We propose $\nabla$-RANSAC, a generalized differentiable RANSAC that allows learning the entire randomized robust estimation pipeline. The proposed approach enables the use of relaxation techniques for estimating the gradients in the sampling distribution, which are then propagated through a differentiable solver. The trainable quality function marginalizes over the scores from all the models estimated within $\nabla$-RANSAC to guide the network learning accurate and useful inlier probabilities or to train feature detection and matching networks. Our method directly maximizes the probability of drawing a good hypothesis, allowing us to learn better sampling distributions. We test $\nabla$-RANSAC on various real-world scenarios on fundamental and essential matrix estimation, and 3D point cloud registration, outdoors and indoors, with handcrafted and learning-based features. It is superior to the state-of-the-art in terms of accuracy while running at a similar speed to its less accurate alternatives. The code and trained models are available at https://github.com/weitong8591/differentiable_ransac.

翻译：我们提出$\nabla$-RANSAC，这是一种广义可微RANSAC方法，能够实现对整个随机化鲁棒估计流程的学习。该方法利用松弛技术估计采样分布中的梯度，并将这些梯度通过可微求解器进行传播。可训练的质量函数通过对$\nabla$-RANSAC内所有模型估计的分数进行边缘化，引导网络学习准确且有用的内点概率，或训练特征检测与匹配网络。我们的方法直接最大化抽取良好假设的概率，从而能够学习更优的采样分布。我们在基础矩阵和本质矩阵估计、室内外三维点云配准等多样真实场景中，分别采用手工特征和基于学习的特征对$\nabla$-RANSAC进行测试。该方法在精度上优于现有最先进技术，同时运行速度与精度较低的替代方法相当。代码与训练模型已开源在https://github.com/weitong8591/differentiable_ransac。