Geomorphologic mapping from hyperspectral data, using Gaussian mixtures and lower confidence bounds

Abstract

Probabilistic classification under the Gaussian mixture model is normally based on posterior probability (p.p.) estimates of class membership. The question, how accurate they are for a given pixel, is traditionally left without attention, which may lead to unreasonable optimism about the classification results obtained. Addressing the issue, Koltunov and Ben‐Dor have proposed an unsupervised, lower confidence bound (l.c.b.)‐based method for thematic interpretation of remote sensing data. This method predicts the sampling properties of the p.p. estimators of a given pixel, to assess reliability of the estimates. The present paper describes a modified version of the method. In particular, instead of defining the l.c. bounds in terms of two first moments of the sampling distribution, as has been suggested previously, we use percentiles. Combining this with a probabilistic model of supervised identification of the mixture components yields the post‐classification uncertainty value for a given pixel and the confidence level, at which this value is proven to be maximal. In the application to an arid landscape in the Southern Negev desert, Israel, the compressed raw hyperspectral data acquired by the Digital Airborne Imaging Spectrometer (DIAS‐7915) was clustered once, whereas two thematic tasks were solved corresponding to different map legends, identification procedures, and the associated requirements to the level of detail and reliability of the thematic maps. The reference data collected in the field have provided evidence for accurate algorithmically estimated confidence bounds of the classification quality. The classification has revealed new information about the geomorphological subunits forming the study area.

Acknowledgements

This research was supported by the German–Israeli Scientific Foundation (GIF), under grant I‐547‐177.02/97. The authors are grateful to Michael Beyth from the Geological Survey of Israel and Dov Avigad from the Geology Department, The Hebrew University of Jerusalem, for their valuable contributions to the project. Thanks also go to the German Aerospace Center (DLR) for conducting the DAIS‐7915 flight. We acknowledge the helpful remarks of Michael Whiting from CalSpace Center of Excellence, University of California, Davis. Lastly, we appreciate the six anonymous reviewers for their very constructive comments on the earlier versions.

Notes

1. see our remark on the term ‘unsupervised’ in § 1