臺灣博碩士論文加值系統

在影像分析的領域中，空間平滑、空間檢定與空間集群分析方法常被用來決定空間的隨機性以及尋找重要的空間區域。在本篇論文中，我們將會修改上述的統計方法且將之應用於兩個真實的資料上。 分別是二維度的晶圓圖 (Wafer Bin Map(WBM)) 資料與四維度 (三維空間維度加上一維時間維度)的功能性核磁共振影像資料 (functional Magnetic Resonance Imaging(fMRI))。
晶圓圖失效圖形的辨識是半導體生產過程中重要的問題。我們利用空間平滑技術(kernel smoothing), 空間檢定(HNF test: Hansen et al. (1997)),與空間分群方法(DBSCAN: Density-Based Spatial Clustering ofApplications with Noise: Estern et al. (1996))來快速的減少資料量以及找到重要的失效圖型特徵。我們的流程可以幫助工程師縮減資料量與縮小問題的範圍，並從失效的晶圓片圖形中找到製程錯誤的原因。另一方面，以分析二維度晶圓片資料的技術為輔，我們利用迴歸分析的方法去處理功能性核磁共振影像資料的時間維度。在處理完時間維度後，再將空間檢定與空間集群方法從二維度推廣到三維空間資料的迴歸分析結果上。這些方法將可以幫助研究人臉辨識的研究人員去確認反應的顯著水準與找出腦部有顯著反應的腦區。

Spatial smoothing, spatial testing, and spatial clustering are often applied to determine the spatial dependence and find the important spatial region in the field of image analysis. In this thesis, we will modify the above statistical methods to analysis two real data sets. They are a two dimensional Wafer Bin Map (WBM) and a four dimensional (three dimensions in space plus one dimension in time) facial recognition functional Magnetic Resonance Imaging (fMRI) data.
Defect pattern recognition of WBM is an important issue for semiconductor fabrication industry to monitor quality. We use spatial smoothing (kernel smoothing), spatial testing (HNF test: Hansen et al. (1997)), and spatial clustering (DBSCAN: Density-Based Spatial Clustering of Applications with Noise: Estern et al. (1996)) to rapidly reduce data size and find the crucial pattern characteristic. Our thesis work can assist engineers to find the process problems from defective patterns in the WBMs by reducing the problem scope and work time. On the other hand, together with techniques of analysis on two dimensional WBM, we use regression method to deal with time dimension in fMRI data. After the dimension reduction of time, we extend the spatial testing and spatial clustering methods to the three dimension data which are the output of the regression analysis. Our approach help the facial recognition researcher to locate the significant level of response and identify the activated response region.

1. Background and Motivation.......................... 1
1.1 Data Description and Exploration.................... 3
1.1.1 WBMs............................... 4
1.1.2 FMRIs............................... 11
1.2 Research Problems and Proposed Methods............... 21
1.2.1 WBMs............................... 21
1.2.2 FMRIs............................... 21
1.2.3 Proposed Methods......................... 22
1.3 Thesis Framework............................. 23
2. Literature Review................................ 24
2.1 WBM Fabrication and Spatial Testing.................. 24
2.2 WBM Classification and Clustering................... 25
2.3 FMRI Data Analysis............................ 26
2.4 FMRI Clustering.............................. 27
2.5 Software and Package........................... 27
3. Methodology................................... 29
3.1 FMR Images Voxelwise Analysis..................... 29
3.2 LOWESS.................................. 30
3.3 Denoising and Enhancement....................... 31
3.3.1 Application to 2D WBMs...................... 32
3.3.2 Extension to 3D FMRIs...................... 32
3.4 Spatial Testing............................... 32
3.4.1 The HNF Test........................... 33
3.4.2 Extension of HNF Test to 3D FMRIs............... 36
3.5 Spatial Clustering. DBSCAN....................... 36
4. Applications to Real Data Sets......................... 40
4.1 2D WBM Images.............................. 40
4.1.1 2D De-noise and Enhance Signal................ 40
4.1.2 2D Spatial Testing......................... 42
4.1.3 2D Clustering........................... 44
4.2 3D fMR Images.............................. 59
4.2.1 Group Analysis........................... 59
4.2.2 3D Spatial Clustering....................... 65
4.2.3 3D Spatial Testing......................... 66
5. Conclusions and Feature Work......................... 88
5.1 Conclusions................................. 88
5.1.1 WBMs............................... 88
5.1.2 FMRIs............................... 89
5.2 Feature Work and Di
culties........................................89
5.2.1 WBMs............................... 89
5.2.2 FMRIs............................... 90
Appendix............................................95
Appendix A. BOLD responses of ten subjects.................... 96
Appendix B. DBSCAN result of the e ect di erence between V1 and V4 under different gender or department............................ 106

Besag, J. (1974), “Spatial Interaction and the StatisticalAnalysis of Lattice Systems, Journal of the Royal Statistical Society Series B (Methodological), Vol. 36. 192-236.
Chao, L., C. and Tong, L., I. (2009), “Wafer Defect Pattern Recognition by Multi-Class Support Vector Machines by Using a Novel Defect Cluster Index, Expert Systems with Applications, Vol. 36, 10158-10167.
Chen, T. (2008), “A SOM-FBPN-Ensemble Approach with Error Feedback to Adjust Classification for Wafer-Lot Completion Time Prediction, International Journal of Advanced Manufacturing Technology, Vol. 37, 782-792.
Chien C. F., Lin T. H., and Liu Q. W. (2002), “Developing A Data Mining Method for Wafer Bin Map Clustering and Emperical Study In A Semiconductor Manufacturing Fab, Journal of the Chinese Institute of Industrial Engineers, Vol. 10, 674-685.
Cleveland, W. S. (1979), “Robust Locally Weighted Regression and Smoothing Scatterplots Journal of the American Statistical Association, Vol. 74, 829-836.
Clif , A. D. and Ord, J. K. (1981), “Spatial Processes, Models and Applications, London: Pion Limited.
Ester, M., Kriegel, H., P., Sander, J., Xu, X. (1996), “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise, Proceedings of 2nd International Conference on Knowledge Discovery and Data Mining, 226-231.
Efron, B. and Tibshirani. R. J. (1993), “An Introduction to the Bootstrap, Chapman ＆ Hall/CRC.
Hansen M. H., Nair V. N., and Friedman D. J. (1997), “MonitoringWafer Map Data from Integrated Circuit Fabrication Processes for Spatially Clustered Defects, Technometrics, Vol. 39, 241-253.
Hsu S. C., and Chien C. F. (2007), “Hybrid Data Mining Approach for Pattern Extraction from Wafer Bin Map to Improve Yield in Semiconductor Manufacturing, International Journal of Production Economics, Vol. 107, 88-103.
Hwang, J. Y. and Kuo, W. (2007), “Model-Based Clustering for Integrated Circuit Yield Enhancement, European Journal of Operational Research, Vol. 178, 143-153.
Jeong, Y. S., Kim, S. J., and Jeong, M. K. (2008), “Automatic Identification of Defect Patterns in Semiconductor Wafer Maps Using Spatial Correlogram and Dynamic Time Warping, IEEE Transections, Vol. 21.
Jiang, F., Dricot, L., Blanz, V., Goebel, R., and Rossion, B. (2009), “Neural Correlates of Shape and Surface Reflectance Information in Individual Faces, Neuroscience, vol, 163,1078-1091.
John, A. (2009), “Preparing fMRI Data for Statistical Analysis, fMRI Techniques and Protocols, Published: 2009, 151-178.
Lee, A. J. (1990), “U-Statistics, Theory and Practice, New York: Marcel Dekker.
Lindquist, M. A.(2008), “The Statistical Analysis of fMRI Data, Statistical Science, Vol. 23, 439-464.
Loffler, G., Yourganov, G., Wilkinson, F., and Wilson, H. R. (2005), “fMRI Evidence for the Neural Representation of Faces, Nature Neuroscience, vol, 10, 1386-1390.
Stanberry, L., Murua, A., and Cordes D. (2008), “Functional Connectivity Mapping Using the Ferromagnetic Potts Spin Model, Human Brain Mapping, Vol. 29, 422-440.
Taam,W. and Hamada, M. (1993), “Detecting Spatial E ects from Factorial Experiments: An Application from Integrated-Circuit Manufacturing, Technometrics, Vol. 35, 149-160.
Tabelow, K., Polzehl, J., Voss, H. U., and Spokoiny, V. (2006), “Analyzing fMRI Experiments with Structural Adaptive Smoothing Procedures, NeuroImage, Vol. 33, 55-62.
Talairach, J. and Tournoux P. (1988), “Co-planar Stereotaxic Atlas of the Human Brain: 3-Dimensional Proportional System - an Approach to Cerebral Imaging, Thieme Medical Publishers, New York.
Tan, P. N., Steinbach, M., Kumar, V. (2006), “Introduction to Data Mining, Pearson Education, Inc.
Wang, C. H. (2009), “Separation of composite defect patterns on wafer bin map using support vector clustering, International Journal of Production Economics, Vol 36, 2554-2561.
Wang, C. H.,Wang, S. J., and Lee,W. D. (2006), “Automatic Identification of Spatial Defect Patterns for Semiconductor Manufacturing, International Journal of Production Economics. Vol. 44, 5169-5185.
Weng, M. C. (2008), “Classification of Wafer Bin Maps by Using Spatial Tests and Invariant Transformation Distance, National Cheng Kung University Master Thesis.
Xia, J., Liang, F., and Wang, Y. M. (2009), “On Clustering fMRI Using Potts and Mixture Regression Models, 31st Annual International Conference of the IEEE EMBS.
Yuan, T. and Kuo,W. (2008), “A Model-Based Clustering Approach to the Recognition of the Spatial Defect Patterns Produced Duing Semiconductor Fabrication, IEEE Transections, Vol. 40, 93-101.