原色偏移色度模型在顯示器上之分析與應用

Abstract

隨著科技的進步，人們對於彩色顯像的要求也日益增加：不僅要求以豐富的色彩顯像，更要求原影像的色彩感知，能真實重現以滿足大眾的喜愛。因此如何在液晶顯示器 (Liquid Crystal display, LCD) 與陰極射線管螢幕 (Cathode ray tubemonitor, CRT monitor) 上真實預測及複製彩色影像，便成為重要的課題。本論文最主要的目標即在準確地描述此兩種顯示器的色彩特徵，藉以精確地預測及重製顯示器的顏色。 原色不變色度模型 (PPrimary-invariance colorimetric model) 經常被用來描述CRT monitor的色彩特徵。然而LCD不同於CRT monitor的特性之一為前者被發現有原色偏移 (Primary-shift)的特性，而後者常被假設為原色不變 (Primary-invariance) 顯示器。針對LCD原色偏移的特性，本論文首先探討色調複製曲線(Tone reproduction curve) 在原色偏移與原色不變顯示器上的差異，並比較LCD輿CRT monitor原色偏移的大小。更進一步則對原色不變色度模型進行測試。發現當LCD原色偏移的最大程度為CRT monitor的5~10倍時，原色不變色度模型無法對LCD做正確地色彩定特徵 (Color characterization)，平均色差≧5ΔEuv。 LCD的光學特性通常係以彈性流體力學理論與廣義Jones矩陣法來分析。然而此種物理模型過於複雜，並不適用於色彩定特徵上。為了滿足色度模型準確性高、計算簡單、及所需量測顏色少的要求，對於LCD的色彩定特徵，本論文係利用多項式回歸分析 (polynomial regression analyses) 來修正原色不變色度模型所產生的誤差。研究顯示：當回歸分析矩陣≧3x9時，在LCD的顏色預測及複製上平均色差都能小於3ΔEuv。多項式回歸分析因為具有計算簡單的解析數學表示式，所以比其他定特徵的方法（如三維內差查表法、類神經網路、物理分析等）更適用於LCD的色彩定特徵。不過利用多項式回歸分析來描述顯示器的色彩特徵所需的量測色依然比原色不變模型多。 為了更進一步減少色彩定特徵時所需的量測色數目，除了模型的改良外，以解析的數學式取代一維內差查表法，來描述顯示器的色調複製曲線亦是方法之一。因此本論文一方面提出原色偏移反向模型 (Primary-shift backward model) 來計算顏色複製時所需的數位訊號值；另一方面，亦提出以四個參數及兩個gamma值來分別描述LCD與CRT monitor的色調複製曲線。若將此修正應用在顏色加成模型及原色偏移反向模型上，平均精確度達到和3x9多項式回歸分析修正相同的水準。而由於所需的量測色較多項式回歸分析少，不管是在CRT monitor或LCD上，本論文提出的反向模型和色調複裂曲線經驗式，都將使得這兩種顯示器的色彩定特徵更有效率。

As color reproduction technology continuously improves, demands on color image presentation become more and more rigid in multimedia era. Images are expected to be presented not only with full-color but also with high fidelity. Therefore, predicting and reproducing colors on liquid crystal displays (LCDs) and cathode-ray-tube (CRT) monitors accurately become necessary. Hence, characterizing color properties of these two displays is the main objective of this thesis. Primary-invariance colorimetric model is usually used to characterize CRT monitors. Nevertheless, one major difference between LCDs and CRT monitors is that the former are found to have the characteristic of primary-shift in RGB channels; yet, the latter are usually assumed to be the primary-invariance color devices. Relationships among three tone reproduction curves (TRCs) of a channel are first discussed in primary-shift and -invariance displays. The characterization accuracy of Primary-invariance colorimetric model in LCDs and CRT monitors is then examined. According to our studies, when the primary-shifts of LCDs are larger than those in CRT monitors by factors about 5~10, this model can not obtain acceptable characterization accuracy. The average color difference is larger than 5ΔEuv. Optical properties of LCDs are usually analyzed based on the continuum elasticity deformation theory and extended Jones matrix. Due to their complexities, these physical analyses are not applicable to characterize color rendering of LCDs. To achieve the desired features ofcolorimetric model: high accuracy, simple computation, and a few colors to be measured, the polynomial regression analysis is utilized to improve the characterization accuracy of primary-shift displays. Our studies indicate that when the regression matrix is larger than 3x9, average color difference can achieve a value of less than 3ΔEuv in both color predictions and reproductions. Compared with other characterization techniques (e.g. 3-dimensional look-up table with interpolation techniques, neural networks, physical models etc.), polynomial regression analysis is more suitable to characterize LCDs, because it has an analytic mathematical expression. Nevertheless, the number of colors measured for the regression method is still more than that of Primary-invariance colorimetric model. The number of colors required can be further reduced by modifying colorimatric models and by using analytic equations instead of 1-dimensional look-up table (1-D LUT) to describe TRCs of displays. Therefore, Primary-shift backward model is proposed to compute digital signals for accurate color reproductions. In addition, an analytic equation containing four parameters and the other one containing two gamma values are also proposed to describe TRCs of LCDs and CRT monitors, respectively. In each channel, our studies found that parameters of TRCs for XYZ values should be derived individually. Applied to Color additive model and Primary-shift backward model, our proposed equations enable LCDs and CRT monitors to be characterized with similar accuracy as using 3x9 regression analysis matrixes. With requiring fewer colors to be measured, the proposed Primary-shift backward model and analytic TRC equations make characterizations in both CRT monitors and LCDs more efficiently.