为解决光谱反射率重建过程中训练样本数目庞大导致工作量大, 重建精度不高等问题, 提出一种基于NSGA-Ⅱ算法的光谱反射率重建样本选择方法。 近日Liang等提出了一种从大量样本数据中选取具有代表性样本的新方法, 定义光谱重建误差为均方根误差与拟合优度系数的乘积, 以这一标准选择光谱重建误差最小的样本作为代表性样本进行光谱反射率重建。 受Liang等人工作的启发结合NSGA-Ⅱ算法选择代表性样本, 先对全体训练样本使用多项式回归算法和伪逆法进行光谱反射率重建, 再使用NSGA-Ⅱ算法, 设定两个目标函数, 一个是所需代表性样本个数的光谱均方根误差的和, 另一个是拟合优度系数倒数的和, 令两个目标函数值最小。 将经过NSGA-Ⅱ算法挑选出的Pareto等级为1的全部样本按照样本出现次数由高至低排序, 以此顺序从高到低依次选为代表性样本, 直至达到所需代表性样本个数。 若从Pareto等级为1的样本集合中挑选的代表性样本数不足所需要的个数则选择下一等级出现次数最多且没有被选择过的样本直至代表性样本数达到需求。 将1 269块无光泽Munsell标准色卡按照样本下标划分为偶数色卡、 奇数色卡, 第一组实验用Munsell奇数色卡为全体训练样本, 从Munsell偶数色卡中随机选择20个色块为测试样本。 第二组实验选用Munsell偶数色卡为全体训练样本, 从Munsell奇数色卡中随机选取20个色块为测试样本。 第三组实验训练样本与第一组相同, RC24色卡为测试样本。 将该方法与Mohammadi、 Cao、 Liang等提出的三种样本选择方法进行对比。 通过实验得到使用NSGA-Ⅱ算法结合多项式回归与伪逆法选择的代表性样本重建的光谱反射率在均方根误差和色差两个指标上均优于现有的样本选择方法, 并且该方法不限于特定系统, 具有通用性。

To solve the problems of heavy workload and low reconstruction accuracy caused by the large number of training samples in the process of spectral reflectance reconstruction, a sample selection method for spectral reflectance reconstruction based on the NSGA-Ⅱ algorithm was proposed. Recently, Liang et al. proposed a new method to select representative samples from many sample data. The spectral reconstruction error was defined as the product of the root mean square error and goodness-of-fit coefficient. Based on this standard, the sample with the smallest spectral reconstruction error was selected as the representative sample for spectral reflectance reconstruction. Inspired by the work of Liang et al., this method combined with the NSGA-Ⅱ algorithm to select representative samples. First, the polynomial regression algorithm and pseudo-inverse method were used to reconstruct spectral reflectance for all training samples. Then, the NSGA-Ⅱ algorithm was used to set two objective functions. One is the sum of the spectral root mean square error of the required number of representative samples; the other is the sum of the reciprocal of the goodness-of-fit coefficients, which minimizes the values of the two objective functions. All samples with Pareto level 1 selected by NSGA-Ⅱ algorithm are sorted according to the occurrence times of samples from high to low and selected as representative samples from high to low until the required number of representative samples is reached. Suppose the number of representative samples selected from the sample set with Pareto level 1 is less than the required number. In that case,the samples that appear most frequently in the next level and have not been selected are selected until the number of representative samples reaches the demand. The experiment divided 1 269 dull Munsell standard color cards into even color cards and odd color cards according to sample subscript. In the first group of experiments, Munsell odd color cards were used as the whole training samples, and 20 color blocks were randomly selected from Munsell even color cards as the test samples. In the second group of experiments, Munsell even color cards were selected as the whole training samples, and 20 color blocks were randomly selected from Munsell odd color cards as the test samples. The third group of experimental training samples is the same as the first group, and the RC24 color card is the test sample. The proposed method is compared with the three sample selection methods proposed by Mohammadi, Cao and Liang. The experimental results show that the NSGA-Ⅱ algorithm combined with polynomial regression and pseudo-inverse method to select representative samples for spectral reflectance reconstruction is superior to the existing sample selection methods in terms of root mean square error and color difference, and this method is not for a specific system has generality.