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17.1. Therefore, the adjusted forgery would appear similar to Figure 17.1; however, the light cells
of Figure 17.1 would be a smooth mix of light and dark, while the dark cells would still be completely
dark. Specifically, the light cells would be adjusted to be 2/3 light and 1/3 dark; hence, the total
amount of light and dark paint in the forgery would equal the total amount of light and dark paint
in the masterpiece. As a result, the agreement between the adjusted forgery and the masterpiece
would be larger than 12/16. The exact agreement would require that we define the agreement between
the light cells of the masterpiece and the partially light cells of the adjusted forgery.
The above analogy prepares the reader for the technical description of the analysis in the
Methods section. In the analogy, the reference map is the masterpiece that represents the ground
information, and the comparison map is the forgery that represents the classification of a remotely
sensed image. The classification rule of the remotely sensed image represents the scientist's best
attempt to replicate the ground information. In numerous conversations with our colleagues, we
have found that it is essential to keep in mind the analogy of painting a forgery. We have derived
all the equations in the Methods section based on the concepts of the analogy.
17.2 METHODS
17.2.1
Example Data
Categorical variables consisting of “forest” and “nonforest” are represented in three maps of
example data (Figure 17.2). Each map is a grid of 12
12 cells. The 100 nonwhite cells represent
the study area and the remaining 44 white cells are located out of the study area. We have purposely
made a nonsquare study area to demonstrate the generalized properties of the methods. The methods
apply to a collection of any cells within a grid, even if those cells are not contiguous, as is typically
the case in accuracy assessment. Each map has the same nested stratification structure. The coarser
stratification consists of two strata (i.e., north and south halves) separated by the thick solid line.
The finer stratification consists of four substrata quadrates of 25 cells each, defined as the northeast
(NE), northwest (NW), southeast (SE), and southwest (SW). The set of three maps illustrates the
common characteristics encountered when comparing map classification rules. Imagine that Figure
17.2 represents the output maps from a standard classification rule (COM1), alternative classification
rule (COM2), and the reference data (REF). Typically, a statistical test would be applied to assess
the relative performance of the two classification approaches and to determine important differences
with respect to the reference data. However, it would also be helpful if such a comparison would
offer additional insights concerning the sources of agreement and disagreement.
Table 17.1a and Table 17.1b represent the standard confusion matrix for the comparison of
COM1 and COM2 vs. REF. The agreement in Table 17.1a and Table 17.1b is 70% and 78%,
respectively. Note that the classification in COM2 is identical to the reference data in the south
stratum. In the north stratum, COM2 is the mirror image of REF reflected through the central
vertical axis. Therefore, the proportion of forest in COM2 is identical to that in REF in both the
north and south strata. For the entire study area, REF is 45% forest, as is COM2. COM1 is 47%
forest. A standard accuracy assessment ends with the confusion matrices of Table 17.1.
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17.2.2
Data Requirements and Notation
We have designed COM1, COM2, and REF to illustrate important statistical concepts. However,
this chapter's statistical techniques apply to cases that are more general than the sample data of
Figure 17.2. In fact, the techniques can compare any two maps of grid cells that are classified as
any combination of soft or hard categories.
This means that each grid cell can have some membership in each category, ranging from no
membership (0) to complete membership (1). The membership is the proportion of the cell that
