本项目旨在探索三维人脸识别问题的微分几何建模方法，聚焦于解决非限制环境下三维人脸识别所面临的若干关键技术瓶颈问题：表情问题、姿态问题、遮挡问题、数据质量及曲率估计问题。针对上述问题，将深入研究：1. 基于拟共形映射和Beltrami系数的非刚性形变人脸曲面配准问题；2. 基于对称共形映射和Ricci流理论的非完整缺失人脸曲面配准及补齐问题；3. 基于黎曼曲面共形表示理论的非完整遮挡人脸曲面遮挡检测、去除及修复问题；4. 基于Ricci流理论和Normal Cycle理论的低质量人脸曲面网格重采样及鲁棒性广义曲率估计问题。在此基础上，进一步探索和评估基于Beltrami系数、共形因子、曲率等特征的三维人脸匹配和识别算法。该项目属于应用基础类研究课题，课题研究将促进微分几何、黎曼几何等基础学科与模式识别、图形学等应用学科的深入交叉，也将推动三维人脸识别迈向实用化，具有重要的学术意义和应用价值。

Aiming at developing three-dimensional (3D) face recognition approaches based on differential geometry theories and algorithms, this proposed project focuses on dealing with the following challenging bottleneck problems for three-dimensional face recognition in uncontrolled environments. They are the expression problem, pose problem, occlusion problem, as well as the data quality and curvature estimation problem. All of these problems will be deeply studied based on the Ricci flow and the Normal Cycle theories. Particularly, four research directions will be considered: 1. large expression deformation non-rigid facial surface registration based on the quasi-conformal mapping theory and the Beltrami coefficients; 2. large pose caused partial facial surface registration based on the symmetric conformal mapping and Ricci flow; 3. occlusion detection, removing and reconstruction for partial occluded facial surface based on the Riemann surface conformal representation theory; 4. high-quality facial mesh generation and robust generalized curvatures estimations based on the Ricci flow and normal cycle theories. Furthermore, we will develop and test new three-dimensional face matching and recognition algorithms based on the Beltrami coefficients, conformal factor, as well as curvature features, etc.. This project is a fundamental and applied research topic, and it will accelerate the deeply fusion of the fundamental subjects such as differential geometry, Riemannian geometry and the applied subjects such as pattern recognition and graphics, and it will also accelerate the development of three-dimensional face recognition for real-life applications. Thus, we say that this project has very important academic significance and application value.