肝臟診斷與治療最常用的方式是超音波影像掃描，二維的超音波影像雜訊多，且缺乏空間方位資訊，容易造成誤診。若能經由影像間對位技術，將超音波影像與電腦斷層影像融合，則可提供醫師三維且更清晰的影像資訊，對提升診斷與手術品質有相當的助益。本研究提出一套藉由肝臟的血管影像特徵，來自動進行電腦斷層影像與超音波影像的對位及融合。
　　先將徒手掃描的超音波影像重建成超音波立體影像，再將電腦斷層影像與超音波立體影像經由影像處理擷取出血管輪廓，血管輪廓經由三維數位拓樸關係，得到血管中心線，最後經由初始對位與疊代最近點(Iterative closest point, ICP)演算法，得到電腦斷層影像與超音波影像的座標轉換關係，並以影像相似性量測來評估其對位準確度。實驗使用自製的肝臟血管假體模型來測試，實驗結果顯示不同方位但相同血管模型的對位準確度大約可達到78%；而不同方位但血管模型變形的對位準確度大約可達到66%。此一研究方法若加入非剛性對位補償，應可用作肝臟電腦斷層影像與超音波影像之對位融合。

　　Ultrasound imaging is the most popular approach for liver diagnosis and surgery. Two-dimensional ultrasound images have terrible noises and are lack of spatial information. Sometimes, it is difficult to avoid misdiagnosis. If CT and US images can be registered and fused through mapping techniques, three-dimensional and clear information will enable doctors to improve diagnosis and surgery quality. This study proposed an image registration method based on the blood vessels of the liver to automatically fuse CT and US images.
　　The freehand-scanned ultrasound images are first reconstructed into 3D ultrasound image model. Then profiles of blood vessels of CT and 3D ultrasound image models are extracted by using image processing. The center lines of the vessels can be determined through 3D digital topology relation. Finally, the transformation matrix between CT and ultrasound images can be found by applying preliminary registration with interactive closest point algorithm. Image similarity measure is used to evaluate the registration accuracy. In the experiments, self-designed liver vessels phantoms are applied to verify the proposed methods. The results show that registration accuracy of the two modalities using identical phantoms but in different positions can reach about 78%, while that using normal and deformed phantoms is approximately 66%. Base on the result, the proposed method integrated with non-rigid deformation offset will enable the registration and fusion of CT and ultrasound liver images.

[1] B. C. Porter, D. J. Rubens, J. G. Strang, J. Smith, S. Totterman, and K. J. Parker, “Three-dimensional registration and fusion of ultrasound and MRI using major vessels as fiducial markers, ” IEEE Transactions on Medical Imaging., Vol. 20, No. 4, pp. 354-359, 2001.
[2] T. Lange, S. Eulenstein, M. Hunerbein, H. Lamecker, and P. Schlag, “Augmenting intraoperative 3D ultrasound with preoperative models for navigation in liver surgery,” in Proceedings Medical Image Computing and Computer-Assisted Intervention 2004, Vol. 3217, pp. 534-541, 2004.
[3] M. Sato, I. Bitter, M. A. Bender, A. E. Kaufman, and M. Nakajima, “TEASAR: tree-structure extraction algorithm for accurate and robust skeletons,” in Proceedings the 8th Pacific Conference Computer Graphics and Applications, pp. 281-289, 2000.
[4] P. Hassenpflug, M. Schobinger, M. Vetter, R. Ludwig, I. Wolf, M. Thorn, L. Grenacher, G. M. Richter, W. Uhl, M. W. Buchler, and H. P. Meinzer, “Generation of attributed relational vessel graphs from three-dimensional freehand ultrasound for intraoperative registration in image-guided liver surgery,” Proceedings of SPIE, Vol. 5029, pp 222-230, 2003.
[5] D. Selle and H. O. Peitgen, “Analysis of the morphology and structures of vessel systems using skeletonization,” Proceedings of SPIE, Vol. 4321, No. 1, pp. 271-281, 2001.
[6] D. Zühlke, S. Arnold, G. Grunst, and P. Wißkirchen, “Intra-interventional registration of 3D ultrasound to models of the vascular system of the liver,” GMS CURAC 2007, Vol. 2(1), 2007.
[7] D. Zühlke, “Vessel extracting gas - using self organization in the extraction of vascular trees,” Proceedings of the 6th International Workshop on Self-Organizing Maps, 2007.
[8] D. Zühlke, “Transform learning - registration of medical images using self organization,” Proceedings of the 6th International Workshop on Self-Organizing Maps, 2007.
[9] B. Dagon, C. Baur, and V. Bettschart, “A framework for intraoperative update of 3D deformable models in liver surgery,” in 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 3235-3238, 2008.
[10] J. Tierny, J. P. Vandeborre, and M. Daoudi, “3D mesh skeleton extraction using topological and geometrical analyses,” in Proceedings the 14th Pacific Conference on Computer Graphics and Applications, pp. 85-94, 2006.
[11] F. Conti, O. Khatib, and C. Baur, “Interactive rendering of deformable objects based on a filling sphere modeling approach,” Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Vol. 3, pp. 3716-3721, 2003.
[12] T. Lange, N. Papenberg, S. Heldmann, J. Modersitzki, B. Fischer, H. Lamecker, and P. Schlag, “3D ultrasound-CT registration of the liver using combined landmark-intensity information,” International Journal of Computer Assisted Radiology and Surgery, Vol. 4, No. 1, pp. 79-88, 2009.
[13] T. Y. Kong and A. Rosenfeld, “Digital topology: introduction and survey,” Computer Vision Graphics and Image Processing, Vol. 48, No. 3, pp. 357-393, 1989.
[14] A. Nakamura and K. Aizawa, “On the recognition of properties of three-dimensional pictures,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 7, No. 6, pp. 708-713, 1985.
[15] J. I. Toriwaki, S. Yokoi, T. Yonekusa, and T. Fukumura, “Topological properties and topology-preserving transformation of a three-dimensional binary picture,” Proceedings of the 6th Intemational Conference on Pattern Recognition, pp. 414-419, 1982.
[16] P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 12, No. 7, pp. 629-639, 1990.
[17] R. W. Prager, R. N. Rohling, A. H. Gee, and L. Berman, “Rapid calibration for 3-D freehand ultrasound,” Ultrasound in Medicine and Biology, Vol. 24, No. 6, pp.855-869, 1998.
[18] Y. K. Dai, J. Tian, and J. Xue, “A real-time and interactive freehand three-dimensional ultrasound imaging system,” Journal of Software, Vol. 17, pp. 28-37, 2006.
[19] L. Mercier, T. Lango, F. Lindseth, and L. D. Collins, “A review of calibration techniques for freehand 3-D ultrasound systems,” Ultrasound in Medicine and Biology, Vol. 31, No. 2, pp. 143-165, 2005.
[20] N. Pagoulatos, D. R. Haynor, and Y. Kim, “A fast calibration method for 3-D tracking of ultrasound images using a special localizer,” Ultrasound in Medicine and Biology, Vol. 27, No. 9, pp. 1219-1229, 2001.
[21] F. Rousseau, P. Hellier, and C. Barillot, “Confhusius: a robust and fully automatic calibration method for 3-D freehand ultrasound,” Medical Image Analysis, Vol. 9, No. 1, pp. 25-38, 2005.
[22] R. S. José-Estépar, M. Martín-Fernández, P. P. Caballero-Martínez, C. Alberola-López, and J. Ruiz-Alzola, “A theoretical framework to three-dimensional ultrasound reconstruction from irregularly sampled data,” Ultrasound in Medicine and Biology, Vol. 29, No. 2, pp. 255-269, 2003.
[23] S. Winitzki, “A handy approximation for the error function and its inverse,” http://homepages.physik.uni-muenchen.de/~Winitzki/erf-approx.pdf
[24] R. N. Rohling, A. H. Gee, and L. Berman, “A comparison of freehand three-dimensional ultrasound reconstruction techniques,” Medical Image Analysis, Vol. 3, No. 4, pp. 339-359, 1999.
[25] R. N. Rohling, A. H. Gee, and L. Berman, “Three-dimensional spatial compounding of ultrasound images,” Medical Image Analysis, Vol. 1, No. 3, pp. 177-193, 1997.
[26] T. R. Nelson and D. H. Pretorius, “Interactive acquisition, analysis, and visualization of sonographic volume data,” International Journal of Imaging Systems and Technology, Vol. 8, No. 1, pp. 26-37, 1997.
[27] K. Siddiqi, S. Bouix, A. Tannenbaum, and S.W. Zucker, “Hamilton-jacobi skeleton,” International Journal of Computer Vision, Vol. 48, No. 3, pp. 215-231, 2002.
[28] S. Bouix, K. Siddiqi, and A. Tannenbaum, “Flux driven automatic centerline extraction,” Medical Image Analysis, Vol. 9, No. 3, pp. 209-221, 2005.
[29] S. Bouix, K. Siddiqi, and A. Tannenbaum, “Flux driven fly throughs,” Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 1, pp. 449-454, 2003.
[30] P. Dimitrov, J. N. Damon, and K. Siddiqi, “Flux invariants for shape,” Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 1, pp. 835-841, 2003.
[31] G. Malandain, G. Bertrand, and N. Ayache, “Topological segmentation of discrete surfaces,” International Journal of Computer Vision, Vol. 10, No. 2, pp. 183-197, 1993.
[32] S. Bouix and K. Siddiqi, “Optics, mechanics, and hamilton-jacobi skeletons,” Advances in Imaging and Electron Physics, Vol. 135, pp. 1-39, 2005.
[33] S. Bouix and K. Siddiqi, “Divergence-based medial surfaces,” Proceedings of the 6th European Conference on Computer Vision, Vol. 1842, pp. 603-618, 2000.
[34] E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, Vol. 1, No. 1, pp. 269-271, 1959.
[35] P. J. Besl, and N. D. Mckay, “A method for registration of 3-D shapes,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 2, pp. 239-256, 1992.
[36] C. Poulsen, P. C. Pedersen, and T. L. Szabo, “An optical registration method for 3D ultrasound freehand scanning,” 2005 IEEE Ultrasonics Symposium, Vol. 2, pp. 1236-1240, 2005.