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 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.