# Loss it right: Euclidean and Riemannian Metrics in Learning-based Visual Odometry

arXiv: https://arxiv.org/abs/2401.05396 · HTML: https://mlsanity.com/paper/2401.05396/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 12 of 12)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [Understanding the Limitations of CNN-based Absolute Camera Pose Regression](https://mlsanity.com/paper/1903.07504/) (2019)
- [DeepVO: Towards End-to-End Visual Odometry with Deep Recurrent Convolutional Neural Networks](https://mlsanity.com/paper/1709.08429/) (2017)
- [TartanVO: A Generalizable Learning-based VO](https://mlsanity.com/paper/2011.00359/) (2020)
- [AtLoc: Attention Guided Camera Localization](https://mlsanity.com/paper/1909.03557/) (2019)
- [Leveraging Equivariant Features for Absolute Pose Regression](https://mlsanity.com/paper/2204.02163/) (2022)
- [LS-VO: Learning Dense Optical Subspace for Robust Visual Odometry Estimation](https://mlsanity.com/paper/1709.06019/) (2017)
- [Offset equivariant networks and their applications](https://mlsanity.com/paper/2207.00292/) (2022)
- [Simultaneously Learning Corrections and Error Models for Geometry-based Visual Odometry Methods](https://mlsanity.com/paper/2007.14943/) (2020)
- [Rigidity Preserving Image Transformations and Equivariance in Perspective](https://mlsanity.com/paper/2201.13065/) (2022)
- [Matrix Difference in Pose-Graph Optimization](https://mlsanity.com/paper/1809.00952/) (2018)

## Built on by (most cited first, 6 of 6)

- [Learning with 3D rotations, a hitchhiker's guide to SO(3)](https://mlsanity.com/paper/2404.11735/) (2024)
- [3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction](https://mlsanity.com/paper/2411.00543/) (2024)
- [Monocular visual simultaneous localization and mapping: (r)evolution from geometry to deep learning-based pipelines](https://mlsanity.com/paper/2503.02955/) (2025)
- [LiteGE: Lightweight Geodesic Embedding for Efficient Geodesics Computation and Non-Isometric Shape Correspondence](https://mlsanity.com/paper/2512.17781/) (2025)
- [Efficient 2D to Full 3D Human Pose Uplifting including Joint Rotations](https://mlsanity.com/paper/2504.09953/) (2025)
- [Edged USLAM: Edge-Aware Event-Based SLAM with Learning-Based Depth Priors](https://mlsanity.com/paper/2603.08150/) (2026)

## Abstract (arXiv)

This paper overviews different pose representations and metric functions in visual odometry (VO) networks. The performance of VO networks heavily relies on how their architecture encodes the information. The choice of pose representation and loss function significantly impacts network convergence and generalization. We investigate these factors in the VO network DeepVO by implementing loss functions based on Euler, quaternion, and chordal distance and analyzing their influence on performance. The results of this study provide insights into how loss functions affect the designing of efficient and accurate VO networks for camera motion estimation. The experiments illustrate that a distance that complies with the mathematical requirements of a metric, such as the chordal distance, provides better generalization and faster convergence. The code for the experiments can be found at https://github.com/remaro-network/Loss_VO_right