Continuous-valued map reconstruction with the Bayesian Maximum Entropy

Thematic maps are one of the most common tools for representing the spatial variation of a variable. They are easy to interpret thanks to the simplicity of presentation: clear boundaries define homogeneous areas. However, especially when the variable is continuous, abrupt changes between cartographic units are often unrealistic and the intra-unit variation is hidden behind a single representative value. In many applications, such non-natural transitions are not satisfactory as is the poor precision of such maps. As additional samples are often cost prohibitive, one should try to use the information in the available map to evaluate the spatial variation of the variable under study. This paper shows how the Bayesian Maximum Entropy (BME) approach can be used to achieve such a goal using only the vague (soft) information in the map. BME is compared to a method frequently used in soil sciences: the legend quantification method. It is illustrated first on a simulated case study that BME increases noticeably the precision of the estimates. Resulting BME maps have smooth transitions between mapping units which is conform to the expected behavior of continuous variables. These observations are then corroborated in a real case study where the sand, silt and clay contents in soils have to be estimated from a soil map. (C) 2002 Elsevier Science B.V All rights reserved.