本篇主要是研究如何將斷層掃瞄的斷面影像轉換為以B-Spline Surface為基礎的立體參數曲面。
在過去的研究中，是運用Marching Cube演算法來將二維序列影像轉換成三維的曲面資料。但轉換出來的曲面，不但會佔用大量的儲存空間，且亦會因為插層的影像不夠密而致使曲面產生階梯化的情形。運用型態幾何法內插出虛構的影像雖然可以降低階梯化的情形，但仍無法完全解決曲面不連續的問題。
以數學函數為基礎的B-Spline Surface不但能節省儲存空間，且因B-Spline的連續性特質而使得所建構出來的曲面不會有階梯化的問題，若配合以型態幾何的膨脹收縮法，將能更正確、平順的重建骨骼曲面。
在重建的過程中本研究使用了兩種方法建立基礎曲線，第一種是找出輪廓曲線的特徵點，藉由影像中的特徵點來還原出原始的輪廓。第二種方法則是運用最小平方法來找出最符合輪廓的B-Spline曲線。在傳統的曲面重建法中，各輪廓之間的對應點關係深深地影響到重建曲面的正確性，錯誤的對應關係將會產生不正確的結果。但以最小平方法重建B-Spline曲面之技術亦能減少因對應錯誤而產生的錯誤。

This thesis is a research about construction of medical series images into 3D model by using B-Spline surface.
In the past research, “Marching-Cube Technique” is usually used to construct the 3D model. But the model consumes lots of storage space and it occurs unsmooth appearance in some cases. Though using “Morphology-based Interpolation” method to calculate fictitious images can improve the result, but it still not smooth enough for medical use. Since B-Spline is a continuous mathematical function, using B-Spline surface to construct 3D model can save lots of storage space and avoid unsmooth problem.
We use two different methods to rebuild B-Spline surface. One is detecting characteristic points in the image, and using these points to build the contour. The other method is using least-square method to build the contour, and merge them to a B-Spline surface.
In the process of merge B-Spline surface, the match points of each contour is very important, irrational match method will bring wrong result. The least-square method can solve this problem very easy.

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