随着三维扫描技术的迅猛发展，高亏格的、具有丰富几何细节特征的、带有彩色纹理等多通道信息的几何数据已经大量涌现，它们的复杂结构以及相应几何信号的非线性非平稳性给几何分析和处理带来了极大的挑战。本项目拟从处理非线性非平稳信号的有效工具——HHT出发，针对其在几何数据上计算的关键问题进行研究，包括研究通过压缩感知和纹理几何分解理论得到三维几何信号稳定和鲁棒的IMF基底的计算方法，研究基于Riesz变换和单演信号理论的三维几何信号的Hilbert谱分析及特征空间的创建方法，研究通过逼近算子、空间降维、GPU并行计算等技术对大规模几何数据的HHT进行快速计算的方法。在此基础上，通过研究HHT在显著性检测、形状匹配和检索、编辑变形、几何数据修复等领域中的应用，形成一整套基于HHT的几何分析和处理方法，为数字几何的理论完善与HHT的广泛应用提供依据。

With the rapid advancement of 3D scanning technologies in recent decades, every day we are routinely acquiring tremendous amount of geometry data with complicated topology structures, rich geometry detail features, and multi-channel information such as color, texture, and material variations. The complex structures and non-linear and non-stationary properties of such geometry data will inevitably give rise to great challenges when conducting geometry analysis and processing in the most effective way. This project will start from the rigorous theory and powerful tool development or processing non-linear and non sationary signals---Hilbert-Huang Transform(HHT), and conduct comprehensive research on several critical theoretic and technical issues relevant to the HHT computation on geometry data. First of all, we will explore the new basis computation theories based on the compressed sensing and texture-eometry decomposition to attain stable, robust, multi-scale, intrinsic mode functions (IMFs). Such theoretic and technical undertakings were never attempted on geometry data with manifold structures. Second, we plan to perform Hilbert spectral analysis on manifold via Riesz transform and monogenic signals, which could be used to generate the feature space of geometry data serving as general signals. Third, we will devise new efficient and powerful algorithms to compute HHT on geometric data of tremendously large size by way of proximity operaters, dimensionality reduction, and GPU parallelization and acceleration technologies. Finally, we will undertake a suite of challenging application tasks based on the brand new HHT theory, including (but not just limited to) saliency visualization, shape matching and retrieval, geometry data repair, and shape editing and deformation, etc. The research outcomes of this project will offer a comprehensive set of new theories and techniques based on HHT for geometry analysis and processing. The anticipated success of our project could lay a sound technical foundation for the future technical advancement of digitial geomety theories as well as much more extensive applications of HHT in this "big data" era.