The normalized eight-point algorithm has been widely viewed as the cornerstone in two-view geometry computation, where the seminal Hartley's normalization has greatly improved the performance of the direct linear transformation algorithm. A natural question is, whether there exists and how to find other normalization methods that may further improve the performance as per each input sample. In this paper, we provide a novel perspective and propose two contributions to this fundamental problem: 1) we revisit the normalized eight-point algorithm and make a theoretical contribution by presenting the existence of different and better normalization algorithms; 2) we introduce a deep convolutional neural network with a self-supervised learning strategy for normalization. Given eight pairs of correspondences, our network directly predicts the normalization matrices, thus learning to normalize each input sample. Our learning-based normalization module can be integrated with both traditional (e.g., RANSAC) and deep learning frameworks (affording good interpretability) with minimal effort. Extensive experiments on both synthetic and real images demonstrate the effectiveness of our proposed approach.

翻译：归一化八点算法被广泛视为双视图几何计算的基石，其中哈特利提出的经典归一化显著提升了直接线性变换算法的性能。一个自然的问题是：是否存在其他归一化方法，以及如何针对每个输入样本找到可能进一步提升性能的归一化方案？本文针对这一基本问题提出了新颖的视角，并做出两项贡献：1）我们重新审视了归一化八点算法，通过证明存在不同且更优的归一化算法，做出了理论贡献；2）我们引入了一种采用自监督学习策略的深度卷积神经网络进行归一化。给定八对对应点，我们的网络直接预测归一化矩阵，从而学习如何对每个输入样本进行归一化。基于学习得到的归一化模块可以轻松集成到传统（如RANSAC）和深度学习框架（具有良好的可解释性）中。在合成图像和真实图像上的大量实验证明了我们提出方法的有效性。