Geoscience Reference
In-Depth Information
14.1.2.2
Fuzzy Set Analysis
An alternative method of analysis of thematic accuracy uses fuzzy set theory (Zadeh, 1965).
Adapted from its original application to describe the ability of the human brain to understand vague
relationships, Gopal and Woodcock (1994) developed fuzzy set theory for thematic accuracy
assessment of digital maps. A fuzzy set analysis provides more information about the degree of
agreement between the reference and mapped cover types. Instead of a right or wrong analysis,
map labels are considered partially right or partially wrong, generally on a five-category scale. This
is more useful for assessing vegetation types that may grade into one another yet must be classified
into discrete types by a human observer (Gopal and Woodcock, 1994). The fuzzy set analysis
provides a number of measures with which to judge the accuracy of a LC map.
Fuzzy set theory aids in the assessment of maps produced from remotely sensed data by
analyzing and quantifying vague, indistinct, or overlapping class memberships (Gopal and Wood-
cock, 1994). Distinct boundaries between LC types seldom exist in nature. Instead, there are often
gradations from one cover (vegetation) type to another. Confusion results when a location can
legitimately be labeled as more than one cover type (i.e., vegetation transition zones). Unlike a
binary assessment, fuzzy set analysis allows partial agreement between different LC types. Addi-
tionally, the fuzzy set analysis provides insight into the types of errors that are being made. For
example, the misclassification of ponderosa pine woodland as juniper woodland may be a more
acceptable error than classifying it as a desert shrubland. In the first instance, the misclassification
may not be important if the map user wishes to know where all coniferous woodlands exist in an area.
14.1.2.3
Spatial Analysis
Advanced techniques in assessing the thematic accuracy of maps are continually evolving. A
new technique proposed in this chapter uses the spatial locations of the reference data to interpolate
accuracy between sampling sites to create a continuous spatial view of accuracy. This technique is
termed a
thematic spatial analysis
; however, it should not be confused with assessing the
spatial
error of the map. The thematic spatial analysis portrays thematic accuracy in a spatial context.
Reference data inherently contain spatial information that is usually ignored in both binary and
fuzzy set analyses. For both analyses, the spatial locations of the reference data are not utilized in
the summary statistics, and results are given in tabular, rather than spatial, format. The most
fundamental drawback of the confusion matrix is its inability to provide information on the spatial
distribution of the uncertainty in a classified scene (Canters, 1997). A thematic spatial analysis
addresses this spatial issue by using the geographic locations gathered using a global positioning
system (GPS) with the reference data. These locations are used in an interpolation process to assign
accuracy to locations that were not directly sampled. Accuracy is not tied to cover type, but rather
to the location of the reference sites. Therefore, accuracy can be displayed for specific locations
on the LC map.
Data that are close together in space are often more alike than those that are far apart. This
spatial autocorrelation of the reference data is accounted for in spatial models. In fact, spatial
models are more general than classic, nonspatial models (Cressie, 1993) and have less-strict
assumptions, specifically about independence of the samples. Therefore, randomly located reference
data will be accounted for in a spatial model.
Literature on the spatial variability of thematic map accuracy is limited. Congalton (1988)
proposed a method of displaying accuracy by producing a binary difference image to represent
agreement or disagreement between the classified and reference images. Fisher (1994) proposed a
dynamic portrayal of a variety of accuracy measures. Steele et al. (1998) developed a map of accuracy
illustrating the magnitude and distribution of classification errors. The latter used kriging to inter-
polate misclassification estimates (produced from a bootstrapping method) at each reference point.
The interpolated estimates were then used to construct a contour map showing accuracy estimates
