臺灣博碩士論文加值系統

許多不同的彩色座標均企圖想要指定一個能夠與人眼感知一致的色彩空間，而國際照明委員會(CIE, International Commission on Illumination) 制定了CIE L*a*b*色彩座標系統，此色彩座標較接近人類視覺系統，一般所常使用的彩色座標均可先以線性轉換到XYZ座標系統，再以一非線性轉換到L*a*b*彩色座標。
在非線性的計算中有一開立方根的電路，此論文中，我們提出近似的數學求解法與其相對應的硬體架構，替代之前所常使用的查表法(LUT)。座標轉換的模擬、演算法的計算與誤差的估計，我們均使用Matlab來完成，然後以Verilog硬體描述語言與SYNOPSYS合成軟體，來驗證與評估我們所設計出的硬體的效能。最後，所完成的近似開立方根架構可以比查表法有更快的速度與更少的硬體花費，在色彩座標轉換非線性的部份經過此一替代後，所佔用的硬體面積也就更小了。

Various color spaces have been reported in an attempt to identify a uniform perceptual color space for color measurement and prediction purposes. CIE (Commission Internationale de l''Eclairage) recommends one linear transformation to get the XYZ color space, and then, one non-linear transformation is used to get the L*a*b* color space. The design and implementation of hardware architecture, which can perform real time conversion from the RGB color coordinates to standard CIE L*a*b* color coordinates, is studied in this thesis.
To calculate the cube-root in non-linear transformation, we propose the approximate arithmetic algorithms and the corresponding hardware architecture to replace the look-up tables. The accuracy of the color coordinate transform is simulated under Matlab programming tool. Then using the Verilog HDL programming language and SYNOPSYS synthesis tool to estimate and forecast its hardware performance. Finally, the implemented architecture for cube-root is faster than the LUT, and the presented combinational logic is less than the most recent published works for color space conversion.

中文摘要------------------------------------------------------------------------ Ⅰ
英文摘要------------------------------------------------------------------------ Ⅱ
誌謝------------------------------------------------------------------------------ Ⅲ
目錄------------------------------------------------------------------------------ Ⅳ
表目錄--------------------------------------------------------------------------- VII
圖目錄--------------------------------------------------------------------------- VIII
第一章　緒論------------------------------------------------------------------ 1
1.1　介紹-------------------------------------------------------------------- 1
第二章　色彩學--------------------------------------------------------------- 3
2.1 介紹---------------------------------------------------------------------- 3
2.2 心理上的基本色（psychological primary）----------------------- 3
2.3 生理學上的色彩------------------------------------------------------- 4
2.3.1 眼睛的光學組織-------------------------------------------------- 4
2.3.2 視網膜的構造----------------------------------------------------- 5
2.3.3 「三原色學說」與「四色學說」----------------------------- 7
2.4 物理學上的色彩------------------------------------------------------- 8
2.4.1 CIE XYZ簡介------------------------------------------------------ 8
2.4.2 CIE LAB的起源--------------------------------------------------- 11
第三章　彩色座標系統的介紹與應用------------------------------------ 12
3.1 彩色座標系統介紹---------------------------------------------------- 12
3.1.1 RGB彩色系統----------------------------------------------------- 12
3.1.2 CMY彩色系統----------------------------------------------------- 13
3.1.3 Y.U.V彩色系統--------------------------------------------------- 14
3.1.4 Y.I.Q彩色系統---------------------------------------------------- 15
3.1.5 YCbCr彩色座標--------------------------------------------------- 15
3.1.6 XYZ彩色座標----------------------------------------------------- 16
3.1.7 CIE L*a*b*彩色座標---------------------------------------------- 16
3.2 CIE LAB的應用-------------------------------------------------------- 17
3.2.1使用CJND模型之彩色影像編碼------------------------------ 17
3.2.2 彩色影像區分(segmentation)------------------------------------ 19
3.2.3 透過標準彩色空間轉換色彩資訊----------------------------- 23
3.2.4 用於彩色影像品質評估----------------------------------------- 24
3.3 Matlab的模擬與分析------------------------------------------------- 24
第四章　彩色座標轉換的ASIC硬體架構------------------------------- 29
4.1 介紹---------------------------------------------------------------------- 29
4.2 分兩階段計算的硬體架構(RGB→XYZ→L*a*b*)--------------- 30
4.3 Lossless color coordinate transform----------------------------------- 34
4.4 直接三維查表法------------------------------------------------------- 36
4.5 低容積三維查表法結合線性內插---------------------------------- 37
4.5.1 傳統的內插系統-------------------------------------------------- 37
4.5.2 三維內差法的計算----------------------------------------------- 38
4.5.3 提升轉換的準確度----------------------------------------------- 42
4.6 討論---------------------------------------------------------------------- 44
第五章　計算開根值的方法------------------------------------------------ 46
5.1 介紹---------------------------------------------------------------------- 46
5.2 切線近似法------------------------------------------------------------- 46
5.3 九章算術-少廣章------------------------------------------------------ 48
5.4 討論---------------------------------------------------------------------- 54
第六章　開立方根的硬體設計--------------------------------------------- 55
6.1 介紹---------------------------------------------------------------------- 55
6.2 《九章算術》的開立方程序---------------------------------------- 55
6.3 控制加減法電路(CAS)------------------------------------------------ 57
6.4 架構分析---------------------------------------------------------------- 58
6.5 開三次方根的硬體架構---------------------------------------------- 62
6.6 邏輯閘與速度的比較------------------------------------------------- 64
6.7 結論---------------------------------------------------------------------- 65
第七章　近似開立方根的硬體設計--------------------------------------- 66
7.1 介紹---------------------------------------------------------------------- 66
7.2 分成十等份------------------------------------------------------------- 66
7.3 將斜率固定------------------------------------------------------------- 68
7.4 再次的精簡，省去一個點------------------------------------------- 69
7.5 割線近似---------------------------------------------------------------- 69
7.6 誤差分析---------------------------------------------------------------- 71
7.7 電路圖------------------------------------------------------------------- 74
7.8 最佳點的選擇與誤差分析------------------------------------------- 80
7.9 結論---------------------------------------------------------------------- 82
第八章　結論及未來研究方向 85
8.1 總結---------------------------------------------------------------------- 85
8.2 貢獻與未來研究方向------------------------------------------------- 85
參 考 文 獻-------------------------------------------------------------------- 88

[1] Sharma, G.; Trussell, H.J.“Digital color imaging,”Image Processing, IEEE Transactions on , Volume: 6 Issue: 7 , July 1997 Page(s): 901 -932
[2] Rafael C. Gonzalez, Richard E. Woods.“Digital image processing,” Reading, Mass. :Addison-Wesley,/c1992./
[3] Tominaga, S.“A color classification method for color images using a uniform color space,” Pattern Recognition, 1990. Proceedings., 10th International Conference on , Volume: i, 1990 Page(s): 803 -807 vol.1
[4] Trussell, H.J.“DSP solutions run the gamut for color systems,” IEEE Signal Processing Magazine , Volume: 10 Issue: 2, April 1993 Page(s): 8 -23
[5] Fukuma, S.; Iwahashi, M.; Kambayashi, N.“Lossless color coordinate transform for lossless color image coding,” Circuits and Systems, 1998. IEEE APCCAS 1998. The 1998 IEEE Asia-Pacific Conference on , 1998 Page(s): 595 -598
[6] Bruekers, F.A.M.L.; van den Enden, A.W.M. ” New networks for perfect inversion and perfect reconstruction,” Selected Areas in Communications, IEEE Journal on , Volume: 10 Issue: 1 , Jan. 1992 Page(s): 129 -137
[7] Funt, B.V. ” Color constancy in digital imagery,” Image Processing, 1999. ICIP 99. Proceedings. 1999 International Conference on , Volume: 3 , 1999 Page(s): 55 -59 vol.3
[8] Andreadis, I.; Iliades, P.; Karafyllidis, Y.; Tsalides, P.; Thanailakis, A. “Design and VLSI implementation of a new ASIC for colour measurement,” Circuits, Devices and Systems, IEE Proceedings- , Volume: 142 Issue: 3 , June 1995 Page(s): 153 -157.
[9] Nsour, M.; Abdel-Aty-Zohdy, H.S. "An improved ASIC design and implementation for color space conversion applications," Circuits and Systems, 1996., IEEE 39th Midwest symposium on , Volume: 2 , 1996 Page(s): 609 -612 vol.2
[10] Asakawa, K.; Sugiura, H.“High-precision color transformation system,” Consumer Electronics, IEEE Transactions on , Volume: 41 Issue: 2 , May 1995 Page(s): 304 —312
[11] Po-chieh Hung,“ Color Correction Method for Digital Color Printer,”Photography Society, A-3 (1987).
[12] Teruo Fumoto.“ High-speed Color Processor,” Color Management system JIEC Seminar Text, pp.52-68 (1993).
[13] Kai Hwang, “ Computer arithmetic: principles, architecture, and design ”, New York: Wiley, 1979.
[14] Behrooz Parhami, ”Computer arithmetic: algorithms and hardware designs”, New York: Oxford University Press, 2000.
[15] Israel Koren, "Computer arithmetic algorithms", Englewood Cliffs, N.J. : Prentice Hall, 1993.
[16] Amos R. Omondi, " Computer arithmetic: algorithms, arithmetic, and implementation," New York: Wiley, 1994.
[17] " Passport CB35RO122 0.35 micron, 3.3 volt ROM Compiler with CE “, Galax! Inc. Version 1.2 , July 1998
[18] Young-Sang Lee; Jun-Woo Kang; Lee-Sup Kim; Seung-Ho Hwang, “Self-timed shared division and square-root implementation using full redundant signed digit numbers”, VLSI and CAD, 1999. ICVC ''99. 6th International Conference on , 1999 Page(s): 541 -544
[19] “ DW02_sqrt, Combinatorial Square Root”, Synopsys Online Document, Vol 1-235, v1999.10
[20] McQuillan, S.E.; McCanny, J.V.; Hamill, R. “ New algorithms and VLSI architectures for SRT division and square root,” Computer Arithmetic, 1993. Proceedings., 11th Symposium on , 1993 Page(s): 80 -86
[21] 譚仁芳,”The construction of color JND model and its applications and wavelete based image coding,”國立雲林科技大學電機工程技術研究所,1998
[22] 黎奕緯,”Color JND model Application for Wavelet based Image Coding,”國立雲林科技大學電機工程技術研究所,1998
[23] 蘇恭弘,”另類速算立方根的方法─2”
http://euler.tn.edu.tw/thinkmenu2000.htm
[24] 施榿樑,”古法求開方”, 數學教育 第四期 Edumath 4 ( 6/97) 86-89. http://www.fed.cuhk.edu.hk/~fllee/mathfor/edumath/9706/19sze_hl.html
[25] 傅海倫,”九章算術開方算法系統及其與現代計算機程序的比較”, 數學教育 第八期 EduMath 8 (06/99)
http://www.fed.cuhk.edu.hk/~fllee/mathfor/edumath/9906/11fu_hl.html
[26] 游志雲,“以C.I.E. LAB1976近似均勻色彩空間及色差公式作為色彩對比指標之研究”, 行政院國家科學委員會補助專題研究報告, 1993
[27] Ian T. Young, Jan J. Gerbrands, Lucas J. van Vliet, “Fundamentals of Image Processing”
[28] “ Color Manager Manual”, http://www.linocolor.com/