Uncertainty characterization in spatial categorical information

Abstract

Uncertainty is an integral component in thematic mapping, and descriptors such as percent correctly classified pixels (PCC) and Kappa coefficients of agreement have been devised as thematic accuracy metrics. However, such spatially averaged measures neither offer hints about spatial variation in accuracy, nor are they useful for error propagation in derivatives due to the deficiency that spatial dependency is not properly accommodated. Geostatistics provides a good framework for spatial uncertainty characterization, as conditional simulation is designed for generating equal-probable realizations of often sparsely sampled fields of concern, which can be summarized for error statistics or subjected to particular geo-processing to facilitate error propagation. Often, for modeling errors in area-class maps depicting distributions of spatial classes, stochastic indicator simulation is employed. Unfortunately, indicator approaches suffer from non-invariant behaviors in simulated classes as class labels are drawn from intervals of class probabilities that are arbitrarily ordered. Discriminant space-based models have been proposed to enhance consistency in mapping spatial classes and replicability in modeling spatial categorical uncertainty. This paper explores bivariate (rather than univariate) discriminant models and extends uncertainty modeling from single-time to bi-temporal area-class maps. Experiment using simulated data sets was carried out to quantify errors in area classes and their propagation in change analysis. It was found that there are significant differences between the results obtained by discriminant models and those by indicator geostatistics. Further investigations are anticipated incorporating real data for mapping and propagating errors in area classes.