基于非完备几何特征测量数据建模的关键技术基础研究

The characteristic of the model reconstruction theory for incomplete geometrical features is to recover the original defect information by analyzing,extracting, correlating,and integrating the characteristics of known data. And the modelling technique for repairing facial defects can be established when the theory is applied in the facial plastic surgery field. For incomplete data with symmetrical features, the data in good condition will be mirrored into the defect region. However, since some points in good condition does not own the corresponding points in the defect area,and in order to ensure continuity and accuracy of convergence,the approach must be taken to judge the authenticity of the temporary corresponding points, getting rid of the point pairs with low credibility. We applied the M estimation ICP-based iterative algorithm integrated with the expansion of Gaussian sphere, using the residual function instead of the residuals in process of minimizing for the outer points suppression, making the outer point of almost no effect on the minimum process. For incomplete data with local deformed symmetrical features, we used the Laplace algorithm with rotation invariants to recover the local deformation.For incomplete data with no self-information is available for the reconstruction, we firstly acquire the incomplete data from its photo by integrating 2D image and the 3D surrounding issue data, then use the constraint-based non-rigid alignment to map the incomplete model to the defect region, ensuring the filled data can be transited smoothly with the surrounding issue data. Thus the construction technique of incomplete data with distorted symmetrical features can be used on the distorted facial defects with symmetrical features ,and the construction technique of incomplete data with feature similarity can be used for asymmetric facial defects (such as nasal defects, etc.).We will used the above modelling techniques of incomplete data and three-dimensional topography acquisition technology to the field of facial defects repair applications,developing a human facial defects repair CAD system for clinical applications to verify if the system can meet the requirements of digital prostheses modelling.This project will contribute to the treatment of facial defect, as well as heritage repair，scan data quality improvement and other areas.

本项目面向有效恢复非完备区三维原貌问题，利用非完备几何特征与先验知识的关联特性，研究先验知识的识别、抽取、关联、集成等关键技术，拟构建基于非完备几何信息的测量数据完备特征建模基本理论，结合颜面缺损赝复，建立颜面缺损赝复的几何建模技术体系。针对对称面的有效提取，结合点云数据几何特性，提出基于扩展高斯球与M估计融合的非完备数据对称特征提取算法；面向对称特征中存在局部变形问题，研究局部变形恢复方法，形成基于旋转不变量拉普拉斯算法的局部变形恢复策略；消除2D图像恢复三维数据的病态问题，通过2D图像与已有3D数据深度融合，形成基于视觉图像特征相似性的非完备数据完备特征建模理论；针对扭曲变形颌面缺损和参照患者照片修复鼻缺损问题展开赝复应用研究。集成本项目研究成果以及三维形貌采集等技术，搭建颜面完备特征建模CAD试验系统，完成临床验证。项目研究对医学颜面修复，文物保护，扫描数据质量提升均具有重要意义。

面向有效恢复非完备区三维原貌问题，本项目研究了基于非完备区域几何特征测量数据完备特征建模的关键技术：对称特征非完备数据几何建模所需的高精度对称面存在获取困难，完好区的数据往往在缺损区找不到正确对应点，错误对应点对将影响最终迭代结果。针对对称面有效提取，结合点云数据几何特性，提出基于扩展高斯球与M估计融合的非完备数据对称特征提取策略。基于扩展高斯球的点云数据初始对齐，使原本无法定量解决的点云数据初始对应问题得到解决，基于M估计的ICP方法能有效去除迭代过程错误对应点对。面向对称特征局部变形问题，提出基于旋转不变量拉普拉斯算法的局部变形恢复策略。为编辑区域每个顶点估计一合适仿射变换矩阵，解决传统拉普拉斯算法不能很好处理旋转问题，线性系统快速求解提供速度优势。研究基于视觉图像特征相似性的非完备数据快速建模方法，根据二维图像特征点与三维形貌特征点对应关系构建缺损区3D模型；经过基于约束的非刚性对齐实现非完备数据有效恢复，并满足有关约束要求。针对颌面摘除手术与颌面赝复手术时间相隔较长导致口腔部软组织明显偏移，提出扭曲变形颌面缺损的几何建模赝复策略：基于旋转不变量的拉普拉斯算法的局部变形恢复；基于扩展高斯球与M估计融合的缺损数据对称面获取；非完备几何特征恢复；改进非完备重建特征初始边界条件，运用双伞形运算使得边界能够达到平滑切向过渡。对于自身无相似信息可利用的非完备数据，可利用特征相似性，获取自身以外与缺损区信息相符的数据源，实现相似特征三维重建；基于约束的非刚性模板模型映射技术，实现满足有关约束要求的非完备数据有效恢复，并可进行虚拟试戴评估，如中心对称面的差异检测以及赝复体与周围组织的贴合程度虚拟评价等。项目研究加深了对基于非完备几何信息的测量数据完备特征建模机理本质的理解，揭示先验知识对于完备特征建模的影响及相互关系，对医学颜面修复，文物保护，扫描数据质量提升均具有重要意义。