近年來，隨著人們對於數位影像品質的要求提升，色彩的準確與否成為一項熱門且重要的研究議題。色彩的形成被光譜分布、物體頻譜反射率與觀測者配色函數三項要素所影響。在實用上，若是能直接由組成數位影像像素中的RGB色頻數值，估計出物體的頻譜反射率，即可透過多頻譜成像方式為原始影像提供更豐富的應用。
　　本研究重點在提出一個新的物體頻譜反射率重建方法，將藉由真實量測的物體頻譜反射率資料，使用自然鄰點內插法(Natural Neighbor Interpolation，NNI)與ISRF (Idea Spectral Reflectance Family)來估計待測物體的頻譜反射率。
　　經由實驗數據證實本研究所估計的物體頻譜反射率相當精準，在物體頻譜重建方面，均方根誤差(Root Mean Square Error，RMSE)平均小於0.0747；曲線配適係數(Goodness-of-Fit Coefficient，GFC)平均大於0.9。在色彩顯像模擬方面，在標準照明體D65下，以色差公式∆E 2000評估計算，平均值小於1.6227，在NBS (National Bureau of Standards)標準中皆屬於人眼可忽略的差異程度。同時，另外一項重要的發現即是導入本研究開發之ISRF方法，與其他使用內插重建物體頻譜反射率方法的研究相比，能夠解決顏色落於該模型凸包範圍(Convex Hull)之外而無法被計算的問題。

In recent years, with the fast growing demand of the quality of digital image, color accuracy becomes a popular and important topic in the research. Color performance is made from three elements, they are spectral power distributions (SPD), spectral reflectance, and human eyes color matching function (CMF). If we can estimate the spectral reflectance of the objects directly from RGB channel values of the pixel in the image, we can provide more rich applications for the original image by using multi-spectral analysis.
In this study, we proposed a new method to reconstruct the spectral reflectance of object by NNI (Natural Neighbor Interpolation) taking limited set of the reflectance data from real measurement, corrected with ISRF (Idea Spectral Reflectance Family) to estimate spectral reflectance of the objects.
The experimental results showed the accuracy of our method is high in estimating the spectral reflectance of objects. In the evaluation of spectral reflectance reconstruction, the RMSE (Root Mean Square Error) is less than 0.0747 and GFC (Goodness-of-fit Coefficient) is larger than 0.9 in average. In evaluation of color imaging simulation, under standard illuminant D65, the color difference is less than 1.6227 in average when evaluated by color difference formula ∆E 2000. It reveals that human eyes can not distinguish the difference according to NBS (National Bureau of Standard). Simultaneously, another important finding is that importing our ISRF method can solve the problem of colors outside the convex hull of model which can not be computed when comparing the other methods of reconstruction by interpolation.

[1]羅梅君(2010)。數位色彩管理科學：色彩度量學。臺北市：羅梅君。
[2]胡國瑞、孫沛立、徐道義、陳鴻興、黃日峰、詹文鑫、羅梅君(2009)。顯示色彩工程學。新北市：全華圖書。
[3]Berns, R. S., Imai, F. H., Burns, P. D., & Tzeng D. Y. (1998). Multi-spectral-based color reproduction research at the Munsell Color Science Laboratory. Proceeding of SPIE , 3409, 14-25. doi:10.1.1.23.6320
[4]Westland, S., & Ripamonti, C. (2004). Computational Colour Science using Matlab. New York, NY: John Wiley & Sons, Ltd.
[5]Mansouri, A., Marzani, F. S., Hardeberg, J. Y., & Gouton, P. (2005). Optical calibration of a multispectral imaging system based on interference filters. Optical Engineering, 44(2), 027004-1–027004-12. doi:10.1117/1.1839889
[6]Vilaseca, M., Mercadal, R., Pujol, J., Arjona, M., de Lasarte, M., Huertas, R., Melgosa, M., & Imai, F. H. (2008). Characterization of the human iris spectral reflectance with a multispectral imaging system. Applied Optics, 47(30), 5622–5630. doi: 10.1364/AO.47.005622
[7]Brauers, J., Schulte, N., & Aach, T. (2008). Multispectral filter-wheel cameras: Geometric distortion model and compensation algorithms. IEEE Transactions on Image Processing, 17(12), 2368–2380. doi: 10.1109/TIP.2008.2006605.
[8]Tzeng, D. Y., & Berns, R. S. (2005). A review of principal component analysis and its application to color technology. Color Research Application, 30(2), 84-98. doi: 10.1002/col.20086
[9]Cohen, J. (1964). Dependency of the spectral reflectance curves of the Munsell color chips. Psychonomic Science, 1(12), 1964, 369-370.
[10]Maloney, L. T. (1986). Evaluation of linear models of surface spectral reflectance with small numbers of parameters. Journal of the Optical Society of America A, 3(10), 1673-1683. doi:10.1364/JOSAA.3.001673
[11]Parkkinen, J. P. S., Hallikainen, J., & Jaaskelainen, T. (1989). Characteristic spectra of Munsell colors. Journal of the Optical Society of America A, 6(2), 318-322. doi:10.1364/JOSAA.6.000318
[12]Fairman, H. S., & Brill, M. H. (2004). The principal components of reflectances. Color Research and Application, 29(2), 104–110. doi: 10.1002/col.10230
[13]Ansari, K., Amirshahi, S. H., & Moradian, S. (2006). Recovery of reflectance spectra from CIE tristimulus values using a progressive database selection technique. Coloration Technology, 122(3), 128-134. doi:10.1111/j.1478-4408.2006.00019.x
[14]Ayala , F., Echávarri, J. F., Renet, P., & Negueruela, A. I. (2006). Use of three tristimulus values from surface reflectance spectra to calculate the principal components for reconstructing these spectra by using only three eigenvectors. Journal of the Optical Society of America A, 23(8), 2020-2026. doi:10.1364/JOSAA.23.002020
[15]Agahian, F., Amirshahi, S. A., & Amirshahi, S. H. (2008). Reconstruction of reflectance spectra using weighted principal component analysis. Color Research and Application, 33(5), 360–371. doi: 10.1002/col.20431
[16]Abed, F. M., Amirshahi, S. H., & Abed, M. R. (2009). Reconstruction of reflectance data using an interpolation technique. Journal of the Optical Society of America A, 26(3), 613-624. doi: 10.1364/JOSAA.26.000613
[17]Kim, B., Han, J., & Park, S. (2012). Spectral reflectivity recovery from the tristimulus values using a hybrid method. Journal of the Optical Society of America A, 29(12), 2612-2621. doi: 10.1364/JOSAA.29.002612
[18]Harifi, T., Amirshahi, S. H., & Agahian, F. (2008). Recovery of reflectance spectra from colorimetric data using principal component analysis embedded regression technique. Optical Review, 15(6), 302-308. doi: 10.1007/s10043-008-0049-1
[19]Zhang, W. F., & Dai, D. Q. (2008). Spectral reflectance estimation from camera responses by support vector regression and a composite model. Journal of the Optical Society of America A, 25(9), 2286-2296. doi: 10.1364/JOSAA.25.002286
[20]CIE(2000). About us. Retrieved from: http://www.cie.co.at/
[21]陳鴻興、陳君彥(譯)(2003)。基礎色彩再現工程(原作：大田登)。臺北市：全華。(原著出版年：1997)
[22]Amidror, I. (2002). Scattered data interpolation methods for electronic imaging systems: A survey. Journal of Electronic Imaging, 11(2), 157–176. doi: 10.1117/1.1455013
[23]Berns, R. S., Billmeyer, F. W., & Saltzman, M. (2000). Billmeyer and Saltzman's principles of color technology. New York, NY: John Wiley & Sons, Ltd.
[24]楊清田、魏碩廷(2007) 。數位色彩之設計與應用。新北市：全華圖書。
[25]BruceLindbloom (2009). Chromatic Adaptation. Retrieved from: http://www.brucelindbloom.com/index.html?ColorCheckerCalculator.html
[26]Sharma, G., Wu, W., & Dalal, E. N. (2005). The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations. Color Research Application. 30(1), 21-30. doi: 10.1002/col.20070
[27]Ergun, G., & Nagas, I. C. (2007). Color stability of silicone or acrylic denture Liners: An in vitro investigation. European Journal of Dentistry, 2007(1), 144-151.
[28]University of Joensuu Color Group (n.d.). Spectral Database. Retrieved from: https://www.uef.fi/spectral/spectral-database.
[29]Munsell Color Science Laboratory (2011). CIE standard illuminant data. Retrieved from: http://www.cis.rit.edu/research/mcsl/online/cie.php.
[30]Babelcolor (2003). Spectral data of the color checker digital SG. Retrieved from: http://www.babelcolor.com/index.htm
[31]Westland, S., Shaw, J., & Owens, H. (2000). Colour statistics of natural and man-made surfaces. Sensor Review, 20(1), 50-55 doi:10.1108/02602280010311392
[32]周遵儒、陳怡君(2008)。快速反射譜模擬方法。2008色彩學研討會論文集。113-120。
[33]呂億德(2009)。自然影像中最佳化物體反射譜估計及其後製應用之研究(未出版之碩士論文)。國立臺灣師範大學，臺北市。
[34]Chou, T. R., & Lin, W. J. (2012). Optimal estimation of spectral reflectance based on metamerism. Proceeding of SPIE-IS&T Electronic Imaging 2012, 8292, 829213-829213-10. doi: 10.1117/12.907606
[35]張智星(2000)。MATLAB程式設計與應用。新竹市：清蔚科技。
[36]The Multi-Parametric Toolbox for Matlab (2010). MPT toolbox. Retrieved from: http://control.ee.ethz.ch/overview.en.html
[37]Imai, F. H., Rosen, M. R., & Berns, R. S. (2002). Metameric correction using parametric decomposition. Proceeding of CGIV 2002: The First European Conference on Colour Graphics, Imaging and Vision, 492-496.
[38]Romero, J., García-Beltrán, A., & Hernández-Andrés, J. (1997). Linear bases for representation of natural and artificial. Journal of the Optical Society of America A, 14(5),1007-1014. doi:10.1364/JOSAA.14.001007