# BA-Net: Dense Bundle Adjustment Network

arXiv: https://arxiv.org/abs/1806.04807 · HTML: https://mlsanity.com/paper/1806.04807/

## Key facts

- Cited by 175 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2018.

## Built on by (most cited first, 30 of 175)

- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://mlsanity.com/paper/2108.10869/) (2021)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [Continuous 3D Perception Model with Persistent State](https://mlsanity.com/paper/2501.12387/) (2025)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion](https://mlsanity.com/paper/2410.03825/) (2024)
- [DepthSplat: Connecting Gaussian Splatting and Depth](https://mlsanity.com/paper/2410.13862/) (2024)
- [Unifying Flow, Stereo and Depth Estimation](https://mlsanity.com/paper/2211.05783/) (2022)
- [NeuralRecon: Real-Time Coherent 3D Reconstruction from Monocular Video](https://mlsanity.com/paper/2104.00681/) (2021)
- [MegaSaM: Accurate, Fast, and Robust Structure and Motion from Casual Dynamic Videos](https://mlsanity.com/paper/2412.04463/) (2024)
- [Visual Geometry Grounded Deep Structure From Motion](https://mlsanity.com/paper/2312.04563/) (2023)
- [MASt3R-SLAM: Real-Time Dense SLAM with 3D Reconstruction Priors](https://mlsanity.com/paper/2412.12392/) (2024)
- [Pixel-Perfect Structure-from-Motion with Featuremetric Refinement](https://mlsanity.com/paper/2108.08291/) (2021)
- [Back to the Feature: Learning Robust Camera Localization from Pixels to Pose](https://mlsanity.com/paper/2103.09213/) (2021)
- [Deep Patch Visual Odometry](https://mlsanity.com/paper/2208.04726/) (2022)
- [NICER-SLAM: Neural Implicit Scene Encoding for RGB SLAM](https://mlsanity.com/paper/2302.03594/) (2023)
- [ESLAM: Efficient Dense SLAM System Based on Hybrid Representation of Signed Distance Fields](https://mlsanity.com/paper/2211.11704/) (2022)
- [PoseDiffusion: Solving Pose Estimation via Diffusion-aided Bundle Adjustment](https://mlsanity.com/paper/2306.15667/) (2023)
- [MeshLRM: Large Reconstruction Model for High-Quality Meshes](https://mlsanity.com/paper/2404.12385/) (2024)
- [Cameras as Rays: Pose Estimation via Ray Diffusion](https://mlsanity.com/paper/2402.14817/) (2024)
- [TTT3R: 3D Reconstruction as Test-Time Training](https://mlsanity.com/paper/2509.26645/) (2025)
- [VGGT-Long: Chunk it, Loop it, Align it -- Pushing VGGT's Limits on Kilometer-scale Long RGB Sequences](https://mlsanity.com/paper/2507.16443/) (2025)
- [RelPose: Predicting Probabilistic Relative Rotation for Single Objects in the Wild](https://mlsanity.com/paper/2208.05963/) (2022)
- [NeuTex: Neural Texture Mapping for Volumetric Neural Rendering](https://mlsanity.com/paper/2103.00762/) (2021)
- [Easi3R: Estimating Disentangled Motion from DUSt3R Without Training](https://mlsanity.com/paper/2503.24391/) (2025)
- [Stereo4D: Learning How Things Move in 3D from Internet Stereo Videos](https://mlsanity.com/paper/2412.09621/) (2024)
- [Point3R: Streaming 3D Reconstruction with Explicit Spatial Pointer Memory](https://mlsanity.com/paper/2507.02863/) (2025)
- [STream3R: Scalable Sequential 3D Reconstruction with Causal Transformer](https://mlsanity.com/paper/2508.10893/) (2025)
- [Large Spatial Model: End-to-end Unposed Images to Semantic 3D](https://mlsanity.com/paper/2410.18956/) (2024)

## Abstract (arXiv)

This paper introduces a network architecture to solve the structure-from-motion (SfM) problem via feature-metric bundle adjustment (BA), which explicitly enforces multi-view geometry constraints in the form of feature-metric error. The whole pipeline is differentiable so that the network can learn suitable features that make the BA problem more tractable. Furthermore, this work introduces a novel depth parameterization to recover dense per-pixel depth. The network first generates several basis depth maps according to the input image and optimizes the final depth as a linear combination of these basis depth maps via feature-metric BA. The basis depth maps generator is also learned via end-to-end training. The whole system nicely combines domain knowledge (i.e. hard-coded multi-view geometry constraints) and deep learning (i.e. feature learning and basis depth maps learning) to address the challenging dense SfM problem. Experiments on large scale real data prove the success of the proposed method.