大规模复杂散乱点云数据的智能分析与处理研究

With the rapid development of three-dimensional scanning technologies and devices during the last ten years, intelligent analysis and processing of complex, scattered, and large-scale point clouds has now become a hot research subject in digital geometry processing. Due to the hardware limitations of available devices, the imperfection of objects and their interaction with surrounding environments, mutual occlusions among objects, the scanned point clouds are inevitably suffered from noises, outliers, and missing data. Moreover, redundant data acquired by repeatedly scanning of complex objects are commonplaces in digital geometry processing, leading to many new technical challenges. To solve the aforementioned problems, we investigate a host of research problems and develop a range of technical solutions in this project. First, we propose a new method based on the theory of principal surfaces (which is essentially equivalent to local nonlinear PCA) to consolidate and simplify redundant data. Second, we extend the one-dimensional empirical mode decomposition algorithm and Hilbert spectral analysis from time series and mesh geometry to 3D point clouds in order to conduct the multi-scale feature extraction, and feature enhancing. We plan to devise a new algorithm to automatically detect and recover sharp features of different scales from incomplete point clouds. Finally, in this project we plan to build a complete software framework that supports a host of intelligent analysis and processing tasks for complex scattered point clouds of large scales, including consolidation and cleaning of redundant point clouds, feature extraction, feature enhancing and automatic data repair. If successful, our framework can afford high accuracy and completeness for data modeling, which will offer new theories and engineering solutions for shape modeling, shape analysis and retrieval, geometric editing, data analysis, that are collectively relevant to intelligent analysis of digital geometry.

随着三维扫描技术的快速发展，大规模散乱点云数据处理已经成为数字几何研究发展过程中的研究热点。在数据获取过程中，受设备的限制、周围环境以及物体间相互遮挡等因素的影响，获取数据不可避免地存在噪声、离群点、数据缺失等问题。此外，由于物体形状的复杂性与反复测量等因素产生的冗余数据是目前点云数据处理中极具挑战性的问题。为此，本项目拟针对扫描获取数据的冗余问题，基于主曲面理论的数据降维方法，研究特征保持的冗余数据精简；针对精简后的点云数据，将一维经验模态分解算法和希尔伯特谱分析理论推广到三维点云数据上，研究复杂点云模型的多尺度特征提取与增强；针对点云数据缺失问题，研究基于特征分析的缺失数据自动修复算法。 最终形成以冗余点云数据精简处理、几何特征提取与增强和缺失特征自动修复为主体算法的点云数据处理框架，实现高精度、完整性数据建模，为形状分析与检索、数据编辑与造型等数字几何处理提供理论与技术支持。

围绕项目的预期研究内容和研究目标，本项目所取得的主要成果如下： 1. 针对经验模态分解算法(EMD)无法保持点云数据几何特征的问题，研究了点云数据特征度量的构建、特征度量指导下的特征保持上下包络计算、特征保持的点云数据信号多尺度分解，提出了一种直接作用在点云上的多尺度无网格EMD算法，并进一步探索其在点云数据分析和处理中的应用。该算法不需要在离散点之间建立显式连接关系，通过迭代地从输入信号中提取细节层并将整体形状保留在残差中，实现了多尺度无网格EMD分解。2. 为了完全恢复缺失的几何图形细节，提出了一种基于EMD的三维曲面多尺度几何细节恢复算法。该方法不依赖于用户交互来指定相似的区域，或者手动添加额外的约束来恢复丢失的形状，该方法可以直接恢复缺失的形状，具有算法简单灵活的特性。 3. 为了有效地对复杂几何细节进行建模，提出了基于经验模态分解的复杂几何细节的交互式建模方法。该方法提供了一种简单易用的交互式建模工具和灵活的建模方法。目前在国内外重要期刊与学术会议上正式发表研究论文12篇，其中SCI论文9篇，EI论文3篇，申请发明专利1项。已圆满完成预定目标。