给定物体三刺激值, 重建物体反射率在跨媒体颜色复制领域有着重要应用。 常见的重建反射率算法包括基向量法、 维纳估计法、 加权伪逆方法等, 这些方法大多都是为了建立由低维度三刺激值或者RGB向高维度光谱反射率的映射关系, 以重建的反射率与原始反射率的接近程度为评价指标, 并且需要光谱反射率数据进行训练。 但是很多工业领域在产品设计时都需要考虑到颜色恒常性(CII)问题, 以保证产品颜色在不同光照条件下具有相近的颜色表现。 光谱反射率是决定物体颜色恒常的重要属性, 为解决重建反射率进行颜色复现后产生颜色恒常性问题, Takahama 和Nyatani提出具有颜色恒常性的线性规划光谱反射率重建方法, 测试结果发现该方法重建的反射率呈现出类似“台阶”的形状, 与实际物体色反射率差别太大。 之后, Berns等在Takahama和Nyatani算法基础上, 增加了色相角等约束, 但重建出的反射率波动太大。 Li和Luo提出具有光滑约束的二次规划颜色恒常性重建反射率算法, 重建的反射率具有光滑性, 比较接近实际物体色的反射率。 提出一种非线性约束优化方法重建物体反射率, 使之具有良好的颜色恒常性和光滑性。 文中使用标准Munsell色卡中1 560个色块测量的反射率数据集对新算法进行测试, 并与其他方法进行比较。 结果表明, 该方法不仅在重建反射率的颜色恒常性指标上远比Takahama和Nyatani方法, Berns等的方法以及Li和Luo的方法要好, 而且重建反射率与原始反射率接近程度指标: 均方根误差(RMSE)和拟合优度系数(GFC)也好于其他方法。 因此该新方法对重建反射率时具有颜色恒常性要求的行业有着重要的应用价值。

Given the tristimulus value of an object, its reflectance reconstruction has important applications in the field of cross-media color reproduction. Common algorithms for reconstruction reflectance, including the basis vector method, Wiener estimation method, weighted pseudo-inverse method, etc., are derived based on the reconstructed reflectance and the original reflectance as the reconstruction and evaluation objective. All algorithms map low dimensional tristimulus value or RGB to high dimensional spectral reflectance. Hence most of these algorithms need to be trained using a training dataset. However, in many application areas, color constancy or color inconstancy index (CII) should be considered in product design to ensure that the object is perceived as the same color under different lighting conditions. Object’s spectral reflectance determines the color constancy property of the object. Takahama and Nyatani developed a linear programming method for reconstructing reflectance based on the given tristimulus values so that the reconstructed reflectance has a better color constancy. However, test results showed that the reflectance reconstructed by this method has stair-like shape, which is much different from the real object reflectance. After that, Berns et al. further improved the Takahama and Nyatani method by introducing further constraints. It was found that the reflectance reconstructed by the improved method is smooth but heavily oscillated. Li and Luo proposed a smoothing constrained quadratic programming algorithm. The reconstructed reflectance is s smooth and close to the reflectance of real object color. In this paper, a new algorithm or more exactly, a new constrained nonlinear optimization algorithm is proposed to reconstruct reflectance based on the given tristimulus values so that the reconstructed reflectance is smooth and has a better color constancy property. The proposed method is tested using the reflectance dataset measured from 1 560 Munsell chips from Munsell Color System and compared with other methods. The comparison results show that our method is not only better than Takahama and Nyatani method, Berns et al. method and Li and Luo method in terms of color constancy index, but also better or similar to other methods in terms of root mean square error (RMSE) and good fitting coefficient (GFC). Therefore, the proposed method has important application in many industries with color constancy requirements for designing products.