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

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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.