PE&RS April 1996

VOLUME 62, NUMBER 4
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
JOURNAL OF THE AMERICAN SOCIETY FOR PHOTOGRAMMETRY AND REMOTE SENSING

Peer-Reviewed Article Abstracts

377-391 Modeling Uncertainty in Photointerpreted Boundaries
G. Edwards and K.E. Lowell

Abstract
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A model based on multiple photointerpretations for estimating local boundary uncertainty (or 'fuzzy boundary width') between forest stands is developed and presented, using an artifical data set consisting of textured images of known class characteristics and locations. A fuzzy width estimator has been developed by breaking down the perceptual process of photointerpretion into two components: discrimination and variability. Discrimination consists of the ability of the photointerpreter to detect a difference in texture. Variability consists of the intrinsic spatial variability of the texture itself. A quantitative analysis of these effects led to a model relating the image construction parameters to the fuzzy boundary widths.

393-399 Evaluation of the Potential for Providing Secondary Labels in Vegetation Maps
Curtis E. Woodcock, Sucharita Gopal, and William Albert

Abstract
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For thematic maps made from remote sensing at the resolution of polygons, there are frequently more data available than the single class assigned to the polygon. One way of using these additional data is to provide secondary labels in maps. A key question concerns the reliability of these data. The optimistic view is that the distribution of classes at the pixel level is representative of the polygon, while the pessimistic view is that classifications are noisy and thus unreliable at this level of detail. Secondary labels for a vegetation map of the Plumas National Forest mirror the errors in the original vegetation map, indicating caution in the use of secondary labels. Results from the analysis of three decision rules indicate that class- conditional thresholds perform better than either of the approaches based on a single threshold.

401-407 Estimating the Kappa Coefficient and Its Variance Under Stratified Random Sampling
Steve Stehman

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The kappa coefficient of agreement is frequently used to summarize the results of an accuracy assessment used to evaluate land-use or land-cover classifications obtained by remote sensing. The standard estimator of the kappa coefficient along with the standard error of this estimator require a sampling model that is approximated by simple random sampling. Formulas are presented for estimating the kappa coefficient and its variance for stratified random sampling. Empirical results demonstrate that these estimators have little bias, and confidence intervals perform well, often even at relatively small sample sizes.

409-412 Unbiased Estimates of Class Proportions from Thematic Maps
Paul C. Van Deusen

Abstract
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A statistical overview is presented for estimating various components related to map accuracy assessment. The emphasis is on estimation of the true proportions of each map class under several common sampling designs. A complete system is presented for relating alternative approaches and estimators using standard rules of probability theory. Covariance matrices for estimates of true class proportions are derived in the Appendices for each of the sampling designs discussed.

413-417 Natural Constraints for Inverse Area Estimate Corrections
Ding Yuan

Abstract
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Though it has been used for marginal area estimate correction in image classification for years, the inverse correction technique has been the most controversial compared with several other marginal area estimate correction techniques, such as the direct and additive methods. In the reported practices, the inverse correction technique provided acceptable corrections to the marginal area estimates. In statistical simulation comparison, however, the inverse method was found unstable and systematically inferior to the direct method. Through theoretic analysis and discussions on the characteristics of inverse correction for image classification, the author concludes that (1) the inverse correction exists if the classifier is minimum practically acceptable and (2) the inverse is not ill-conditioned (ie it is stable) if the classifier is reasonably acceptable.

419-428 Error Propagation through the Buffer Operation for Probability Surfaces
Howard Veregin

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This study explores the propagation of error through the buffer operation in GIS. The study focuses on probability based raster databases, or probability surfaces, in which cell values show the probabilities associated with membership in different land-cover classes. Results indicate that there is a strong positive relationship between error levels in source and derived layers. The strength of the relationship is affected by the degree to which source probabilities tend to be under- or over-estimated, and by the interaction between buffer size and spatial covariation in source probabilities.

429-433 Estimating Positional Accuracy of Data Layers within a GIS through Error Propagation
Lawrence V. Stanislawski, Bon A. Dewitt, and Ramesh L. Shrestha

Abstract
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The positional accuracy of a GIS layer can be separated into absolute and relative components. Accepted standards for estimating horizontal accuracy in cartographic data quantify absolute positional accuracy only. However, relative accuracy values that describe variability in spatial relationships of coordinate information - such as variance of area, azimuth, and distance computations - can be valuable to research and decision making. This paper presents a technique for quantifying absolute and relative positional accuracy estimated through error propagation from a covariance matrix for affine transformation parameters. This technique was developed and tested with a spatial data set manually digitized from a simulated 1:24 000-scale map whose errors were restricted to those of the electrostatic plotter. A sequence of transformation tests was performed, using from 4 to 40 control points per test.