利用空间曲线内蕴几何特征的三维模型表达方法研究

项目名称： 利用空间曲线内蕴几何特征的三维模型表达方法研究

项目编号： No.41301406

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 天文学、地球科学

项目作者： 蓝秋萍

作者单位： 河海大学

项目金额： 25万元

中文摘要： 空间曲线几何特征显著、表达形式简洁。课题探索了完全利用特征空间曲线表达三维模型的方法，考虑到骨架能够支撑模型结构，轮廓线和结构线能够支撑模型的表面几何形态，为了适应三维点云模型的互联网应用需求，提出了"以骨架为轴、以结构线为经、以轮廓线为纬"的模型表达思路。空间曲线内蕴几何特征具有极强的曲线形态自描述能力，课题深入发掘这些内蕴特征的物理含义，探索利用内蕴几何特征实现空间曲线匹配和姿态估计的方法，并设计从三维点云中提取骨架曲线、关键断面轮廓线、模型表面结构线（脊线、谷线）和特征点间测地线这四种模型特征曲线的方法，以及三维骨架自描述和以骨架为活动参考的模型表面特征几何关系描述方法，并在此基础上探索几何约束下，兼顾结构拓扑和表面几何形态的三维模型精确匹配和快速重建方法。

中文关键词： 骨架型对象；三维点云；微分几何属性；表面重建；断面轮廓

英文摘要： Space curve has significant geometric features and concise expression. We will explore the methods of using the space curves to express the three-dimensional model. We hold the view that skeleton can support the 3D model structure, contours and structural line have capability of supporting the geometric shape of surface. In order to meet the needs of Internet applications for point clouds model, we look skeleton as axis of model, look structral line as meridian, and look contour as latituide. The intrinsic geometric characteristics of space curve have very strong self-describing ability. We will researh the physical meanings of these intrincis characteristics systematically and design the methods to achieve space curve matching and pose estimation. We also design the sophisticated methods to extract these critical curves from 3D point clouds and to define their geometric positional relationship. On the basis of foregoing studies, we propose the routines of three-dimensional model retrival and reconstruction with taking into account the topological structure and surface geometry.

英文关键词： Skeleton Object；Three-dimensional Point Clouds；Differential Geometry Property；Surface Reconstruction；Cross-sectional Contours