臺灣博碩士論文加值系統

本研究的目的為利用多張二維腦瘤的超音波影像重建出腫瘤於腦部在三維的相對位置，目的是在臨床應用上能讓醫生明確的知道腫瘤的確切位置，進而提高醫生開刀的準確性。
由於多張的二維超音波影像並非規則的平行切面，所以我們在做影像分割前會先對其作插捕成三維的規則的平行切面，使得許多快速的二維影像處理方法能夠直接地推廣到三維影像上。我們做插補所使用的方法為板條插補法，同時使用了廣義交叉驗證法來決定控制點的個數。
我們接著將分水嶺轉換和影像細胞單元的想法推廣到三維影像上來進行影像切割。首先使用高斯平滑法濾雜訊，再利用Sobel 濾波器求出每個像素的梯度值。接著，經由分水嶺轉換將影像上近似的影像及影像上梯度絕對值小的那些像素聚集起來形成影像細胞單元。最後，影像細胞單元應用無母數的假設檢定和分類法進行合併或分裂，找出腫瘤最後的邊界。我們稱之為無母數的影像細胞單元分群法，並進行模擬與實證研究，證實這個方法的實際可行性。

This study is aimed to segment the tumor in 3D by a volume of 2D ultrasound images. This segmentation can provide the location information of tumor for doctors during operation and improve the accuracy of operation.
Because the images obtained by 2D ultrasound scans are irregularly spaced most of the time, it is necessary to interpolate them into regularly spaced 3D images so that image processing techniques for 2D images can be generalized directly with fast computation speed. Spline interpolation is used in this study. Generalized cross validation is proposed to decide the size of control lattice in interpolation.
After interpolation, we will generalize watershed transform and cell based approaches to 3D images. Gaussian smoothing is first applied to denoise the images. Sobel filters are then used to estimate the gradient. Based on the absolute values of gradients and the regularization term of the image intensities, image cells are obtained by watershed transform. Finally, cells are merged or split to locate the tumor by a new method with nonparametric testing and divisive clustering. This is called “nonparametric cell clustering” in this study. Simulation and empiric studies are performed for this new approach. The results are promising according to these studies.

Contents
Chapter 1 Introduction 1
Chapter 2 Spline Interpolation with GCV 4
2.1 Spline Interpolation . . . . . . . . . . . . . . . . . 4
2.2 GCV and Estimation . . . . . . . . . . . . . . . . . . . . 7
2.3 Test Results . . . . . . . . . . . . . . . . . . . . . . .11
Chapter 3 Segmentation by Nonparametric Cell Clustering 30
3.1 Literature Review . . . . . . . . . . . . . . . . . . . . 30
3.1 Noise Reduction . . . . . . . . . . . . . . . . . . . . . 31
3.2 Watershed Transform . . . . . . . . . . . . . . . . . . . 35
3.3 Nonparametric Tests and Cell Clustering . . . . . . . . . 43
Chapter 4 Results 57
4.1 Data Description and Performance Criteria . . . . . . . . 57
4.2 Noise Reduction . . . . . . . . . . . . . . . . . . . . . 62
4.3 Watershed transform . . . . . . . . . . . . . . . . . . . 63
4.4 2D Clinical Ultrasound Images . . . . . . . . . . . . . . 68
4.5 Segmentation without Interpolation . . . . . . . . . . . 84
4.6.1 Phantom Studies: Type A . . . . . . . . . . . . . . . . 84
4.6.2 Phantom Studies: Type B . . . . . . . . . . . . . . . . 88
4.6.3 Phantom Studies: Type C . . . . . . . . . . . . . . . . 91
4.6.4 Phantom Studies: Type D . . . . . . . . . . . . . . . . 94
4.6.5 Empiric images Type E . . . . . . . . . . . . . . . . . 97
4.6 Segmentation with Interpolation . . . . . . . . . . . . . 98
4.7.1 Regular Spaced Phantom Studies: Type A . . . . . . . . 98
4.7.2 Regular Spaced Phantom Studies: Type B . . . . . . . . 102
4.7.3 Regular Spaced Phantom Studies: Type C . . . . . . . . 105
4.7.4 Regular Spaced Phantom Studies: Type D . . . . . . . . 108
4.7.5 Irregular Spaced Phantom Studies: Type A . . . . . . . 111
4.7.6 Irregular Spaced Phantom Studies: Type B . . . . . . . 114
4.7.7 Irregular Spaced Phantom Studies: Type C . . . . . . . 117
4.7.8 Irregular Spaced Phantom Studies: Type D . . . . . . . 120
Chapter 5 Conclusion and Future Studies 123

[1] Adams, R. and Bischof, L. (1994) ”Seeded Region Growing ,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 6.
[2] Caley, A. (1859) “On contour and slope lines,” Lodon, Edinburgh, Dublin Philosoph. Mag. J. Sci., 18, 264-268.
[3] Canny, J. F. (1986) “A computational Approach to edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, 6, 679-698..
[4] Chen, C.-M., Lu, H. H.-S., and Chen, Y.-L. (2002) “A Discrete Region Competition Approach Incorporating Weak Edge Enhancement for Ultrasound Image Segmentation,” to appear in Pattern Recognition Letters.
[5] Chen, C.-M., Lu, H. H.-S., and Huang, Y.-S. (2002) “Cell-Based Dual Snake Model: A New Approach to Extracting Highly Winding Boundaries in The Ultrasound Images,” to appear in Ultrasound in Medicine and Biology.
[6] Chen, C.-M., Lu, H. H.-S., and Lin, Y.-C. (1999) “An Early Vision Based Snake Model for Ultrasound Image Segmentation,” Ultrasound in Medicine and Biology, 26, 2, 273-285.
[7] Dutt, V., Greenleaf, J.F., (1996) “Adaptive speckle reduction filter for
log-compressed B-scan images,” MedImg(15), 6.
[8] Gauch, J. M. (1999) “Image segmentation and analysis via multiscale gradient watershed hierarchies,” IEEE Trans. On Image Processing, 8, 1, 66-79.
[9] Gibbons, J.D. and Chakraborti, S. (1992): Nonparametric statistical interference. 3 rd Ed., Marcel Dekker, Inc.Dekker : New York.
[10] Golub, G. H., Heath, M., and Wahba, G. (1979) “Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter,”
Technometrics, 21, 2, 215-224.
[11] Huang, S.-Y. and Lu, H. H.-S. (2001) “Extended Gauss-Markov Theorem for Nonparametric Mixed-Effects Models, Journal of Multivariate Analysis, 76, 2, 249-266.
[12] Jansen, M. (2001). “Noise Reduction by Wavelet Thresholding.” Lecture Notes in Statistics, 161, Springer-Verlag, New York
[13] Jansen, M. and Bultheel, A. (1999). “Multiple wavelet threshold estimation by generalized cross validation for images with correlated noise.” IEEE Trans. Image Proc., 8(7), 947—953.
[14] Jansen, M. and Bultheel, A. (2001). “Asymptotic behavior of the minimum mean squared error threshold for noisy wavelet coefficients of piecewise smooth signals.” IEEE Trans. Signal Proc.
[15] Kass, M. A. and Witkin, D. Terzopolos. (1987) “Snakes : active contour models ,” Int. J. Comput. Vision, 1, 321-331
[16] Kolmogorov, A. N (1933) “Sulla determinazione emperica di una legge di distribuzione Giornale dell” Istituto Italiano degli Attuari 4 83-91
[17] Kaufman,L. and Rousseeuw, P. J. (1990)“Finding Groups in Data --An Introduction to cluster analysis,” John Wiley & Sons
[18] Li, K.C. (1985). “From Stein’s unbiased risk estimates to the method of generalized cross validation,” Ann. Statist., 13, 1352—1377.
[19] Li, K.C. (1986). “Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing,” Ann. Statist., 14, 1101—1112.
[20] Li, K.C. (1987). “Asymptotic optimality for Cp, CL, cross-validation and generalized cross-validation,” discrete index set. Ann. Statist., 15, 958—975.
[21] Lu, H. H.-S., Wells, M. T., and Tiwari, R. C. (1994) “Inference for Functions in the Two-Sample Problem with Right Censored Data: With Applications,” Journal of the American Statistical Association, 89, 427, 1017-1026.
[22] Lu, H. H.-S., Huang, S.-Y. and Lin, F.-J. (2002) "Generalized Cross-Validation for Wavelet Shrinkage in Nonparametric Mixed-Effects Models," Technical Report, Institute of Statistics, National Chiao Tung University.
[23] Macnaughton-Smith, P., Williams, W. T. , Dale,M. B. and Mockett, L. G.(1964) Dissimilarity analysis: A new technique of hierarchical sub-division, Nature, 202, 1034-1035. [6.1, 6.4.1,6.5.1,7.5.3]
[24] Maxwell, J.C. ” On hills and dales,” London, Edinburgh, Dublin Philosoph. Mag. J. Sci, 40, 421-425, 1870.
[25] Smirnov, N. (1933) “Estimate of deviation between emperical distribution functions in two independent samples, “ Bull. Moscow Univ. 2 (2) 3-16
[26] Smirnov, N. (1948) “Table for estimating the goodness of fit of empirical distribution,” Ann. Math. Statist. 19 279-281
[27] Seungyong Lee, George Wolberg, and Sung Yong Shin. (1997) “Scattered Data Interpolation with Multilevel B-Splines,” IEEE Transaction on visualization and computer graphics, 3.
[28] Su, P.-H. (2001) “Cell Competition: A new Approach To Extracting Multiple Objects From Ultrasound Images,” M.S. Thesis, Institude of Statistics, National Chiao Tung University.
[29] Vincent, L., Soille. P. (1991) ”Watersheds in digital spaces: an efficient algorithm basd on immersion simulations” IEEE Trans. On Patt. Anal. And Machine Intell., 13, 6, 583-597.
[30] Wahba, G. (1990). “Spline Models for Observational Data,” CBMS-NSF Series of Applied Mathematics, SIAM, Philadelphia.
[31] Wang, D. (1997) “A multiscale gradient algorithm for image segmentation using watersheds.” Pattern Recognition, 30, 12, 2043-2052,
[32] Weyrich, N. and Warhola, G.T. (1995). “De-noising using wavelets and cross validation,” Approximation Theory, Wavelets and Applications, 523—532.
[33] Weyrich, N. and Warhola, G.T. (1998). “Wavelet shrinkage and generalized cross validation for image denoising,” IEEE Tran. Image Processing, 7(1), 82—90.
[34] Zhu, S. C., Yuille. A. (1996) “Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation,” IEEE Trans. PAMI., 18, 884-900.