ABSTRACT

The study of earth's topography has fundamental impacts on society, from flood and landslide prevention and control to the understanding of climate change impacts, management of land-use practices, as well as design of roads and other man-made projects in an environmentally sustainable way. The recent availability of high resolution (0.5 m spacing) digital topography from airborne laser swath mapping and ground-based lidar offers opportunities to develop a new class of environmental predictive models that explicitly incorporate important features of the landscape and thus enhance the accuracy of predictions. The goal of this project is to develop modern computational geometric image analysis methodologies applicable to hydrologic and eco-geomorphologic hazard prediction and control. Specifically, the project studies high-resolution, multiscale, and dynamic topography with the goal of extracting channel networks, channel banks and shapes, floodplains and hazard-relevant features such as landslide prone areas and service roads which contribute to increased sediment production and thus stream habitat deterioration.
The mathematical and computational techniques to be exploited and developed come from the area of geometric non-linear partial differential equations and energy formulations, combined with differential and computational geometry. Specifically, a combination of methodologies ranging from geometric scale-space theory to singularity theory and geometric variational principles, combined with optimal algorithms for computing special curves on surfaces, will be exploited to derive a complete and automatic analysis of the topography at multiple relevant scales.

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