近年來在重建3-D人體解剖器官和結構的影像是一個相當有趣課題，惟大部分之生醫輪廓乃屬自然形狀且非對稱曲面，若欲獲得準確的重建輪廓是一項艱難的工程技術。本研究提出SA-NURBS法，將模擬退火法(Simulated Annealing, SA)整合於非均勻有理化B-spline (Non-uniform rational B-spline, NURBS)，並針對開放層狀點資料來進行非對稱曲面擬合之最佳化，可應用於三維物件與電腦斷層掃描來源點資料(Computed Tomography, CT)。另外，模擬退火法的全區域最佳化策略被應用於擬合曲線與曲面之權重與控制點的最佳化調整，可得平滑且最小平方距誤差之結果，對於43x 50x 39 mm尺寸之人體骨頭點資料，可獲得平均0.0291 mm平方距誤差及0.2105 mm 最大距誤差之擬合結果；實驗結果亦顯示，匯入經最佳化之輸出結果於電腦輔助設計軟體Pro/E，將可改善軟體所顯示輪廓之準確度。未來研究可套用最小能量法於進行非對稱曲面擬合，進一步地改善表面之平滑度。

Recently, reconstructing the 3-D human anatomical organs and structures from series of cross section images is an interesting problem. Since most bio-surfaces are natural and non-symmetric objects, it is very difficult to reconstruct them accurately. In this research, a proposed method of an optimal NURBS fitting schema integrated with Simulated Annealing method, named SA-NURBS for fitting of non-symmetric surfaces has been developed to fit the data points that are obtained from the opened layer contours. It is applied to rebuild 3-D physical models of acetabulum, which is one of two surfaces of a hip joint from 2-D medical image data obtained from Computed Tomography (CT) image processing. The global optimization strategy of Simulated Annealing is applied to optimize weights and control points of NURBS for curve and surface fitting. The objective is the minimization sum of squared distance errors to obtain smooth curves and surfaces. Finally, the smooth acetabulum model obtained from the optimization weights and control points can be achieved a mean of distance error of 0.0291 mm with a standard deviation of 0.0390 mm and a minimum value of the maximum distance error of 0.2105 mm from the given bone data of dimension 43x50x39 mm. The results indicate that the developed method can overcome the surface fitting problem of Pro/E and improve the fitting accuracy. To improve smoothness of the reconstructed surfaces of concave data, further study can consider minimizing bending energy of the non-symmetric surfaces.

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