Geoscience Reference
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remotely sensed imagery can evaluate the appropriateness of different maps on their particular
application and subsequently decide to retain one classification vs. another.
Accuracy statistics, however, express different aspects of classification quality and consequently
appeal differently to different people, a fact that hinders the use of a single measure of classification
accuracy (Congalton, 1991; Stehman, 1997; Foody, 2002). Recent efforts to provide several mea-
sures of map accuracy based on map value (Stehman, 1999) constitute a first attempt to address
this problem, but in practice map accuracy is still communicated in the form of confusion-matrix-
based accuracy statistics. The confusion matrix, and all derived accuracy statistics, however, is a
regional (location-independent) measure of classification accuracy: it does not pertain to any pixel
or subregion of the study area. For example, user's accuracy denotes the probability that any pixel
classified as forest is actually forest on the ground. In this case, all pixels classified as forest have
the same probability of belonging to that class on the ground, a fact that does not allow identification
of pixels or subregions (of the same class) that warrant additional sampling. A new sampling
campaign based on this type of accuracy statistic would just place more samples at pixels allocated
to the class with the lower user's accuracy measure, irrespective of the location of these pixels and
their proximity to known (training) pixels. In other words, confusion-matrix-based accuracy assess-
ment has no explicit spatial resolution; it only has explicit class resolution.
In this chapter, we capitalize on the fact that conventional (hard) class allocation is typically
based on the probability of class occurrence at each particular pixel calculated during the classifi-
cation procedure. Maps of such posterior probability values portray the spatial distribution of
classification quality and are extremely useful supplements to traditional accuracy statistics (Foody
et al., 1992). As opposed to confusion-matrix-based accuracy assessment, such maps could identify
pixels of the same category where additional sampling is warranted, based precisely on a measure
of uncertainty regarding class occurrence at each particular pixel.
Evidently, the above classification uncertainty maps will depend on the classification algorithm
adopted. Conventional classifiers typically use the information brought by reflectance values (fea-
ture vector) collocated at the particular pixel where classification is performed. In some cases,
however, classes are not easily differentiated in the spectral (feature) space, due to either sensor
noise or to the inherently similar spectral responses of certain classes. Improvements to the above
classification procedures could be introduced in a variety of ways, including geographical stratifi-
cation, classifier operations, postclassification sorting, and layered classification (Hutchinson, 1982;
Jensen, 1996; Atkinson and Lewis, 2000). The above methods enhance the classification procedure
by introducing, explicitly or implicitly, contextual information (Tso and Mather, 2001). Within this
contextual classification framework, one of the most widely used avenues of incorporating ancillary
information is that of pixel-specific prior probabilities (Strahler, 1980; Switzer et al., 1982).
Along these lines, we propose a simple, yet efficient, method for modeling pixel-specific context
information using geostatistics (Isaaks and Srivastava, 1989; Cressie, 1993; Goovaerts, 1997).
Specifically, we adopt indicator kriging to estimate the conditional probability that a pixel belongs
to a specific class, given the nearby training pixels and a model of the spatial correlation for each
class (Journel, 1983; Solow, 1986; van der Meer, 1996). These context-based probabilities are then
combined with conditional probabilities of class occurrence derived from a conventional (noncon-
textual) classification via Bayes' rule to yield posterior probabilities that account for both spectral
and spatial information. Steele (2000) and Steele and Redmond (2001) used a similar approach
based on Bayesian integration of spectral and spatial information, the latter being derived using
the nearest neighbor spatial classifier. In this work, we also use Bayes' rule to merge spatial and
spectral information, but we use the indicator kriging classifier that incorporates texture information
via the indicator covariance of each class. De Bruin (2000) and Goovaerts (2002) also adopted
similar approaches using indicator kriging but did not link them to contextual classification. This
research extends the above approaches in a formal contextual classification framework and illus-
trates their use for mapping thematic classification uncertainty.
