晶圓圖為半導體產業在晶圓片完成後，經過電信檢測的結果。不同bin code形成的特殊晶圓圖像，可以協助工程師判斷發生錯誤的製程步驟，進而找出良率下降的原因。但半導體晶圓代工產業為大量化生產，產出晶圓片成品數以十萬計，要以人力區分不同的晶圓圖像並不容易，在這種時空背景下，利用統計與機器學習方式以演算法進行自動化的圖像辨識、分群，成為一個可行的解決方案。
晶圓圖雜訊干擾的處理是圖像辨識的重要前置步驟，其中一個雜訊干擾來源為晶圓片上晶粒功能的量測機制，該機制使得晶粒在發現一種功能錯誤時，便會停止其他功能的量測，使得先量測功能的bin code會是最完整的，而越後量測bin code的晶圓圖像，會受到先量測bin code的遮蔽。過去文獻提出的方法主要針對輕微隨機雜訊干擾進行處理，但對於bin code交疊可能造成的大面積圖像遮蔽，以及高比例隨機干擾則沒有著墨。本文利用bin code量測順序的資訊，提出一種迭代插補的方法masking iteration interpolation(MII)。
本研究亦提出一種基於Radon transform的新轉換方法J-transform，該方法相較於舊有的方法，能保留更多Radon transform的原始資訊，使其在做為分群特徵時更具辨識力，並能同時具有旋轉與平移不變性的性質。
而本文使用模擬資料，對上述提出之方法進行探討，說明對於不同程度雜訊、大面積遮蔽與不同分群特徵於使用上的限制與優缺點。本文主要結果有二，第一，使用MII方法，將有效處理遮蔽與雜訊對於分群分析的干擾。第二，在本文使用的模擬資料下，其以分群分析得到的圖像識別正確率與對於雜訊處理的穩健程度，本文提出之J-transform明顯勝於舊有的方法。

A wafer bin map (WBM) is the result of a circuit probe test on a wafer after the completion of the manufacturing process. The special failure patterns of WBMs can help engineers to identify the potential manufacturing problems and find the cause of the yield decline. A wafer fabrication facility produces hundreds of thousands of wafers in short time. It is difficult to identify all the failure patterns by human eyes only. Using statistical and data mining methods to achieve automatic image recognition and clustering is a feasible solution.
De-noise is an importance pre-step in WBM recognition. One of the noise comes from the mechanism of the functional test of dies on the wafer. The mechanism is that if the die is identified to a defect in a test, other functional tests will be stopped. So that information of a bin code (result of the test) is complete only if the bin code is detected first. Other bin codes will be masked by the detected bin codes. In the past, the methods proposed for WBM recognition in the literature has mainly focused on the case with slight noise. But the issues here are that the bin codes induces a large area of image masking and the WBM may have a high proportion of noise. To solve these problems, this study proposes a method masking iteration interpolation (MII), which is a iteration method for interpolation by using the information of measurement sequence of bin codes.
To improve the WBM recognition, this study also presents a novel approach J-transform which based the Radon transform. Compared to the existing methods, the J-transform can retain more original information of Radon transform and has more power for WBM recognition. Furthermore, the features by J-transform possesses translation and rotation invariance at the same time.
The simulated data is from the observations of many real WBMs. We explore advantages and disadvantages of MII and J-transform approaches by varying the levels of noise and the large areas of masking of the simulation data. We have two main results in this study. First, MII is effective in reconstructing the masked WBMs. Second, compared with the existing methods, J-transform has more power for image recognition and more robust for noise.

Deans, S. R. (2007). The Radon transform and some of its applications. Courier Corporation.
Hansen, M. H., Nair, V. N., and Friedman, D. J. (1997). Monitoring wafer map data from integrated circuit fabrication processes for spatially clustered defects. Technometrics, 39(3):pages 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, 107(1):pages 88–103.
Jeng, S.-L. and Liu, Y.-T. (2011). Adaptive tangent distance classifier on recognition of handwritten digits. Journal of Applied Statistics, 38(11):pages 2647–2659.
Kaufman, L. and Rousseeuw, P. J. (2009). Finding groups in data: an introduction to cluster analysis, volume 344. John Wiley & Sons.
Khan, M. A., Khan, T. M., Bailey, D., and Kong, Y. (2016). A spatial domain scar removal strategy for fingerprint image enhancement. Pattern Recognition, 60:pages 258–274.
Kim, B., Jeong, Y.-S., Tong, S. H., Chang, I.-K., and Jeong, M. (2015). Step-down spatial randomness test for detecting abnormalities in dram wafers with multiple spatial maps. Semiconductor Manufacturing, IEEE Transactions on, 29:pages 57–65.
Meng, J. and Wang, S. (2015). The recognition of overlapping apple fruits based on boundary curvature estimation. In 2015 Sixth International Conference on Intelligent Systems Design
and Engineering Applications (ISDEA), pages 874–877. IEEE.
Nazari, N. H., Tan, T., and Chiang, Y.-Y. (2016). Integrating text recognition for overlapping text detection in maps. Electronic Imaging, 2016(17):pages 1–8.
Rousseeuw, P. J. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of computational and applied mathematics, 20:pages 53–65.
Simard, P., LeCun, Y., and Denker, J. S. (1993). Efficient pattern recognition using a new transformation distance. In Advances in neural information processing systems, pages 50–58.
Simard, P. Y., LeCun, Y. A., Denker, J. S., and Victorri, B. (1998). Transformation invariance in pattern recognition—tangent distance and tangent propagation. In Neural networks: tricks of the trade, pages 239–274. Springer.
Taam, W. and Hamada, M. (1993). Detecting spatial effects from factorial experiments: An application from integrated-circuit manufacturing. Technometrics, 35(2):pages 149–160.
Tabbone, S., Wendling, L., and Salmon, J.-P. (2006). A new shape descriptor defined on the radon transform. Computer Vision and Image Understanding, 102(1):pages 42–51.
Wang, C.-H., Kuo, W., and Bensmail, H. (2006). Detection and classification of defect patterns on semiconductor wafers. IIE Transactions, 38(12):pages 1059–1068.
Weng, M.-Q. (2008). Classification of wafer bin maps by using spatial tests and invariant transformation distance. National Cheng Kung University Master Thesis.
Wu, M.-J., Jang, J.-S. R., and Chen, J.-L. (2015). Wafer map failure pattern recognition and similarity ranking for large-scale data sets. Semiconductor Manufacturing, IEEE Transactions
on, 28(1):pages 1–12.