# 臺灣博碩士論文加值系統

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 就影像處理而言, 彩色影像量化是一個產生高品質壓縮影像非常有用的技巧。在這篇論文中, 我們提出一個新的彩色影像量化技巧, 改良自權重MinMax 演算法。我們的方法是MinMax 和K-Means 這兩種演算法的混合並基於權重的histogram而產生的新的演算法。我們的演算法並不嚐試去尋求量化問題的最佳解答, 取而代之的是去尋求每一個群最佳的切割方式, 最主要的觀念是基於將每一個群內部的最大群距最小化。不同於權重MinMax演算法的是我們的方法具有較佳的效率, 而且經過量化處理之後的影像品質也非常好。同時我們提出的改良式演算法亦具有容易實作的優點。
 For image processing, the color image quantization is a useful technique to produce high quality compression image. In this thesis, we present a new color image quantization technique that modifies the weighted MinMax algorithm. It is a hybrid method of MinMax and K-Means algorithms and based on weighted histogram. Instead of trying to solve an optimization problem, our algorithm is aiming to get the best-spread representation of the cluster in the color space. The main concept is based on minimizing the maximum intercluster distance. Unlike weighted MinMax algorithm, our method is more efficient and the quality of quantized image is good. In the mean time it is easy to implement also.
 CONTENTS ABSTRACT(CHINESE) i ABSTRACT(ENGLISH) ii ACKNOWLEDGEMENTS iii CONTENTS iv LIST OF FIGURES vii LIST OF TABLES xi 1. Introduction 1 1.1 Motivation 1 1.2 Introduction to Quantization 3 1.3 Organization of This Thesis 4 2. Overview of Color Image Quantization 6 2.1 Color Fundamentals 6 2.1.1 The RGB Color Space 6 2.1.2 The Luminance Considered 8 2.2 Original and Quantized Images 9 2.3 3-D Histogram of The Color Image 10 2.4 Sampling (prequantization) The Original Image for Color Statistics 11 2.5 Color Palette Generation 13 2.6 Pixel Mapping 15 2.7 Color Distance and Quantization Error Measured 16 2.8 Dithering 17 2.8.1 Ordered Dithering 18 2.8.2 Error Diffusion 19 3. Survey of Related Works 21 3.1 Uniform Quantization 21 3.1.1 Fixed 256-Color Palette 21 3.1.2 Discussion 23 3.2 Non-Uniform Quantization 24 3.2.1 Median-Cut Algorithm 24 3.2.2 Mean-Split Algorithm 26 3.2.3 K-Means algorithm 28 3.2.4 Discussion 30 4. The Weighted MinMax Algorithm and Its Modification 33 4.1 The Original Weighted MinMax Algorithm 33 4.1.1 Distance Function 33 4.1.2 Luminance Consideration and Spatial Activity Weighting 34 4.1.3 Pseudocode for Weighted MinMax Algorithm 36 4.2 Modification of Weighted MinMax Algorithm 38 4.2.1 The Idea of modify Weighted MinMax Algorithm 38 4.2.2 The 3-D Histogram Generation 40 4.2.3 The Modified Algorithm Details 41 4.2.3.1 Reducing the Color Space for Representative Color Selection 41 4.2.3.2 Fast Reassign Color to New Cluster 41 4.2.3.3 Representative Colors Selection 43 4.2.4 Destined Pixel Mapping 46 4.2.5 Dithering 47 4.3 Experimental Results 48 4.4 Discussion 65 5. Conclusions and Future Work 67 5.1 Conclusions 67 5.2 Future work 68 References 69
 [1] Heckbert, P., “Color image quantization for frame buffer display,” Comput. Graph. on Volume 16, Number 3, 297-307, (1982)[2] Zhigang Xiang, “Color image quantization by minimizing the maximum intercluster distance,” ACM Transactions on Graphics, Vol. 16, No. 3, 260-276, (July 1997)[3] Balasubramanian, R; Bounman, C.A.; Allebach J.P., “Sequential scalar quantization of color image,” J. Electron Image, 3, 1, 45-59, (1994)[4] Hsieh, Ing-Sheen; Fan, Kuo-Chin “An adaptive clustering algorithm for color quantization,” Pattern Recognition Letters, Volume 21, Issue 4, 337-346, (April 2000,)[5] Ching-Yung, Yang; Ja-Chen, Lin, “RWM-cut for color image quantization,” Computers & Graphics, Volume 20, Issue 4, 577-588, (July 1996)[6] Joy, Gregory; Zhigang, Xiang “Reducing false contours in quantized color images,” Computers & Graphics, Volume 20, Issue 2, 231-242, (March 1996)[7] Garey, M.R.; Johnson, D.S.; Witsenhausen, H.S., “The complexity of the generalized Lloyd-Max problem,” IEEE Trans. Inf. Theory, IT-28, 2, 255-256, (1982)[8] Reinhard, E.; Adhikhmin, M.; Gooch, B.; Shirley, P., “Color transfer between images,” IEEE Computer Graphics and Applications, Volume 21, Issue 4, 34 —41, (2001)[9] Blinn, J.F., “Quantization error and dithering,” IEEE Computer Graphics and Applications, Volume 14, Issue 4, 78 —82, (July 1994)[10] Wells, S.C.; Williamson, G.J.; Carrie, S.E., “Dithering for 12-bit true-color graphics,” IEEE Computer Graphics and Applications, Volume 11, Issue 5, 18 —29 (Sept. 1991)[11] Cheng, Shyi-Chyi; Yang, Chen-Kuei, “A fast and novel technique for color quantization using reduction of color space dimensionality,” Pattern Recognition Letters, Volume 22, Issue 8, 845-856, (June 2001)[12] Tasdizen, Tolga; Akarun, Lale; Ersoy, Cem, “Color quantization with genetic algorithms,” Signal Processing: Image Communication Volume 12, Issue 1, 49-57, (March 1998)[13] Lin, Wu-Ja; Lin, Ja-Chen, “Color quantization by preserving color distribution features,” Signal Processing, Volume 78, Issue 2, 201-214, (October 1999)[14] Tsann-Shyong, Liu; Long-Wen, Chang, “Fast color image quantization with error diffusion and morphological operations,” Signal Processing, Volume 43, Issue 3, 293-303, (May 1995)[15] Yang, Chen-Kuei; Tsai, Wen-Hsiang, “Color image compression using quantization, thresholding, and edge detection techniques all based on the moment-preserving principle,” Pattern Recognition Letters, Volume 19, Issue 2, 205-215, (February 1998)[16] Gregory Joy, Zhigang Xiang, “Center-cut for color-image quantization,” The Visual Computer: International Journal of Computer Graphics, Vol. 10, No.1, 62-66, (1993)[17] Xiaolin Wu, “Color quantization by dynamic programming and principal analysis,” ACM Transactions on Graphics (TOG), Vol.11, No. 4, 348-372, (Oct. 1992)[18] Zhigang Xiang; Joy, G., “Color image quantization by agglomerative clustering,” IEEE Computer Graphics and Applications, Volume 14, Issue 3, 44 —48, (May 1994)[19] Scheunders, P., “A genetic c-means clustering algorithm applied to color image quantization,” Pattern Recognition, Volume 30, Issue 6, 859-866(June 1997)[20] R. Balasubramanian, C.A. Bouman, J.P. Allebach, “Sequential scalar quantization of color images,” J. Electron. Imaging, vol. 3, No. 1, 45-59,(January 1994)[21] Paula J. Reitan, “Weighted minmax algorithm for color image quantization,” Computer Science Department United States Naval Academy.[22] Wan, S.J., Prusinkiewicz, P., Wong, S.K.M., “Variance-base color image quantization for frame buffer display,” Color Research and Application, 15, 52-58, (1990)[23] Orchard, M.T., Bouman, C.A., “Color quantization of images,” IEEE Trans. Signal processing, Vol. 39, No. 12, 2677-2690, (1991)[24] Friedman, J.J., Bentley, J.L., Finkel, R.A., “An algorithm for finding best matches in logarithmic expected time,” ACM Trans. Math. Software 3, 209-226, (1977)[25] R.W. Floyd, L. Steinberg, “An adaptive algorithm for spiatial greyscale,” Journal of the Society for Information Display, vol. 17, No. 2, 75-77, (1976)[26] R. S. Gentile, J. P. Allebach, and E. Walowit, “Quantization of color images based on uniform color spaces,” J. Imaging Technol., vol. 16, 11-21, (Feb 1990)[27] R.C. Gonzalez, R.E. Wools, Digital Image Processing, Addison-Wesley Publishing, (1992)[28] Wu, X., Witten I.H., “A fast k-means type clustering algorithm,” Dept. Computer Science, Univ. of Calgary, Canada, (May 1985)[29] T.F., Gonzalez, “Clustering to minimize the maximum intercluster distance,” Theoretical Computer Science, 38(2-3), 293-306, (June 1985)
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 1 最佳服務中心點數目及位置決策資訊系統 2 多重限制多容器裝填問題最佳化系統之研究 3 一個解決色彩量化問題的幾何學方法

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 1 利用可移除之可視浮水印技術作影像版權保護及驗證 2 以影像內涵之形狀及色彩為基礎的影像檢索系統 3 影像隱藏學之研究 4 定期船運之空櫃調度—以越太平洋航線為例 5 以利潤最大化為目標之貨櫃船隊定線模式 6 利用公車GPS定位資料推估路段行車速率之研究 7 國道客運業服務品質、顧客滿意度與移轉障礙對消費者行為意向之影響 8 以系統安全管理方法檢核我國軌道運輸之安全─以台鐵站務系統為例 9 台鐵司機員工作壓力與影響因素之研究 10 高解析方法之巨觀車流模式數值解 11 捷運車站乘客動線人流模式與干擾量度之研究 12 考慮公平性之後艙組員派遣模式---以座艙長為例 13 台灣地區海洋貨櫃運輸商品運量預測方法之研究 14 投資組合管理：資產最佳配置、保本與套利之模型規劃 15 員工對福利系統之滿意度與組織公民行為之關係

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