A Multi-resolution Approach to Modeling and Visualizing Multi-dimensional Scalar Fieldsu

教育部分紧密地整合到拟议的研究计划中，包括生产用于形状建模和可视化的软件工具。我们计划在计算机图形学和几何建模的研究生课程中使用这些工具，并将它们分发给科学界。所提出的研究的智力价值在于通过创新的多分辨率模型增强了当前分析和可视化时变标量场的工具的能力。这不仅可以减少复杂性和结果表示的大小，还可以有效地集中在显著的可视化特征上。另一个重要的挑战是通过开发新的多尺度形态模型来增强多分辨率表示。这将允许为多维标量场设计新的外部表示，它还将支持分层方法来分析、可视化和理解多维科学数据集。本研究的更广泛影响在于对大型科学数据集和动态三维形状的分析、理解和可视化，从而加强可视化、计算机图形学和可视化数据挖掘方面的创新研究。这项研究将极大地受益于许多应用领域，包括科学计算、生物医学工程、外科模拟、动画和文化遗产。

The educational component is tightly integrated into the proposed research plan, that includes producingsoftware tools for shape modeling and visualization. We plan to use such tools in graduate courses onComputer Graphics and Geometric Modeling, and distribute them to the scientific community.The intellectualmerit of the proposed research lies in enhancing the power of current tools for analyzingand visualizing time-varying scalar fields through innovative multi-resolution models. This will not onlyreduce the complexity and the size of the resulting representations, but will allow effectively focusing onsalient visualization features. An other important challenge is to enhance multi-resolution representationsthrough the development of new multi-scale morphological models. This will allow designing new out-ofcorerepresentations for multi-dimensional scalar fields and it will also support a hierarchical approach toanalyzing, visualizing and understanding multi-dimensional scientific data sets.The broader impact of the proposed research lies in the analysis, understanding and visualization of large scientific data sets, and of dynamic 3D shapes, thus enhancing innovative research in visualization, computer graphics and visual data mining. Many application fields will highly benefit from this research, including scientific computing, biomedical engineering, surgical simulation, animation, and cultural heritage.