The task of color consistency correction for multiple images mainly arises from applications like orthoimage producing, panoramic image stitching and 3D reconstruction. In these applications, images usually have been geometrically aligned. So correspondences can be easily extracted and used to solve color correction models. Almost all previous methods assume that the color residuals of correspondences follow Gaussian distribution and solve color models based on least squares. However, correspondences often contain unreliable ones due to altered areas and misalignments, which results in unusual large color residuals, namely, outliers. Imposing color consistency constaints on unreliable correspondences significantly affects the performance of color correction since Gaussian is highly sensitive to outliers. In this paper, to solve this problem theoretically, we first propose a unified probabilistic framework that formulates global color correction as a maximum posteriori probability (MAP) estimation. It is flexible enough to allow for any assumptions of residual distribution. And most color correction methods can be explained in this unified framework. Then, to robust against outliers, we use t-distribution with heavier tails than Gaussian to fit the color residuals. It is more robust because higher probabilities can be assigned to outliers. We show that the MAP formulation based on t-distribution actually leads to weighted least squares, which downweights outliers adaptively. Besides, our framework requires no user-defined robustness parameter. Because all parameters of color models and t-distribution are optimized jointly. In addition, to decrease the huge computational cost of large scale dataset, we extend the proposed framework to a parallel vesion which can achieve efficiency and global optimal at the same time. In the experiments, we compare our approach with the state-of-the-art approaches of Shen et al., Xia et al., etc. on several challenging datasets with outliers. The results demonstrate that our approach achieves the best robustness (average color consistency scores CD=$5.4$, DeltaE2000=$5.7$ and PSNR=$24.0$) and the best efficiency (given 100 images, non-parallel/parallel runs more than 5/50 times faster than others). The implementation is available at https://github.com/yinxuanLi/ColorConsistencyCorrectionForMultipleImages.

多幅图像颜色一致性校正的任务主要来自于正射图像生成、全景图像拼接和 3D 重建等应用。在这些应用中，图像通常是几何对齐的。因此可以很容易地提取对应关系并用于解决颜色校正模型。几乎所有以前的方法都假设对应的颜色残差遵循高斯分布，并基于最小二乘法求解颜色模型。然而，由于区域改变和未对齐，对应通常包含不可靠的对应，这会导致异常大的颜色残差，即异常值。对不可靠的对应施加颜色一致性约束会显着影响颜色校正的性能，因为高斯对异常值高度敏感。在本文中，为了从理论上解决这个问题，我们首先提出了一个统一的概率框架，将全局颜色校正公式化为最大后验概率（MAP）估计。它足够灵活，可以允许任何残差分布的假设。而大部分的色彩校正方法都可以在这个统一的框架下进行解释。然后，为了对抗异常值，我们使用t分布的尾部比高斯分布更重，以拟合颜色残差。它更稳健，因为可以将更高的概率分配给异常值。我们表明，基于t分布的 MAP 公式实际上会导致加权最小二乘，从而自适应地降低离群值的权重。此外，我们的框架不需要用户定义的鲁棒性参数。因为颜色模型的所有参数和t-分布是共同优化的。此外，为了降低大规模数据集的巨大计算成本，我们将所提出的框架扩展到可以同时实现效率和全局最优的并行版本。在实验中，我们在几个具有异常值的具有挑战性的数据集上将我们的方法与 Shen 等人、Xia 等人等人的最新方法进行了比较。结果表明，我们的方法实现了最好的鲁棒性（平均颜色一致性分数 CD=$5.4$, DeltaE2000=$5.7$和 PSNR=$24.0$) 和最佳效率（给定 100 张图像，非并行/并行运行速度比其他方式快 5/50 倍以上）。该实现可在 https://github.com/yinxuanLi/ColorConsistencyCorrectionForMultipleImages 获得。