Realization of three-dimensional laminography

计算机断层摄影（ectomography或tomosynthesis）是一种应用于诊断或非破坏性检查的医学成像的断层成像技术。但是，由于X射线源扫描轨道的不完整性，这种成像技术只能提供被成像物体的不完整三维数据。提出了一种完整三维图像重建的X射线源扫描轨道。除了三维成像外，物体的三维几何建模对于有效的存储、传输和显示都是非常重要的。针对隐函数几何建模，提出了扩展超二次曲面，并考虑了基于函数优化的形状参数确定;针对更详细的几何建模，研究了物体的三角网格表示。该方法由基网格细分曲面生成的域网格和域网格上的方向位移组成。利用得到的网格结构的规则性，可以实现高效的表示。提出了该几何造型的数据压缩方案。通过对各种三维数据的实现，验证了所提出的几何建模方法在精确性和紧凑性方面的表现能力，通过对物体的完整三维成像和有效的几何建模，实现了三维断层成像。

The computed laminography (ectomography or tomosynthesis) is a kind of tomographic imaging technology which is applied to medical imaging for diagnosis or non-destructive inspection. But, this imaging technology provides only incomplete 3-D data of imaged objects because of the incomplete scanning orbit of X-ray source.In this research project, the relationship between the acquired data and the reconstructed image quality was considered. A scanning orbit of X-ray source for complete 3-D image reconstruction was proposed. The theoretical results were confirmed by simulation studies.In addition to 3-D imaging, the 3-D geometric modeling of objects is very important for efficient storage, transmission and display. The accurate and compact geometric modeling of reconstructed images was also investigated in this research project.For a geometric modeling by implicit function, we proposed the extended Hyperquadrics, and the determination of shape parameters based on the functional optimization was considered.For a further detailed geometric modeling, the triangular mesh representation of objects was investigated. The proposed method consists of the domain mesh resulting from the subdivision surface of base mesh and the directional displacements over domain mesh. The efficient representation can be realized by using the regularity of obtained mesh structure. The data compression scheme for this geometric modeling was proposed. The representation power of proposed geometric modelings based on the accuracy and the compactness could be confirmed by the implementations for various kinds of 3-D data.The 3-D laminography can be realized by the complete 3-D imaging and the efficient geometric modeling of objects.