Towards a systems approach to the visualization of spatial uncertainty

Phaedon C. Kyriakidis
Department of Geography 
University of California Santa Barbara
Santa Barbara, CA 93106-4060, USA
Tel.: + 001 805 893 2266; Fax: + 001 805 893 3146

Most existing approaches for spatial uncertainty visualization are concerned with the depiction of local or per-pixel uncertainty measures, such as standard errors of attribute prediction in a spatial interpolation setting or posterior probabilities of class occurrence in a classification setting. Most vision operations, however, are pattern-detection endeavors, which are by definition multi-pixel in nature. Consequently, per-pixel uncertainty measures cannot adequately characterize uncertainty in the outcomes of vision operations applied on maps. To overcome the above limitations, a formal quantitative framework for  the visualization of spatial uncertainty is advocated, building on an analogy from engineering systems. A system is a model of some aspect or process of the  real world, often approximated by a set of mathematical equations, which is excited by a set of inputs to produce a set of outputs or model predictions. In a similar fashion, a map  user can be viewed as a system: his or her visual perception and cognition are extremely complex operations that via map analyses lead to decisions and actions. In analogy with engineering systems, quantification of the impact of an uncertain input map on vision-related tasks requires that these tasks be applied to a set of alternative input maps, all of which are processed by the user to arrive at a set of possible analysis results. The proposed framework can thus be seen as a two-step data mining endeavor: (i) exploration of the attribute uncertainty model via stochastic simulation by generating alternative, synthetic, attribute realizations, and (ii) exploration the outputs of early-vision operations applied on this set of realizations in meaningful ways that enable the user to distill the uncertainty in these outputs.

Keywords: spatial uncertainty assessment, geostatistical simulation, early-vision operations, image segmentation

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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