Adaptive Curvature-Based Topography for Learning Symbolic Descriptions of Terrain Maps

We present an adaptive curvature scale space technique for extracting symbolic topographical descriptions from image data such as that of three dimensional digital terrain maps where specific image interpretation constraints play a significant role in defining the scale of analysis. In our approach we use machine learning techniques to learn efficient segmentation of image data, the Topograph, which satisfies the constraints of the application task and guarantees the quality of the solutions returned. The Topograph representation is evaluated empirically using a flight trajectory planning application where the problem involves minimising the integral under the path (sum of altitude) while satisfying the constraints of flight. It is shown how the Topograph hierarchy can be used to guarantee lower bounds on solutions for search problems of this nature by incorporating multiple resolution states and using dynamic programming techniques.