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stage samples are chosen for their diversity, this indicates that the entire map also has no or few
polygons with these classes. Considering the location of the prototype, it is reasonable to assume
that ice/snow, agriculture-rice, and mangrove do not exist in the area. However, a few reference
sites (
= 5) were labeled barren/sparse vegetation and wet, permanent herbaceous, indicating that
these classes do exist in the area and may be underrepresented in the map.
The error matrix or contingency table has become widely accepted as the standard method for
reporting the accuracy of GIS data layers derived from remotely sensed data. The matrix provides
descriptive statistics including overall, producer's, and user's accuracies as well as sample size
information by category and in total. In addition, the matrix is a starting point for a variety of
analytical tools, including normalization and Kappa analysis. More recently, the incorporation of
fuzzy accuracy assessment has been suggested and adopted by many remote sensing analysts. As
proposed, most of these current techniques use a variety of metrics to represent the fuzzy analysis.
This chapter introduces the use of a fuzzy error matrix for applying fuzzy accuracy assessment.
The fuzzy matrix has the same benefits as a traditional deterministic error matrix, including the
computation of all the descriptive statistics. A detailed, practical case study is presented to dem-
onstrate the application of this fuzzy error matrix.
A total of 311 accuracy assessment sites were utilized to estimate the accuracy of the initial
prototype area. The traditional estimate of overall accuracy is 48.6%. Accounting for fuzzy class
membership and variation in interpretation, overall accuracy is estimated at 74%. The spread
between the deterministic and fuzzy assessment estimates is large, but not unusual. Part of this
spread is a function of the lack of NTM for several of the reference sites (
= 84), resulting in the
reference label's being determined from manual interpretation of the TM data. Hopefully, more
NTM will be available as the project progresses, which will reduce the spread between deterministic
and fuzzy logic estimates. However, some spread will remain because of fuzziness in the boundaries
of LC classes. Therefore, acceptable fuzziness between deciduous and evergreen forest (especially
in mixed conditions) and deciduous forest and shrub will remain.
Congalton, R., A comparison of sampling schemes used in generating error matrices for assessing the accuracy
of maps generated from remotely sensed data,
, 54, 587-592, 1988.
Congalton, R., A review of assessing the accuracy of classifications of remotely sensed data,
Photogram. Eng. Remote Sens.
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Congalton, R. and G. Biging, A pilot study evaluating ground reference data collection efforts for use in forest
58, 1669-1671, 1992.
Congalton R. and K. Green, A practical look at the sources of confusion in error matrix generation,
Photogram. Eng. Remote Sens.,
59, 641-644, 1993.
Congalton, R. and K. Green,
Eng. Remote Sens.,
Assessing the Accuracy of Remotely Sensed Data: Principles and Practices,
Lewis Publishers, Chelsea, MI, 1999.
Gong, P. and J. Chen, Boundary Uncertainties in Digitized Maps: Some Possible Determination Methods, in
Proceedings of GIS/LIS'92, San Jose, CA, 1992, pp. 274-281.
Gopal, S. and C. Woodcock, Theory and methods for accuracy assessment of thematic maps using fuzzy sets,
, 60, 181-188, 1994.
Lowell, K., On the Incorporation of Uncertainty into Spatial Data Systems
Photogram. Eng. Remote Sens.
Proceedings of GIS/LIS'92
San Jose, CA, 1992, pp. 484-493.
Story, M. and R. Congalton, Accuracy assessment: a user's perspective,
Photogram. Eng. Remote Sens.,
397-399, 1986.
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