【作者】 李丹；

【导师】 韩丽；

【作者基本信息】 辽宁师范大学 ， 计算机科学与技术， 2018， 硕士

【摘要】 随着三维几何模型的研究对象逐渐从低层次的几何属性迈向高层次的语义属性,对称性的分析已成为几何处理领域的重要问题。当前,3D模型的对称检测工作主要集中在外蕴对称检测,然而内蕴对称在三维几何模型中更具普遍性,由于其需要考虑对称和分割等问题而更为复杂,内蕴对称检测仍然是三维形状分析的难点问题。近年来,3D模型的可视化、可获得性技术不断提高与完善,形状分析中的图形配准问题也随之成为计算机图形学等众多领域中的热点研究内容。三维模型的对称匹配是指在局部图形间建立保持结构的对应,主要包括点对点匹配,稀疏谱匹配,弹性网约束匹配,以及两个曲面间的函数映射匹配等,更成为三维模型形状配准的广泛研究课题之一。在三维图形匹配过程中主要涉及两个重要问题,一个是匹配精度,另一个匹配效率,尤其是模型形变同时避免左右翻转的高效、高精的匹配问题。为了解决这两个基本问题,本文提出了一种基于谱对称的三维模型配准方法。首先,通过热核信号与几何约束选择模型内蕴自对称点对,使用融合策略除去相同区域的冗余点;之后,基于谱嵌入特征空间分析,提取模型的内蕴对称平面,并依据模型表面法向量,有效的识别模型左右结构的翻转;进一步,根据空域中的对称点对映射到谱域中的对称点对,来获取模型的一致性谱对称结构描述;最终,引入一致性点漂移算法(CPD),实现基于谱对称的非刚性模型的形状配准,有效避免了模型配准中的左右结构翻转问题。实验结果表明该方法不但可以改善模型的配准效率,还能有效识别同类几何形状的结构属性,对于非刚性形状的配准具有较强的稳定性,为实现模型压缩、检索、重建等应用提供了坚实的理论基础。更多还原

【Abstract】 With the research object of the 3D geometric model moving towards high-level shape analysis and understanding,aiming at discovering the underling semantic information of a 3D shape.Symmetry analysis is one of the most important problems of geometry processing.Existing approaches to symmetry detection have so far been concerning extrinsic symmetry.However,the intrinsic symmetry is more general in 3D shapes.Its detection is harder since it need to consider both symmetry and segmentation.Meanwhile,it is more complex.Currently,the visualization and availability of 3D shapes have been continuously improved.Shape matching is one of the fundamental problems in computer Graphics.3D models symmetrical matching,which is to establish of local shapes between correspondences and stay structure.It includes point to point matching,sparse spectral matching,elastic net matching,or functional map between two surfaces.It has become one of the extensive research topics in 3D model registration.In this paper,in order to two fundamental problems,i.e.robustness and efficiency,3D shape correspondence analysis based on spectral symmetry.In particular,the deformation of the shapes avoid right and left flip in high-efficiency and high-precision.Firstly,intrinsic symmetric point pairs of the model are constructed by heat kernel signature(HKS)and geometric constraints,at the same time,remove some redundant points and add a few “helpful points” by the fusion method.Secondly,based on the spectral embedding space analysis,the intrinsic symmetric plane of the model is extracted and the symmetrical properties of the model are effectively identified according to the model surface normal vector,getting intrinsic symmetry point pair.Therefore the consistent spectral symmetry structure of the model is presented.Finally,combining the Coherent Point Drift method,the shape registration of non-rigid model based on spectral symmetry is implemented.The experimental results show that the matching method is efficient and robust to the non-rigid deformable shape matching.Moreover,the structural features in same category models also are effectively identified.It provides a solid theoretical basis for the application of model compression,retrieval,and reconstruction.更多还原