從電腦斷層醫學影像重建出具區域拓樸資訊的表面模型

Abstract

三度空間醫學影像之表面重建長久以來對於拓樸關係上，多半僅要求其正確性，以達到表面重建的連續性與正確性，但卻往往忽略了在拓樸資訊上的提供。但在電腦輔助設計與製造的領域上，表面重建的過程，由於後續處理與繪圖的應用，對於拓樸資訊記錄的研究相當普遍。 本研究即是利用工業中，同時產生拓樸資訊之表面重建的想法，應用到電腦斷層醫學影像，使得醫學影像的表面重建結果，也能夠得到區域性的拓樸關係，以便後續的相關應用。 在本研究中的軟體演算，是藉由對影像資料的編號，以及資料間鄰接關係的推斷與歸類，可以對電腦斷層影像產生表面的重建。並且在此過程中，可以收集此一表面重建模型之區域拓樸關係，提供了表面模型中，三角網格之頂點與網格之區域拓樸關係，並且可以此推算出頂點與邊，邊與網格等等的區域拓樸關係。 利用區域拓樸關係之資訊，可以利用圍繞各頂點的每一項三角網格資料，計算出每個頂點所在位置之平均法向量可以得到平滑的彩現陰影效果。另外利用拓樸關係資訊，可以便利地對重建模型進行切割，為本研究結果所產生區域拓樸關係的應用實例。

In the past, researches on surface reconstruction from 3D medical image only focused on topological correctness in order to get continuous and smooth surface representation. The collection of topology information of the reconstructed surface has been ignored in the reconstruction process. On the other hand, in the fields of computer aided design and computer aided manufacturing (CAD/CAM), the collection of topology information has attracted enormous attention due to its subsequent applications, such as reverse engineering modification and process planning. In this study, the topology information collection technique developed in CAD/CAM fields will be applied to the surface reconstruction from 3D medical image. While the surface is reconstructed, the local topology information of the reconstructed surface is created as well. The developed algorithm utilizes the indexing of the image voxel and the neighborhood relation between the image voxel and their surrounding surfaces to process the image data into surface representation. In the reconstruction process, the information between vertices, edges, and meshes is inferred to help the collection of the local topology. To demonstrate how the local topology information can improve the effectiveness of the subsequent process on the reconstructed meshes, two examples are investigated. The first example is to effectively calculate the averaged normal vector of the triangle mesh vertex using the local topology information. The averaged normal vector can improve the display quality in model rendering. The second example is to calculate the intersection of the reconstructed model and any oblique plane. It is shown that the calculation time can be greatly reduced when the local topology is used.