CAREER: Signal Processing for Surfaces

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Complex geometry becomes increasingly common in applicationsarising in diverse areas. Plastic surgeons use computermodels to plan and perform operations. Mechanical engineersvirtually assemble and test cars and planes. Animatorscreate complex characters and effects indistinguishable fromreality. Geometric modeling has found its way into artconservation: it is now feasible to create computer modelsof sculptures capturing the most subtle of details.Increasing complexity of geometric data calls for newefficient representations and algorithms. The goal of ourlong-term research plan is to study representations ofcomplex geometric data, surfaces in particular. We plan tolaunch a broad and fundamental program to explore threetypes of representations: piecewise-smooth surfaces,multiscale surfaces and combined volume-surfacerepresentations. Our approach to designing complex surfacerepresentations is based on the concept of subdivision, apowerful technique for modeling smooth surfaces. Subdivisionalgorithms, while being more flexible and general, retain anumber of useful properties of splines. Most importantly,the surfaces generated by these algorithms have a naturalhierarchical structure and are computed using efficientlocal rules; subdivision algorithms can be easily extendedto represent multiscale data. The general goal of ourresearch is to design representations supporting efficientalgorithms for construction, rendering, manipulation,processing, transmission and storage of surface data. Wewill explore in close coordination both theoreticalproperties of these representations (regularity, convergencerates, fairness, stability) and their practicalapplications. The specific goal of the proposed project isto generalize to surfaces the signal processing tools thatwere designed and are extensively used for images. Theresearch program is integrated with the education plan,which has three main goals: (1) prepare graduate studentsfor research in computer graphics and related areas, (2)incorporate the latest advances in research into curriculumat all levels, including undergraduate, and engage motivatedundergraduate students in research (3) transfer knowledgeabout latest research advances to professionals in theindustry.