The Normalized Eight-Point algorithm has been widely viewed as the cornerstone in two-view geometry computation, where the seminal Hartley's normalization greatly improves the performance of the direct linear transformation (DLT) 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 make two contributions towards this fundamental problem: 1) We revisit the normalized eight-point algorithm and make a theoretical contribution by showing the existence of different and better normalization algorithms; 2) We present a deep convolutional neural network with a self-supervised learning strategy to the 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 could be integrated with both traditional (e.g., RANSAC) and deep learning framework (affording good interpretability) with minimal efforts. Extensive experiments on both synthetic and real images show 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中的基石，其中Hartley提出的开创性归一化方法极大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优化性能的归一化方案？本文针对这一基本问题提出全新视角并做出两项贡献：1）重新审视归一化八点算法，从理论上证明存在不同且更优的归一化算法；2）提出一种基于自监督学习策略的深度卷积神经网络用于归一化。给定八组对应点，我们的网络可直接预测归一化矩阵，从而学习对每个输入样本进行归一化。基于学习的归一化模块可轻松集成至传统算法（如RANSAC）和深度学习框架（具备良好可解释性）中。在合成图像与真实图像上的大量实验验证了所提方法的有效性。