邊緣偵測是影像處理中用來尋找影像中某特定物體邊緣的基本方法。然而對於存在低對比，多雜訊的醫學影像而言，要獲取某一特定的邊緣輪廓有其困難度。而主動式輪廓模型定義了邊緣曲線上的能量。其由兩種力所組成：內在力代表著曲線上所具有的連續性與平滑度的特性關係，而外在力是由影像中邊緣所具有的吸引力所構成。在我們的研究中係利用主動式輪廓模型的方法以求出牙根管的路徑。首先使用者必須於牙根管的路徑附近手動地描繪出起始輪廓，然後控制點與所需的搜尋點也就相繼地產生。由於此研究中的起始輪廓為開放式的曲線，所以在曲線上的頭尾端點無法獲得應有的平滑特性。因此我們加入由最佳方向性的邊緣偵測的概念所量化的能量於此兩端點中以增加在此兩端點中路徑搜尋的正確性。同時我們也修改曲線上平滑度的特性並增加由影像中邊緣所呈現的亮度所具有平滑特性。之後並應用動態可程式化的方法以累加每控制點群組中的能量並且記錄此能量以及相對應的最小能量位置於兩個陣列中。最後再從最終的群組中找出最小的能量以及相對應的位置，並藉由上述的位置而自位置陣列中利用往回搜尋的方法以求出最佳化的輪廓。而從評估相似度與位移誤差的結果證明出我們的電腦化系統能夠得到7個像素（大約3釐米）以內的誤差，因此我們所得到的結果有很好的表現。

Edge detector is a fundamental method that is used to search for the edge of some objects in the image processing. However for the medical image existed in low-contrast, many noises, it is difficult to acquire the contour of the special object. And the active contour model defines the energy on the curve of the edge. It is combined by two forces: the internal force represents the relationship to the property of the continuity and the smoothness on the curve, and the external force is composed of the attraction by the edge of the image. In our experiment, we also use the method of the active contour model in order to find out the path of teeth root tube. First, user has to draw the initial contour manually near to the path, and then the controlling- and searching-points are produced one after another. Due to the initial contour is opened curve in our research, so the property of the smoothness can’t be acquired in the beginning and the terminal point of the curve. Therefore we add the quantitative energy by the concept of the best-orientation edge detector into the two groups for increasing the accuracy in searching the path. At the same time, we revise the smooth item and add the smooth property of the intensity displayed by the edge of the image. After that we apply the method of the dynamic programming to accumulate the energy in every controlling-point group and record the corresponding energy and the position of the minimizing energy into two matrixes. At last we find out the minimizing energy and the corresponding position of the searching-point from the last group. And then we use the trace back to find out the optimal contour begun from the position of the above-mentioned in the position matrix sequentially. From the result in evaluating the similarity and the displacement, our computerized system can obtain the approximate contour under the error of 7 pixels (about 3mm) with the artificial contour. Therefore the result is shown the best performance.

[1] A. A. Amini, S. Tehrani, and T.E. Weymouth,” Using dynamic programming for
minimizing the energy of active contours in the presence of hard
constraints,” Proceeding of the Second International Conference on Computer
Vision, pp. 95-99, 1988.
[2] A. A. Amini, T. E. Weymouth, and R. C. Jain,” Using dynamic programming for
solving variational problems in vision,” IEEE Transactions on Pattern
Analysis and Machine Intelligence, Vol.12, No.9, pp. 855-867, 1990.
[3] A. A. Amini, P. Shi, R. T. Constable, K. Johnson, J. S. Duncan, J. C. Gore,”
Energy-minimizing deformable grids for tracking tagged MR cardiac images,”
in Computers in Cardiology. Durham, NC, Germany: Springer-Verlag, pp.
651–654, 1992.
[4] A. J. Pinho and L. B. Almeida,” On the partition of binary edge maps as a
first step for quantitative quality evaluation,” Proceeding of the 3rd IEEE
Internal Conference on Image Processing, pp 343-346, 1996.
[5] A. J. Pinho and L. B. Almeida,” Figures of merit quality assessment of
binary edge maps,” Proceeding of the 3rd IEEE Internal Conference on Image
Processing, pp. 591-594, 1996.
[6] C. H. Chuang and W. N. Lie,” Fast and accurate active contours for object
boundary segmentation,” Proceeding of the IEEE Asia-Pacific Conference on
Circuits and Systems, pp. 473 – 476, 2000.
[7] D. J. Williams, and M. Shah,” A fast algorithm for active contours,” CVGIP:
Image Understanding. Vol. 55, No. 1, pp. 14-26, 1990.
[8] D. J. Williams, M. Shah,” A fast algorithm for active contours,”
Proceedings of the 3rd IEEE International Conference on Computer Vision, pp.
592 – 595, 1990.
[9] F. Mohanna and F. Mokhtarian,” Improved curvature estimation for accurate
localization of active contours,” Proceeding of the IEEE International
Conference on Image Processing, pp. II: 781-784, 2001.
[10] H. Tang and T. Zhuang,” An improved adaptive B-spline active contour
model,” Proceeding of the 20th Annual Internal Conference of the IEEE
Engineering Medicine and Biology Society, Vol.20, No.2, pp. 990-993, 1998.
[11] J. Lilian and Y. Hong,” An intelligent and attractable active contour model
for boundary extraction,” Proceeding of the IEEE Internal Conference on
Acoustics, Speech, and Signal processing, Vol.6, pp. 3309-3312, 1999.
[12] K. C. Suriamoorthy and A. C. Bovik,” Modeling of growth via active contour
models,” Proceeding of the IEEE Southwest Symposium on Image Analysis and
Interpretation, pp. 41-46, 1998.
[13] K. Fujimura, N. Yokoya, and K. Yamamoto,” Motion tracking of deformable
objects based on energy minimization using multiscale dynamic programming,”
Proceeding of the IEEE Conference on Computer Vision and Pattern
Recognition, pp. 83-86, 1992.
[14] K. -M. Lam and, H. Yan,” Fast greedy algorithm for active contours,”
Electronics Letters, Vol. 30, No. 1, pp. 21 – 23, 1994.
[15] L. Ji and H. Yan,” An attractable snake model for contour extraction in MRI
images,” Proceeding of the 20th Annual International Conference of the IEEE
on Engineering in Medicine and Biology Society, pp. 609–612, 1998.
[16] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models”,
International Journal of Computer vision, pp.321-331, 1988.
[17] M. Yachida, M. Ikeda, and S. Tsuji,” A plan-guided analysis of
cineangiograms for measurement of dynamic behavior of heart wall,” IEEE
Transactions on Pattern Analysis and Machine Intelligence, Vol. 2, No6, pp.
537-543, 1980.
[18] O. Gérard, S. Makram-Ebeid,” Automatic contour detection by encoding
knowledge into active contour models,” Proceedings of the 4th IEEE Workshop
on Applications of Computer Vision, pp.115 – 120, 1998.
[19] P. Radeva, J. Serrat, and E. Marti,” A snake for model-based
segmentation,” Proceeding of the 5th IEEE International. Conference on
Computer Vision, pp. 816-821, 1995.
[20] S. Menet, P. Saint-Marc, G. Medioni,” Active contour models: overview,
implementation and applications,” Proceeding of the IEEE International
Conference on Systems, Man and Cybernetics Conference, pp. 194–199, 1990