A Revisit of the Normalized Eight-Point Algorithm and A Self-Supervised Deep Solution

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.