Geoscience Reference
In-Depth Information
The aim of the error matrix is to estimate the mapping accuracy (i.e., the
proportion of correctly mapped pixels) within an image. An error matrix is
constructed from points sampled from the image. The reference (or verifica-
tion) data are normally represented along the columns of the matrix, and are
compared with the classified (or image) data represented along the rows. The
major diagonal of the matrix represents the agreement between the two data
sets (table 11.3).
To check every cell for correctness would be impossible except in the small-
est map area, so various sampling schemes have been proposed to select pixels
to test. The design of the sampling strategy, the number of samples required,
and the area of the samples have been debated by the remote sensing and
GIS
community.
As with any sampling problem, one is obviously trying to select the sam-
pling design that gives the smallest variance and highest precision for a given
cost (Cochran 1977). A number of alternative designs have been proposed for
sampling the pixels to be used in constructing the error matrix. Berry and
Baker (1968) recommended the use of a stratified systematic sample.
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The
advantage of systematic sampling over random sampling is that sample units
are distributed equitably over the area. The disadvantage is that the resulting
sample is weighted in favor of the class covering the largest area and that classes
with a small area may not be sampled at all.
Simple random sampling in land evaluation surveys emphasizes larger areas
and undersamples smaller areas (Zonneveld 1974). Zonneveld (1974) sug-
gested that a stratified random sample was preferable, and Van Genderen et al.
(1978:1135) agreed that a stratified random sample is “the most appropriate
method of sampling in resource studies using remotely sensed data.”
Rosenfield et al. (1982; see Berry and Baker 1968) suggested a stratified
systematic unaligned sampling procedure (i.e., an area weighted procedure) as
a first-stage sample to assist in identifying categories occupying a small area,
followed by further stratified random sampling for classes with fewer than the
desired minimum number of points. Todd et al. (1980) argued that single-
stage cluster sampling is the cheapest sampling method because multiple
observations can be checked at each sample unit on the ground.
Congalton (1988) simulated five sampling strategies (simple random sam-
pling, stratified random sampling, cluster sampling, systematic sampling, and
stratified systematic unaligned sampling) using a different number of samples
over remotely sensed images of forest, rangeland, and grassland. The aim of the
study was to ascertain the effect of different sampling schemes on estimating
map accuracies using error matrices. He concluded that great care should be
