本篇論文提出了腕骨生長骨化模型的建立，以及利用此模型基於模糊理論和統計方法，所作的腕骨生長預估及腕骨年齡判斷之應用。這個生長模型著重於探討在孩童時期，亦即腕骨主要的生長時期的生長狀況。它包含了腕骨型態上的幾項特徵，以及生長描述子：生長權重矩陣。我們所抽取的型態上的特徵包含五個種類：T-Ratio, Ratio-I, II, 和Compactness-I, II。它們是由經過人工切割以及一些影像處理方法所做前處理過的腕骨X光數位影像，所抽取計算出的參數所計算來的。這些特徵可以將各歲腕骨骨化的狀態量化。而生長權重矩陣包含了縱向和橫向在每個增長一歲的階段所生長的比率的描述子，它們可以用以描述每一個部分的腕骨生長的動態過程以及趨勢。結合這些幾何特徵，我們可以得到一套能涵蓋許多方面，以及助益於分析腕骨骨化的生長模型。

在本篇論文中，我們發展了利用此生長模型所作的腕骨骨化預估以及年齡辨識的方法。腕骨生長預估方法是利用生長權重矩陣所建立的，使用者可以使用一個已知腕骨種類及年齡的檔案，來預估該骨頭或該病例在其它歲的生長狀態。此外，我們也發展了腕骨年齡辨識方法。利用型態特徵的線性特性，我們以模糊理論的概念來發展此辨識方法。我們結合了主成分分析和特徵對於年齡的相關係數的計算等方法，來發展出三種腕骨年齡判斷的過程。這是為了提升判斷的正確率以及能提供合理的判斷結果，供醫生或使用者在判斷年齡的幫助。在醫學上，判斷誤差在1.5歲之內算是可接受的結果。以我們的資料庫所實驗，最佳的方法在誤差1.5歲內的正確率結果女性為92.4%，男性為89.5%。這個辨識結果在實際運用上算是理想的。

The thesis describes the construction of a carpal ossified model, and its applications to carpal bone age assessment and bone growth estimation procedures based on fuzzy criterion and statistical analysis. The growth model is focused on the childhood, i.e., the main growth stage of carpals. It’s composed of the statistics of morphological features of carpals, and the growth descriptors—weighting matrices. The morphological features we extracted are five kinds—T-Ratio, Ratio-I and II, and Compactness-I and II, and they are calculated from the preprocessed digital carpal images by hand and image processing methods. They can quantify the carpal ossified status in different ages. The weighting matrices include the longitudinal and transverse descriptions of the increase rate of a bone in each one-year-old growth stages. The weighting matrices we evaluated can indicate the overall dynamic processes and trends of the ossification of each part of carpals. Combining the geometric features, we can obtain the carpal growth model that can cover many aspects and benefit for the analysis of the ossification.

In thesis, we also developed procedures for the bone ossification estimation and the bone age assessment based on the constructed model. The bone estimation procedures are investigated by the weighting matrices. The users can use a carpal image file that in well-known age and bone type, to estimate the status of its bone in all the other ages. Besides, we develop the carpal bone age assessment procedures based on fuzzy concept for the linearity of the morphological features. We combine the principle component analysis and the evaluation of correlation coefficients between feature value and age, to develop three categories of the bone age assessment procedures. The purpose is to make an attempt to acquire high-performed procedures that can provide reasonable results for helping the doctors or users judge the bone age. In clinic, error within 1.5 years old is acceptable. After simulations, the best correct rates within 1.5 years old error are 92.4% in female and 89.5% in male, respectively. The assessment by the proposed procedures is satisfactory for practice.

[1] G. R. Milner, R. K. Levick and R. Kay, ”Assessment Of Bone Ages: A Comparison Of The Greulich and Pyle, and The Tanner and Whitehouse Methods”, Clin Radiol, Vol.37, pp.119-212, 1986

[2] E. Pietka, “Computer-Assisted Bone Age Assessment Based On Features Automatically Extracted From A Hand Radiograph”, Computerized Medical Imaging and Graphics, Vol.19, No.3, pp.251-259, 1995.

[3] E. Pietka, A. Gertych, S. Pospiech, F. Cao, H. K. Huang, “Computer-Assisted Bone Age Assessment: Image Preprocessing and Epiphyseal/Metaphyseal ROI Extraction”, IEEE Transactions On Medical Imaging, Vol.20, No.8, pp.715-729, August 2001.

[4] Tristan, A.; Arribas, J.I., ”A Radius and Ulna Skeletal Age Assessment System” Machine Learning for Signal Processing, 2005 IEEE Workshop on 28-30 Sept. 2005 Page(s):221 – 226

[5] C.W. Hsieh, B.C. Chu, T.L. Jong and C.M. Tiu, “Bone Age Classification Using Fuzzy Concept with Support Vector Machine Neural Network”,12th International Conference on BioMedical Engineering (ICBME 2005), 1A4-05, Singapore, Singapore, Dec., 2005.

[6] D. J. Michael and A. C. Nelson, “HANDX: A Model-Based System For Automatic Segmentation Of Bones From Digital Hand Radiographs”, IEEE Trans. Med. Imag., Vol.8, No.1, March 1989.

[7] E. Pietka, L. Kaabi, M. L. Kuo, and H. K. Huang, “Feature Extraction in Carpal-Bone Analysis”, IEEE Trans. Med. Imag., Vol.12, No.1, March 1993.

[8] E. Pietka, M. F. McNitt-Gray, M. L. Kuo and H. K. Huang, “Computer-Assisted Phalangeal Analysis in Skeletal Age Assessment”, IEEE Trans. Med. Imag., Vol.10, No.4, December 1991.

[9] E. Pietka and H. K. Huang, “Epiphyseal Fusion Assessment Based On Wavelets Decomposition Analysis”, Computerized Medical Imaging and Graphics, Vol.19, No.6, pp.465-472, 1995.

[10] A. M. M. D. Silva, S. D. Olabarriaga, C. A. Dietrich and C. A. A. Schmitz, “On Determining A Signature For Skeletal Maturity”, Computer Graphics and Image Processing, 2001 Proceedings of XIV Brazilian Symposium, pp.246-251, 15-18 Oct. 2001.

[11] F. Cao, H. K. Huang, E. Pietka and V. Gilsanz, “Digital Hand Atlas and Web-Based Bone Age Assessment: System Design and Implementation”, Computerized Medical Imaging and Graphics 24 (2000), pp. 297-307.

[12] B.C. Fan, “Computerized Bone Age Estimation Using the Carpal-Bone Images”, Master Thesis, EE Nthu, 1999.

[13] J.H. Chen, “A Computerized Skeleton Age Assessment Based On Phalangeal Image and Neural Network Approach”, Master Thesis, EE Nthu, 2002.

[14] C. W. Hsieh, T. L. Jong, C. H. Chang, “An Investigation of Computerized Automatic Bone Age Assessments Based on Phalanges Image Features”, 16th Conference on CVGIP03, Hsinchu, Aug. 2003.

[15] Pietka E, Gertych A, Pospiech-Kurkowska S, et al., ”Computer-assisted bone age assessment: Graphical user interface for image processing and comparison”, JOURNAL OF DIGITAL IMAGING 17 (3): 175-188 SEP 2004.

[16] M. J. Huang, C. W. Hsieh, T. L. Jong, and C. M. Tiu, “The Study of Carpal Bone Age Assessment Based on Fuzzy Growth Model”, 19th Conference on CVGIP06, Taoyuan, Aug. 2006.

[17] C.W. Hsieh, M.J. Huang, and T.L. Jong, “Growth Evaluation Based on Morphological Description of carpals”, Conference on wc2006, Seoul, Aug. 2006.

[18] Greulich WW, Pyle SI “Radiography atlas of skeletal development of the hand and wrist”, Stanford University Press, Stanford, California 1959.

[19] Rafeal C. Gonzales, Richard E. Woods, Digital Image Processing, 2nd Edition, Prentice-Hall, Inc., New Jersey, 2002.

[20] L.A.Zadeh, “Fuzzy Sets”, Information and Control, vol.8, pp 338-353, 1965.

[21] Chin-Teng Lin, C.S.Georage Lee, Neural Fuzzy Systems, Prentice Hall P T R Prentice-Hall, Inc., A Simon & Schuster Company, New Jersey, 1996.

[22] 蘇木春, 張孝德, 機器學習：類神經網路、模糊系統以及基因演算法則, 全華科技圖書股份有限公司, 1999.

[23] Jurgen Schurmann, Pattern Classification, a Wiley-Interscience Publication John Wiley & Sons, inc. New York/Chicherster/Brisbane/Toronto/Singapore, 1996.