隨著數位影像的發展與演進，對於色彩複製的精準度要求日漸提升。然而，目前大多數硬體設備所採用的三維色彩數值，其色彩會受光源、物體特性、觀測者色匹配函數的影響，在影像處理的鏈結中轉換使用較不切實際。因此，物體頻譜反射率的量測與重建技術備受產業與學術界關注，若能採用不受觀測條件影響的物體頻譜反射率作為色彩描述的數值，實有助於色彩在各種觀測條件下的重現。
本研究提出以線性內插法為基礎的物體頻譜反射率重建演算法(INMSEP)，並輔以非參數化極點的同色異譜。以常見的三色式相機取得的三維色彩數值模擬高維度的頻譜資訊，將提出的方法應用於重建常見的色票材質和其他多樣材質樣本的頻譜反射率，與典型主成分分析法(PCA)、權重主成分分析法(wPCA)和利用模式化色域極點同色異譜的自然鄰點內插法(MMSEP+NNI)進行比較，並以均方根誤差、曲線配適係數及A光源及TL84光源下的色差評估重建結果。實驗結果表明，INMSEP方法在重建色票和壓克力顏料等人造材質樣本的頻譜反射率具有較高的準確性，然而，相對於基於PCA的方法，INMSEP方法在重建自然材質樣本的效果並沒有提升。綜合來看，INMSEP方法與wPCA方法在頻譜重建的實用性考量上都十分良好。

With the development and evolution of digital images, the demand of accurate color reproduction has been increasing. However, most of the hardware equipment uses the three-dimensional color values, meaning that color appearance could be affected by the illuminant, object characteristics, and color matching function. In terms of the color conversion of image processing link, the usage of three-dimensional color values would be considered unrealistic. Therefore, the measurement and recovery of spectral reflectance of object has drawn great attention to the industry and the academic community. As the spectral reflectance of object is inactive to the viewing condition, it could be applied as the color description, resulting in the more efficient reproduction of the color under various viewing conditions.
This paper presented a recovery of spectral reflectance method based on linear interpolation(INMSEP), supplemented by 8 nonparametric metameric spectra of extreme points. The three-dimensional color values obtained by the common trichromatic camera are used to simulate the spectral information of high dimension. We conducted experiments that selected the color chips material and compared the reconstructed results of various types of materials. The effectiveness of this suggested method was evaluated with a comparison of the classical PCA method, weighted PCA method, and natural neighbor interpolation method with model-based metameric spectra of extreme points (MMSEP+NNI). There is a color difference under illuminant A and TL84. The RMSE and the GFC values are used as the criteria of the recovered spectrum. The experimental results show that the INMSEP method has high accuracy in reconstructing the spectral reflectance of artificial materials such as color chips and acrylic pigments. However, compared with the PCA-based method, the INMSEP method does not have the better effect of reconstructing natural material samples. In summary, the INMSEP method and the wPCA method are very good in the practical consideration of spectrum reconstruction.

呂億德（民99）。自然影像中最佳化物體反射頻譜估計及其後製應用之研究（碩士論文）。國立臺灣師範大學，臺北市。
林瑋如（民102）。以ISRF內插法應用於物體頻譜反射率重建之研究（碩士論文）。國立臺灣師範大學，臺北市。
徐明景（民104）。光柵式多頻譜影像系統應用於平面文物數位典藏之研究。國立臺灣博物館學刊。68(4)，53-62。
孫琮傑（民104）。以自然鄰點內插法與頻帶分段線性修正重建物體頻譜反射率之研究（碩士論文）。國立臺灣師範大學，臺北市。
張智星（民89）。MATLAB程式設計與應用。新竹市：清蔚科技。
謝奇恆（民106）。利用模式化色域極點同色異譜重建物體頻譜反射率（未出版之碩士論文）。國立臺灣師範大學，臺北市。
羅梅君（民99）。數位色彩管理科學：色彩度量學。臺北市：藍海文化。
Abed, F. M., Amirshahi, S. H., & Abed, M. R. (2009). Reconstruction of reflectance data using an interpolation technique. Optical Society of America, 26(3), 613-624. doi: 10.1364/JOSAA.26.000613
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
Álvarez, J. M., & Ĺopez, A. M. (2011). Road detection based on illuminant invariance. IEEE Transactions on Intelligent Transportation Systems, 12(1), 184-193. doi: 10.1109/TITS.2010.2076349
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
Amiri, M. M., & Amirshahi, S. H. (2015). A step by step recovery of spectral data from colorimetric information. Journal of Optics, 44(4), 373-383. doi: 10.1007/s12596-015-0299-9
Ansari K., Amirshahi S. H., & Moradian S. (2005). 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
Attarchi, N., & Amirshahi, S. H. (2009). Reconstruction of reflectance data by modification of Berns' Gaussian method. Color Research and Application, 34(1), 26-32. doi: 10.1002/col.20458
Babaei, V., Amirshahi, S. H., & Agahian, F. (2011). Using weighted pseudo-inverse method for reconstruction of reflectance spectra and analyzing the dataset in terms of normality. Color Research and Application, 36(4), 295-305. doi: 10.1002/col.20613
Berns, R. S., Taplin, L. A., Imai, F. H., Day, E. A., & Day, D. C. (2003). Spectral imaging of Matisse’s Pot of Geraniums: a case study. Proceeding of IS&T/SID Eleventh Color Imaging Conference, 149-153.
Byrd, R. H., Gilbert, J. C. & Nocedal, J. (2000). A trust region method based on interior point techniques for nonlinear programming. Math. Program, 89, 149-185. doi: 10.1007/s101070000189.
Byrne, A., & Hilbert, D. R. (2003). Color realism and color science. Behavioral and Brain Sciences, 26(1), 3-21.
Chen, Z., Wang, X., & Liang, R. (2014). RGB-NIR multispectral camera. Optics Express, 22(5), 4985-4994.
Chou, T. R., & Lin, W. J. (2012). Optimal estimation of spectral reflectance based on metamerism. Proceeding of SPIE-IS&T Electronic Imaging 2012, 8292, 829213-1-829213-10. doi:10.1117/12.907606
CIE 1931 color space. (2009, March 15). In Wikipedia, the free encyclopedia. Retrieved June 6, 2017, from https://en.wikipedia.org/wiki/CIE_1931_color_space
Cohen, J. (1964). Dependency of the spectral reflectance curves of the Munsell color chips. Psychonomic Science, 1(1), 369-370. doi: 10.3758/BF03342963
Cultural Heritage Science Open Source. (n.d.). Pigments Checker [data of spectra]. Retrieved from http://chsopensource.org/tools-2/pigments-checker/
Deshpande, K., Green, P., & Pointer, M. R. (2015). Gamut evaluation of an n-colour printing process with the minimum number of measurements. Color Research and Application, 40(4), 408–415. doi: 10.1002/col.21909
El-Rifai I., Mahgoub H., & Ide-Ektessabi A. (2016). Multi-spectral imaging system (IWN) for the digitization and investigation of cultural heritage. Proceeding of Cultural Heritage: Documentation, Preservation, and Protection, 232-240. doi: 10.1007/978-3-319-48496-9_19
Ergun, G., & Nagas, I. C. (2007). Color stability of silicone or acrylic denture Liners: An in vitro investigation. European Journal of Dentistry, 1(3), 144-151.
Fairchild, M. D. (2013). Color appearance models (3rd ed.). Retrieved from https://ebookcentral.proquest.com/lib/ntnutw/reader.action?docID=1211852
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
Farajikhah, S., & Amirshahi, S.H. (2012). Initialization of nonnegative matrix factorization by Gaussian primaries for reconstruction of spectral data. Optical Review, 19(5), 294-305. doi: 10.1007/s10043-012-0046-2
Glassner, A., & Haines, E. (2014). Golden Paint Spectra [data of spectra]. Retrieved from http://www.realtimerendering.com/golden.html
Haneishi, H., Miyahara, S., & Yoshida, A. (2006). Image acquisition technique for high dynamic Range Scenes Using a Multiband Camera. Color Research and Application, 31(4), 294-302. doi: 10.1002/col.20231
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
Hawkyard, C. J. (1994). Synthetic reflectance curves. Journal of the Society of Dyers and Colourists, 110(11), 386-389. doi:10.1111/j.1478-4408.1994.tb01604.x
Hébert, M., & Hersch, R. D. (2015). Review of spectral reflectance models for halftone prints: Principles, Calibration, and prediction accuracy. Color Research and Application, 40(4), 383–397. doi: 10.1002/col.21907
Imai, F. H., Rosen, M. R., & Berns, R. S. (2001). Multi-spectral imaging of van Gogh’s self-portrait at the National Gallery of Art, Washington, D.C., Proceeding of IS&T’s 2001 PICS Conference, 185-189.
Interview helper - printing technology. (2013). Retrieved from http://sheriffblathur.blogspot.tw/2013/07/cie-lab-color-space.html
[ISO/TR 16066:2003] ISO/TR 16066:2003: Graphic technology -- Standard object colour spectra database for colour reproduction evaluation (SOCS), 2003-03-15, International Organization for Standardization, Geneva, Switzerland. Retrieved from https://www.iso.org/standard/37358.html
Kim, A., Oh, I. H., Kim, H. S., Park, S. O., & Park, Y. (2015). Recovering the colors of objects from multiple near-IR images. Journal of the Optical Society of Korea, 19(1), 102-111.
Kim, B. G., Han, J. W., & Park, S. O. (2012). Spectral reflectivity recovery from the tristimulus values using a hybrid method. Journal of the Optical Society of America A, 29(12), 2612-2621.
Kim, B. G., Werner, J. S., Siminovitch, M., Papamichael, K., Han, J., & Park, S. O. (2014). Spectral reflectivity recovery from tristimulus values using 3D extrapolation with 3D interpolation. Journal of the Optical Society of Korea, 18(5), 507-516.
Krinov, E. L. (1953). Spectral Reflectance Properties of Natural Formations (G. Belkov, Trans.). National Research Council of Canada, Ottawa.
Lam, K. M. (1985). Metamerism and color constancy (Doctoral dissertation). Retrieved from http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355236
Liang, J., Wan, X., Liu, Q., Li, C., & Li, J. (2015). Research on filter selection method for broadband spectral imaging system based on ancient murals. Color Research and Application, 41(6), 585-595. doi: 10.1002/col.22004
Luo, M. R., & Hunt, R. W. G. (1998). A chromatic adaptation transform and a colour inconstancy Index. Color Research and Application, 23(3), 154–158. doi: 10.1002/(SICI)1520-6378(199806)23:3<154::AID-COL7>3.0.CO;2-P
MacAdam, D. L. (1993). Selected Papers on Colorimetry-Fundamentals (SPIE Milestone Series; V. Ms 77). Washington: Society of Photo Optical.
Nahavandi, A. M., & Tehran, M. A. (2017). A new manufacturable filter design approach for spectral reflectance estimation. Color Research and Application, 42(3), 316-326. doi: 10.1002/col.22075
PixelCam™ Multispectral CamerasPixelteq. (2016). Retrieved from https://pixelteq.com/pixelcam/
Rudolf, M., Koren, T., & Žiljak-Vuji, J. (2012). New postage stamp design with tone gradation in infrared design technology. Acta Graphica: Journal For Printing Science and Graphic Communications, 23(3-4), 57-64.
Shen, H. L., & Xin, J. H. (2004). Spectral characterization of a color scanner by adaptive estimation. Journal of the Optical Society of America A, 21(7), 1125-1130.
Shi, M., & Healey, G. (2002). Using reflectance models for color scanner calibration. Journal of the Optical Society of America A, 19(4), 645-656.
Süsstrunk, S., Holm, J., & Finlayson, G. D. (2000). Chromatic adaptation performance of different RGB sensors. Proceeding of SPIE 4300, Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts VI, 4300, 172-183. doi: 10.1117/12.410788
Tominaga, S., Nishioka, D., & Horiuchi, T. (2015). An integrated spectral imaging system for producing color images of static and moving objects. Color Research and Application, 40(4), 329-340. doi: 10.1002/col.21893
Tzeng, D. Y., & Berns R. S. (2005). A review of principal component analysis and its applications to color technology. Color Research and Application, 30(2), 84-98. doi: 10.1002/col.20086
Wyble, D. R., & Berns, R. S. (2000). A critical review of spectral models applied to binary color printing. Color Research and Application, 25(1), 4-19. doi: 10.1002/(SICI)1520-6378(200002)25:1<4::AID-COL3>3.0.CO;2-X
Zhang, X., Wang, Q., Li, J., Zhou, X., Yang, Y., & Xu, H. (2017). Estimating spectral reflectance from camera responses based on CIE XYZ tristimulus values under multi-illuminants. Color Research and Application, 42(1), 68-77. doi: 10.1002/col.22037
Zhang, X., & Xu, H. (2008). Reconstructing spectral reflectance by dividing spectral space and extending the principal components in principal component analysis. Journal of the Optical Society of America A, 25(2), 371-378.
Zhao, Y., & Berns, R. S. (2007). Image-based spectral reflectance reconstruction using the matrix R method. Color Research and Application, 32(5), 343-351. doi: 10.1002/col.20341
Žiljak-Vuji, J., Žiljak-Stanimirović, I., & Međugorac, O. (2012). Hidden information in visual and infrared spectrum. Informatologia, 45(2), 96-102
Zuffi, S., Santini, S., & Schettini, R. (2008). From color sensor space to feasible reflectance spectra, Proceeding of IEEE Transactions on Signal Processing, 518-531. doi: 10.1002/col.20211