The Spectral Prediction of Original Primary Pigment Based on Constrained Non-Negative Matrix Factorization
HE Song-hua1, CHEN Qiao1*, DUAN Jiang2
1. School of Communication, Shenzhen Polytechnic, Shenzhen 518055, China 2. Computer Science Department of Southwestern University of Finance and Economics, Chengdu 610075, China
Abstract：With direct prediction in the spectral reflectance space with principal component analysis, the numbers of eigenvectors will surpass the numbers of real primary pigments while the eigenvectors and the corresponding coefficients have negative value, which can not directly presented original primary pigment spectral characteristics and corresponding concentration. We proposed an innovative spectral prediction method in which a complete linear spectral space was created according to optical properties of originals pigment. A constrained non-negative matrix factorization algorithm to predict the numbers and spectral curve shapes of real primary pigments was used in the space. So, this paper designed an overall research plan and implementation process about spectral prediction method firstly, and studied how to select and establish a spectral linear space which was conformed to optical properties of originals; taking transparent pigments as example, and spectra constrained non-negative matrix factorization (SCNMF) algorithm was established to predict primary pigment spectra based on basic non-negative matrix factorization algorithm (BNMF). Aiming at realizing multiple optimal solution of BNMF and improving the prediction accuracy as well as make the matrix decomposition results to be clearly physically meaningful; the proposed SCNMF needs to satisfy four constraints: non negative constraint, additive constraint, smoothness constraint and sparseness constraint. The objective function and iterative algorithm to meet four constraints were set up. The prediction results show that the proposed method can realize accurate prediction of original primary pigments’ numbers and spectra effectively.
Key words：Spectral estimation of primary pigments;Spectral color reproduction;Non-negative matrix factorization;Linear mixing space;Principal component analysis
[1] HE Song-hua, CHEN Qiao, DUAN Jiang(何颂华, 陈 桥, 段 江). Spectroscopy and Spectral Analysis(光谱学与光谱分析), 2015, 35(6): 1459. [2] KONG Ling-wang, ZHU Yuan-hong, LI Qiong(孔令罔, 朱元泓, 李 琼, 等). Geomatics and Information Science of Wuhan University(武汉大学学报·信息科学版), 2006, 31(9): 788. [3] WANG Ying, ZENG Ping, WANG Yi-feng(王 莹，曾 平，王义峰). Acta Optica Sinica(光学学报), 2009, 29(8): 2122. [4] LI Jin-cheng, LIU Zhen, CHEN Guang-xue(李金城, 刘 真, 陈广学). Acta Optica Sinica(光学学报), 2009, 29(8): 2122. [5] Xu Dongbo, Wang Xiangzhao, Bu Yang. Chinese Optics Letters, 2012, 10(12): 121202-1. [6] XU Fa-qiang, WAN Xiao-xia, ZHU Yuan-hong(许法强, 万晓霞, 朱元泓). Optics and Precision Engineering(光学 精密工程), 2008, 16(3): 518. [7] HE Song-hua, LIU Zhen, CHEN Qiao(何颂华, 刘 真, 陈 桥). Acta Optica Sinica(光学学报), 2014, 34(2): 0233001-1. [8] Wang Ying, Zeng Ping, Luo Xuemei, et al. Journal of Southeast University·English Edition, 2013, 2(4): 486. [9] Tzeng D Y, Berns R S. Color Research and Application, 2005, 30(2): 84. [10] He Songhua, Liu Zhen. Procedia Engineering, 2011, 23: 320. [11] Heinz D C, Chang C I. IEEE Geoscience and Remote Sensing Letters, 2001, 39(3): 529. [12] Lee D, Seung H. Nature, 1999, 401: 788.
