Geoscience Reference
In-Depth Information
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
