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研究生:陳建成
研究生(外文):Chien-Chen Chen
論文名稱:演色性評估之相關性指標
論文名稱(外文):Correlation Index for Evaluation of Color Rendition
指導教授:楊宗勳楊宗勳引用關係
指導教授(外文):Tsung-Hsun Yang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:光電科學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:89
中文關鍵詞:演色性相關性主成分分析
外文關鍵詞:correlationprincipal component analysiscolor rendition
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雖然在CIE的方式外,仍有許多評估演色性質的方法,由CIE提出的CRI仍然是最廣為利用且是目前唯一國際通用的方法,但事實上卻存在著許多本質上的問題。
本文提出以線性相關係數(Linear Correlation Coefficient)為基礎的新評估方式,試圖解決現今演色性根本的問題。其中,採用fundamental metamer 的觀念與 Matrix-R 的計算方式來得到光譜直流的成分。此外,利用Munsell Book of Colors 各色塊之間的等色覺差異的特性,做為新評估指標的建立標準。從中並發現
fundamental metamer的線性相關係數與Munsell hue、value、chroma存在著特定的關聯性,且已在分析上得到極佳的驗證。另外,在取樣測量色塊顏色與數量的決定上,採用了主成分分析(PCA)來得到色塊樣本的獨立子空間,此獨立子空間代表了色塊樣本實際有用的光譜資,且在與前述fundamental metamer之線性相關係數的合併架構中,此結果經與CIEDE2000的對應結果顯示,在評估演色性上,此架構確實可行,而且具有相當的客觀性。
Up to date, there are a lot of evaluation methods for rating the color rendition having
been proposed. Among them, the CRI recommended by CIE is the most utilized withinthe lighting community, and is the only internationally agreed metric currently. However,some intrinsic drawbacks do make those evaluation methods inactive in certain special cases.
In this thesis, the basic concept of the Linear Correlation Coefficient has been proposed
to solve the fundamental problems of color rendering. In calculating the linear correlation
coefficient, the fundamental metamer and the Matrix-R have been applied for obtaining the invariant components of the spectrum. Besides, the chips of Munsell Book of Colors are also adapted for the requirement of the sample set with equal perceptual distance. It is found that there exists certain relation between the Linear Correlation Coefficient of the obtained fundamental metamers and Munsell hue, value, and chroma. Some preliminary fitting models for the specific relation has been established and proved to work very well.
Finally, as considering the least number of samples of the specified data set, the well known Principal Component Analysis, which is the important and useful tool in color technology, was used to find the independent subspace which the specified sample data set actually localize. i.e. the truly useful spectral information of a specified sample data set. As compared with the result from CIEDE2000, the proposed scheme of the process in this thesis is really practical and very feasible.
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

List of Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

1 Introduction. . . . . . . . . . . . . . . .. . . . . . . . . .. . . . . . 1
1.1 Nature of light and color . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Cone Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Color Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Describing Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 CIE 1931 RGB Color Space. . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 CIE 1931 XYZ Color Space. . . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 CIE 1960 Luv Color space . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 CIE 1976 L a b Color Space . . . . . . . . . . . . . . . . . . . . 14
2.1.5 Munsell Color Order System . . . . . . . . . . . . . . . . . . . . . 16
2.2 Color Rendition . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Color Difference formulae. . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Color Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 CIE Standard Illuminant. . . . . . . . . . . . . . . . . . . . . . . 22
2.2.4 Color Rendering Index. . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.4.1 CIE Color Rendering Index . . . . . . . . . . . . . . . . . . . . 25
2.2.4.2 Hisdal’s Rx . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.4.3 Flattery Index, Rf . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.4.4 Color Preference Index, CPI . . . . . . . . . . . . . . . . . . . 29
2.2.4.5 Color Discrimination Index, CDI . . . . . . . . . . . . . . . . . 29
2.2.4.6 Cone Surface Area, CSA . . . . . . . . . . . . . . . . . . . . . . 29
2.2.4.7 Color Rendering Capacity, CRC . . . . . . . . . . . . . . . . . . 30
2.3 Essential Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3 Theories and Methods . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Metamerism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Vector Representation for Spectral Data . . . . . . . . . . . . . . . 34
3.3 The Wyszecki Hypothesis . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Matrix-R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5 Linear Correlation Coefficient . . . . . . . . . . . . . . . . . . . . 40
3.6 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . 41

4 Simulating Eye Perception . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Simulation Using Munsell Color Chips . . . . . . . . . . . . . . . . . 46
4.2 Result of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Correlation Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1 Spectral information . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Simulation of Color Rendering . . . . . . . . . . . . . . . . . . . . 65
5.2.1 Simulation of Color Rendering - Model A . . . . . . . . . . . . . . 68
5.2.2 Simulation of Color Rendering - Model B . . . . . . . . . . . . . . 74
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
A A proof of Matrix R . . . . . . . . . . . . . . . . . . . . . . . . . . 88
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