在艺术品制造、建筑装饰、影视动画等领域中，存在大量具有丰富几何细节特征的复杂几何模型，它们的研究与应用为数字几何处理带来了困难和挑战。本项目拟从处理非平稳信号的有效工具- - EMD出发，针对将经典一维EMD理论推广到三维几何曲面上存在的基本问题，诸如三维几何信号IMF的定义、流形薄板样条插值与逼近、三维几何信号的EMD方法、分解准确性的评价标准等进行研究，以建立能够处理任意复杂几何模型的EMD理论和方法。在此基础上，通过EMD的多尺度自适应分解特性，研究保特征的多尺度平滑去噪方法，提高复杂几何模型平滑去噪的质量；研究基于EMD的多尺度自适应增强方法，解决复杂几何模型特征增强中出现的大尺度变形问题；研究基于EMD的快速编辑变形技术，使得复杂几何模型在编辑变形过程中能较好的兼顾变形质量和效率。最终形成一套比较完整的基于EMD的复杂几何模型的处理理论和方法，为数字几何处理研究的完善提供依据。

There are many complicated geometry models with abundant geometry details and features in artwork manufacture, architecture and decoration, movie and animation, and so on. The researches and applications of them bring some challenges and difficulties to digital geometry processing. This project will start from the powerful tool for processing non-sationary signals- - -EMD(Empirical mode decomposition), and do some research on several problems brought by extending the 1D EMD therory to 3D geometry surfaces, such as the definition of IMF of 3D geometry signals, interploation and approximation by thin plate splines on manifold, EMD algorithm of 3D geometry signals, the evaluation standard of decompostion by EMD, and so on. It's aim is to build the theory and algorithm about EMD of 3D geometry signals for arbitrary complicated geometry models. And then, according to the multiscale adptive decomposition of EMD, the project intends to do some research on the multiscale technique based on EMD for denoisiong complicated geometry models in order to improve the denoising results; the project also intends to do some research on the multiscale adptive enhancement technique based on EMD in order to solve the large distortion problem during feature enhancement of complicated geometry models; Besides, the projects intends to do some research on the fast editing and deformation techniques based on EMD in order to get a good tradeoff on the efficiency and quality when editing and deformation of complicated geometry models. Finally, this project will get a series of theories and techniques based on EMD for processing complicated geometry models, which will provide some basises for the perfection of the research of digitial geomety processing.