The uncertainty visualization problem in remote sensing analysis

Remote sensing analyses usually result in maps of discrete or continuous variables. Ideally, each value in such a map should be accompanied by an uncertainty description, that is, a quantitative statement about the probability of error. A full description of uncertainty at each pixel is usefully represented using a probability distribution. Such a probability distribution may be based on an understanding of potential errors in position, spatial support (the area measured by the sensor's field of view), model parameters, the model structure, and the input variables to the model. Visualizing uncertainty in the products of remote sensing analysis presents the challenge that at least four dimensions are required. These are the spatial dimensions (x and y), the dimension of the variable being mapped and finally the probability dimension. Current visualization tools and techniques do not support these data sets directly. Even animation, a logical choice to represent other four dimensional problems, is not fully satisfactory for probability distribution data sets. We have first addressed the problem of visualizing uncertainty by creating interactive maps of first, second and third order statistics summarizing the distributions. Next, we have experimented with shaded surface rendering of distributions from a user-selectable profile (row or column) in the image. We demonstrate these methods using a data set generated by a geostatistical conditional simulation algorithm and a single band image and we discuss the future promise of visualizing all four dimensions at once.