Geoscience Reference
In-Depth Information
Gopal and Woodcock (1994) proposed the use of fuzzy sets to “allow for explicit recognition
of the possibility that ambiguity might exist regarding the appropriate map label for some locations
on a map. The situation of one category being exactly right and all other categories being equally
and exactly wrong often does not exist.” They allowed for a variety of responses, such as absolutely
right, good answer, acceptable, understandable but wrong, and absolutely wrong. While dealing with
the ambiguity, this approach does not allow the accuracy assessment to be reported as an error matrix.
This chapter introduces a technique using fuzzy accuracy assessment that allows for the analyst
to incorporate the variation or ambiguity in the map label and also present the results in the form
of an error matrix. This approach is applied here to a worldwide mapping effort funded by the
National Imagery and Mapping Agency (NIMA) using Landsat Thematic Mapper (TM) imagery.
The Earth Satellite Corporation (Earthsat) performed the mapping and Pacific Meridian Resources
of Space Imaging conducted the accuracy assessment. The results presented here are for one of
the initial prototype test areas (for an undisclosed location of the world) used for developing this
fuzzy accuracy assessment process.
12.2 BACKGROUND
The quantitative accuracy assessment of maps produced from remotely sensed data involves
the comparison of a map with reference information that is assumed to be correct. The purpose of
a quantitative accuracy assessment is the identification and measurement of map errors. The two
primary motivations include: (1) providing an overall assessment of the reliability of the map (Gopal
and Woodcock, 1994) and (2) understanding the nature of map errors. While more attention is often
paid to the first motivation, understanding the errors is arguably the most important aspect of
accuracy assessment. For any given map class, it is critical to know the probability of the site's
being labeled correctly and what classes are confused with one another. Quantitative accuracy
assessment provides map users with a consistent and objective analysis of map quality and error.
Quantitative analysis is fundamental to map use; without it, users would make decisions without
knowing the reliability of the map as a whole or the sources of confusion.
The error matrix is the most widely accepted format for reporting remotely sensed data clas-
sification accuracies (Story and Congalton, 1986; Congalton, 1991). Error matrices simply compare
map data to reference data. An error matrix is an array of numbers set out in rows and columns
that expresses the number of pixels or polygons assigned to a particular category in one classification
relative to those assigned to a particular category in another classification (Table 12.1). One of the
classifications is considered to be correct (reference) and may be generated from aerial photography,
airborne video, ground observation, or ground measurement, while the other classification is
generated from the remotely sensed data (observed).
An error matrix is an effective way to represent accuracy because both the total and the individual
accuracies of each category are clearly described and confusion between classes is evident. Also
indicated are errors of inclusion (commission errors) and errors of exclusion (omission errors) that
may be present in the classification. A commission error occurs when an area is included into a
category when it does not belong. An omission error is excluding an area from the category in
which it does belong. Every error is an omission from the correct category and a commission to a
wrong category. For example, in the error matrix in Table 12.1 four areas were classified as
deciduous but the reference data showed that they were actually coniferous. Therefore, four areas
were omitted from the correct coniferous category and committed to the incorrect deciduous
category. Utilizing this information, users can ascertain the relative strengths and weaknesses of
each map class, creating a more solid basis for decision making.
Additionally, the error matrix can be used to compute overall accuracy and producer's and
user's accuracies (Story and Congalton, 1986). Overall accuracy is simply the sum of the major
diagonal (i.e., the correctly classified sample units) divided by the total number of sample units in
