., Deuze, J.L., Herman, M. and Morcrette, J.J. (1997). Second simulation of the satellite signal in the solar spectrum (6S): user's guide. Technical Report Version 2, Dept. of Geography, Univ. of Maryland, NASA-Goddard Space Flight Center - Code 923, Greenbelt, MD 207771, USA.