CDI-Type I: Geometric image analysis for computational knowledge discovery in geosciences

地球地形的研究对社会有着根本性的影响，从洪水和滑坡的预防和控制到对气候变化影响的理解，土地使用实践的管理，以及以环境可持续的方式设计道路和其他人造项目。最近通过机载激光测绘和地面激光雷达获得的高分辨率（0.5 m间距）数字地形为开发一类新的环境预测模型提供了机会，这些模型明确地包含了景观的重要特征，从而提高了预测的准确性。该项目的目标是发展适用于水文和生态地貌灾害预测和控制的现代计算几何图像分析方法。具体而言，该项目研究高分辨率、多尺度和动态地形，目标是提取河道网络、河道堤岸和形状、洪泛平原和与危险相关的特征，如滑坡易发地区和服务道路，这些特征会导致泥沙产量增加，从而导致河流栖息地恶化。要开发和发展的数学和计算技术来自几何非线性偏微分方程和能量公式领域，结合微分和计算几何。具体地说，从几何尺度空间理论到奇点理论和几何变分原理的方法组合，结合计算曲面上特殊曲线的最佳算法，将被用来在多个相关尺度上推导出完整和自动的地形分析。

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.