本研究以膨脹侵蝕法為基礎，應用於影像內插技術，以改善三維影像重建之階梯化的問題。
研究首先探討以三角網格表示演算法於影像實體模型建構時，因原始二維影像資料不足，導致表面階梯化的問題癥結。為改善曲面外觀，因此提出膨脹法距離轉換與幾何距離的差異及優缺點，進而選擇以膨脹法距離轉換配合侵蝕法順利產生內插影像，彌補原始二維影像資料不足的缺點。此外，在內插過程中，還加入輪廓像素點對應的考量，建立了相應的關聯性，對於參數式平滑曲面的建構，提供了合理的對應點群，可減少曲面扭曲程度，增加曲面的正確性。
此研究直接利用曲面設計系統將二維影像重建三維模型之外，另新增影像即時展現及標籤功能，於電腦輔助醫學工程方面，讓系統使用者在診療上獲得更快速、精確、真實的應用效果。

In this research, image interpolation based on the dilation and erosion techniques is developed to improve the step-shape of the geometric model used in 3D medical reconstruction.
Basically, the discontinuous step-shape surface existing with the reconstructed geometric model based on the traditional Marching-Cube technique is unavoidable, if the gap between two cross sectional 2D images is large, or the image resolutions between horizontal and vertical images is not compatible. To improve this disadvantage, some interpolated images are necessary between any two cross section images. In this research, the interpolation technique based on the dilation distance and Euclidean distance is discussed respectively, and the interpolation algorithms based on the dilation/erosion transform are developed accordingly. In addition, search algorithms for different contour pixels matching are also developed, which can be used to generate suitable point sets for parametric surface reconstruction.
In the operation interface, not only the model reconstruction function, the real time cross sectional image generation and image isolines labeling are also developed, which can provide more quickly, precise, and real visual effect for medical diagnosis or inspection.

[1]Berry, E., Brown, J.M., Connell, M., Craven, C.M., Efford, N.D., Radjenovic, A., and Smith, M.A., Jan 1997 “Preliminary experience with medical applications of rapid prototyping by selective laser sintering,”Med. Eng. Phys., vol. 19, pp.90-96.
[2]Guo, J.F., Cai, Y.L., and Wang, Y.P., 1995 “Morphology-based interpolation for 3D medical image reconstruction,”Computer Medical Imaging Graphics, vol. 19, no. 3, pp.267-279.
[3]Lee, T.Y., and Wang, W.H., July 2000 “Morphology-based three-dimensional interpolation,”IEEE Transaction on Medical Imaging, vol. 17, no. 7, pp.711-721.
[4]Lin, W.C., Liang, C.C., and Chen, C.T., 1988 “Dynamic elastic interpolation for 3-D medical image reconstruction from cross sections,”IEEE Transaction on Medical Imaging, vol. 7, pp.225-232, Sept.
[5]Lorensen, W.E., and Cline, H.E., July 1987 “Marching cubes：A high resolution 3D surface construction algorithm,”Computer Graphics, vol. 21, pp.163-169.
[6]Zhang, L., Li, L., Zheng, Y., and Clark, R., 2000 “3D-Visualization of CT Images under IDL Environment,”Signal Processing Proceedings, 2000. WCCC-ICSP 2000. 5th International Conference on, vol. 2, pp.869-872.
[7]王文秀，1999“體積變形技術及其在三維人體器官動態顯示之應用”, 碩士論文, 成功大學資訊工程研究所.
[8]林子源，2000“實體模型與電腦輔助技術於口腔顎面術前計劃之應用”, 碩士論文, 成功大學機械工程研究所.
[9]鐘永彬，2001“三角網面為基礎之曲面設計系統發展與應用”, 碩士論文, 中央大學機械工程研究所.