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

arXiv: https://arxiv.org/abs/2304.10771 · HTML: https://mlsanity.com/paper/2304.10771/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 21 Apr 2023.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [DSAC - Differentiable RANSAC for Camera Localization](https://mlsanity.com/paper/1611.05705/) (2016)
- [Improved Texture Networks: Maximizing Quality and Diversity in Feed-forward Stylization and Texture Synthesis](https://mlsanity.com/paper/1701.02096/) (2017)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)
- [BA-Net: Dense Bundle Adjustment Network](https://mlsanity.com/paper/1806.04807/) (2018)
- [Deep Image Homography Estimation](https://mlsanity.com/paper/1606.03798/) (2016)
- [DPSNet: End-to-end Deep Plane Sweep Stereo](https://mlsanity.com/paper/1905.00538/) (2019)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [Unsupervised Deep Homography: A Fast and Robust Homography Estimation Model](https://mlsanity.com/paper/1709.03966/) (2017)
- [Rolling Shutter Camera Relative Pose: Generalized Epipolar Geometry](https://mlsanity.com/paper/1605.00475/) (2016)
- [Robust Fitting in Computer Vision: Easy or Hard?](https://mlsanity.com/paper/1802.06464/) (2018)
- [Deep Fundamental Matrix Estimation without Correspondences](https://mlsanity.com/paper/1810.01575/) (2018)
- [Quantum Robust Fitting](https://mlsanity.com/paper/2006.06986/) (2020)
- [Rolling Shutter Inversion: Bring Rolling Shutter Images to High Framerate Global Shutter Video](https://mlsanity.com/paper/2210.03040/) (2022)
- [Searching Dense Point Correspondences via Permutation Matrix Learning](https://mlsanity.com/paper/2210.14897/) (2022)

## Built on by (most cited first, 1 of 1)

- [CAD-NeRF: Learning NeRFs from Uncalibrated Few-view Images by CAD Model Retrieval](https://mlsanity.com/paper/2411.02979/) (2024)

## Abstract (arXiv)

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.