Remote Sensing and GIS Accuracy Assessment - Chapter 13

CHAPTER 13 Mapping Spatial Accuracy and Estimating Landscape Indicators from Thematic Land-Cover Maps Using Fuzzy Set Theory Liem T. Tran, S. Taylor Jarnagin, C. Gregory Knight, and Latha Baskaran CONTENTS 13.1 Introduction...........................................................................................................................173 13.2 Methods................................................................................................................................174 13.2.1 Multilevel Agreement...............................................................................................176 13.2.2 Spatial Accuracy Map ..............................................................................................177 13.2.3 Degrees of Fuzzy Membership................................................................................177 13.2.4 Fuzzy Membership Rules.........................................................................................178 13.2.5 Fuzzy Land-Cover Maps..........................................................................................180 13.2.6 Deriving Landscape Indicators.................................................................................180 13.3 Results and Discussion.........................................................................................................180 13.4 Conclusions...........................................................................................................................186 13.5 Summary...............................................................................................................................186 Acknowledgments..........................................................................................................................187 References......................................................................................................................................187 13.1 INTRODUCTION The accuracy of thematic map products is not spatially homogenous, but rather variable across most landscapes. Properly analyzing and representing the spatial distribution (pattern) of thematic map accuracy would provide valuable user information for assessing appropriate applications for land-cover (LC) maps and other derived products (i.e., landscape metrics). However, current thematic map accuracy measures, including the confusion or error matrix (Story and Congalton, 1986) and Kappa coefficient of agreement (Congalton and Green, 1999), are inadequate for analyzing the spatial variation of thematic map accuracy. They are not able to answer several important scientific and application-oriented questions related to thematic map accuracy. For example, are errors distributed randomly across space? Do different cover types have the same spatial accuracy pattern? How do spatial accuracy patterns affect products derived from thematic maps? Within this context, methods for displaying and analyzing the spatial accuracy of thematic maps and bringing the spatial accuracy 173 © 2004 by Taylor & Francis Group, LLC 174 REMOTE SENSING AND GIS ACCURACY ASSESSMENT information into other calculations, such as deriving landscape indicators from thematic maps, are important issues to advance scientifically appropriate applications of remotely sensed image data. Our study objective was to use the fuzzy set approach to examine and display the spatial accuracy pattern of thematic LC maps and to combine uncertainty with the computation of landscape indicators (metrics) derived from thematic maps. The chapter is organized by (1) current methods for analyzing and mapping thematic map accuracy, (2) presentation of our methodology for con-structing fuzzy LC maps, and (3) deriving landscape indicators from fuzzy maps. There have been several studies analyzing the spatial variation of thematic map accuracy (Campbell, 1981; Congalton, 1988). Campbell (1987) found a tendency for misclassified pixels to form chains along boundaries of homogenous patches. Townshend et al. (2000) explained this tendency by the fact that, in remotely sensed images, the signal coming from a land area represented by a specific pixel can include a considerable proportion of signal from neighboring pixels. Fisher (1994) used animation to visualize the reliability in classified remotely sensed images. Moisen et al. (1996) developed a generalized linear mixed model to analyze misclassification errors in con-nection with several factors, such as distance to road, slope, and LC heterogeneity. Recently, Smith et al. (2001) found that accuracy decreases as LC heterogeneity increases and patch sizes decrease. Steele et al. (1998) formulated a concept of misclassification probability by calculating values at training observation locations and then used spatial interpolation (kriging) to create accuracy maps for thematic LC maps. However, this work used the training data employed in the classification process but not the independent reference data usually collected after the thematic map has been constructed for accuracy assessment purposes. Steele et al. (1998) stated that the misclassification probability is not specific to a given cover type. It is a population concept indicating only the probability that the predicted cover type is different from the reference cover type, regardless of the predicted and reference types as well as the observed outcome, and whether correct or incorrect. Although this work brought in a useful approach to constructing accuracy maps, it did not provide information for the relationship between misclassification probabilities and the independent reference data used for accuracy assess-ment (i.e., the “real” errors). Furthermore, by combining training data of all different cover types together, it produced similar misclassification probabilities for pixels with different cover types that were colocated. This point should be open to discussion, as our analysis described below indicates that the spatial pattern of thematic map accuracy varies from one cover type to another, and pixels with different cover types located in close proximity might have different accuracy levels. Recently, fuzzy set theory has been applied to thematic map accuracy assessment using two primary approaches. The first was to design a fuzzy matching definition for a crisp classification, which allows for varying levels of set membership for multiple map categories (Gopal and Wood-cock, 1994; Muller et al., 1998; Townsend, 2000; Woodcock and Gopal, 2000). The second approach defines a fuzzy classification or fuzzy objects (Zhang and Stuart, 2000; Cheng et al., 2001). Although the fuzzy theory-based methods take into consideration error magnitude and ambiguity in map classes while doing the assessment, like other conventional measures, they do not show spatial variation of thematic map accuracy. To overcome shortcomings in mapping thematic map accuracy, we have developed a fuzzy set-based method that is capable of analyzing and mapping spatial accuracy patterns of different cover types. We expanded that method further in this study to bring the spatial accuracy information into the calculations of several landscape indicators derived from thematic LC maps. As the method of mapping spatial accuracy was at the core of this study, it will be presented to a reasonable extent in this chapter. 13.2 METHODS This study used data collected for the accuracy assessment of the National Land Cover Data (NLCD) set. The NLCD is a LC map of the contiguous U.S. derived from classified Landsat © 2004 by Taylor & Francis Group, LLC MAPPING SPATIAL ACCURACY AND ESTIMATING LANDSCAPE INDICATORS 175 Figure 13.1 The Mid-Atlantic Region; 10 watersheds used in later analysis are highlighted on the map. Thematic Mapper (TM) images (Vogelmann et al., 1998; Vogelmann et al., 2001). The NLCD was created by the Multi-Resolution Land Characterization (MRLC) consortium (Loveland and Shaw, 1996) to provide a national-scope and consistently classified LC data set for the country. Method-ology and results of the accuracy assessment have been described in Stehman et al. (2000), Yang et al. (2000, 2001), and Zhu et al. (1999, 2000). While data for the accuracy assessment were taken by federal region and available for several regions, this study only used data collected for Federal Geographic Region III, the Mid-Atlantic Region (MAR) (Figure 13.1). Table 13.1 shows the number of photographic interpreted “reference” data samples associated with each class in the LC map (Level I) for the MAR. Note that the reference data for Region III did not include alternate reference cover-type labels or information concerning photographic interpretation confidence, unlike data associated with other federal geographic regions. © 2004 by Taylor & Francis Group, LLC 176 REMOTE SENSING AND GIS ACCURACY ASSESSMENT Table 13.1 Number of Samples by Andersen Level I Classes Class Name Water Developed Barren Forested Upland Shrubland Nonnatural Woody Herbaceous Upland Natural/Seminatural Vegetation Herbaceous Planted/Cultivated Wetlands Total MRLC Code 11 20s 30s 40s 51 61 71 80s 90s No. of Samples 79 222 127 338 0 0 0 237 101 1104 Major analytical study elements were: (1) to define a multilevel agreement between sampled and mapped pixels, (2) to construct accuracy maps for six LC types, (3) to define cover-type-conversion degrees of membership for mapped pixels, (4) to develop a cover-type-conversion rule set for different conditions of accuracy and LC dominance, (5) to construct fuzzy LC maps, and (6) to develop landscape indicators from fuzzy LC maps. 13.2.1 Multilevel Agreement In the MRLC accuracy assessment performed by Yang et al. (2001), agreement was defined as a match between the primary or alternate reference cover-type label of the sampled pixel and a majority rule LC label in a 3 ¥ 3 window surrounding the sample pixel. Here we defined a multilevel agreement at a sampled pixel (Table 13.2) and applied it for all available sampled pixels. It has been demonstrated that the multilevel agreement went beyond the conventional binary agreement and covered a wide range of possible results, ranging from “conservative bias” (Verbyla and Hammond, 1995) to “optimistic bias” (Hammond and Verbyla, 1996). We define a discrete fuzzy set A (A = {(a1, m1),…,(a6, m6)}) representing the multilevel agreement at a mapped pixel regarding a specific cover type as follows: n dk Ik n dk p p k=1 k k=1 k i i Maxi Á n dk pk n dk ˜ Maxi(Mi ) k=1 k k=1 k (13.1) where ai, i = 1,…,6 are six different levels (or categories) of agreement at a mapped pixel; mi is fuzzy membership of the agreement level i of the pixel under study; d is the distance from sampled point k to the pixel (k ranges from 1 to n, where n is the number of nearest sampled points taken Table 13.2 Multilevel Agreement Definitions Levels Description I A match between the LC label of the sampled pixel and the center pixel’s LC type as well as a LC mode of the three-by-three window (662 sampled points) II A match between the LC label of the sampled pixel and a LC mode of the three-by-three window (39 sampled points) III A match between the LC label of the sampled pixel and the LC type of any pixel in the three-by-three window (199 sampled points) IV A match between the LC label of the sampled pixel and the LC type of any pixel in the five-by-five window (84 sampled points) V A match between the reference LC label of the sampled pixel and the LC type of any pixel in the seven-by-seven window (31 sampled points) VI Failed all of the above (89 sampled points) © 2004 by Taylor & Francis Group, LLC MAPPING SPATIAL ACCURACY AND ESTIMATING LANDSCAPE INDICATORS 177 into consideration); I is a binary function that equals 1 if the sampled point k has the agreement level i and 0 otherwise; p is the exponent of distance used in the calculation; and dk is the photographic interpretation confidence score of the sampled pixel k. As information on photographic interpretation confidence was not available for the Region III data set, dk was set as constant (dk = 1) in this study. The division by the maximum of Ai was to normalize the fuzzy membership function (Equation 13.1). Verbally, the fuzzy number of multilevel agreement at a mapped pixel defined in Equation 13.1 is a modified inverse distance weighted (IDW) interpolation of the n nearest sample points for each agreement level defined in Table 13.2. But instead of using all n data points together in the interpolation, as in conventional IDW for continuous data, the n sample pixels were divided into six separate groups based on their agreement levels and six iterations of IDW interpolation (one for each agreement level) were run. For each iteration of a particular agreement level, only those samples (among n sample pixels) with that agreement level would be coded as 1, while other reference samples were coded as 0 by the use of the binary function Ik. IDW then returned a value between 0 and 1 for Mi in each iteration. In other words, Mi is an IDW-based weight of sample pixels at the agreement level i among the n closest sample pixels surrounding the pixel under study. With the “winner-takes-all” rule, the agreement level with maximum M (i.e., maximum membership value mi = 1) will be assigned as the agreement level of the mapped pixel under study. After the multilevel agreement fuzzy set A was calculated (Equation 13.1), its scalar cardinality was computed as follows (Bárdossy and Duckstein, 1995): 6 car(A) = mi (13.2) i=1 Thus, the scalar cardinality of the multilevel agreement fuzzy set A is a real number between 1 and 6. This is an indicator of the agreement-level “homogeneity” of sampled pixels surrounding the pixel under study. If car(A) is close to 1, the majority of sampled pixels surrounding the mapped pixel under study have the same agreement level. Conversely, the greater car(A) is, the more heterogeneous in agreement levels the sampled pixels are. Note that there is another way for a mapped pixel to have a near 1 cardinality. That is when the distance between the mapped pixel and a sampled pixel is very close compared to those of other sampled pixels, reflecting the local effect in the IDW interpolation. However, this case occurs only in small areas surrounding each sampled pixel. 13.2.2 Spatial Accuracy Map Using the above equations, discrete fuzzy sets representing multilevel agreement and their cardinalities were calculated for all mapped pixels associated with a particular cover type. Then, the cardinality values of all pixels were divided into three unequal intervals (1–2, 2–3, and > 3). They were assigned (labeled) to the appropriate category, representing different conditions of agreement-level heterogeneity of neighboring sampled pixels. The three cardinality classes were then combined with six levels of agreement to create 18-category accuracy maps. 13.2.3 Degrees of Fuzzy Membership This step calculated the possible occurrence of multiple cover types for any given pixel(s) locations expressed in terms of degrees of fuzzy membership. This was done by comparing cover types of mapped pixels and sampled pixels at the same location based on individual pixels and a 3 ¥ 3 window-based evaluation. To illustrate, assume that the mapped pixel and the sampled pixel had cover types x and y, respectively. In the one-to-one comparison between the mapped and sampled pixels, if x and y are the same, then it is reasonable to state that the mapped pixel was classified correctly. In that case, the degree of membership for cover type x to remain the same is © 2004 by Taylor & Francis Group, LLC ... - tailieumienphi.vn