bundle adjustment

Nonlinear least-squares optimization jointly refining camera poses and 3D scene structure (or projection maps) to minimize reprojection error. Used to calibrate projector–camera systems, register sensing over large areas, and iteratively refine satellite camera poses with minimal parameterizations.

bundleadjustment

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Towards Initialization-free Calibrated Bundle Adjustment

Jun 30, 2025
CO
Carl Olsson
🏛️ Lund University

Existing initialization-free calibration-aware bundle adjustment methods rely on pseudo-object-space errors (pOSE), which are inherently constrained by projective invariance and cannot exploit known camera intrinsics—resulting in reconstructions defined only up to a projective equivalence class, lacking metric scale and Euclidean structure. Method: We propose a novel initialization-free calibrated Structure-from-Motion (SfM) framework that incorporates known camera calibration into pairwise relative rotation estimation, then jointly optimizes rotations via rotation averaging and pOSE refinement, directly solving for a near-metric reconstruction under the similarity transformation group. Contribution/Results: Our method breaks free from projective ambiguity, explicitly preserving scale and rigid-body geometry. It converges with high probability to the global optimum even from completely random initializations. Experiments demonstrate significantly higher reconstruction accuracy and robustness compared to conventional pOSE-based approaches, establishing a new paradigm for unsupervised calibrated SfM.

Achieving initialization-free bundle adjustment with calibrationIncorporating camera calibration for near metric reconstructionsIntegrating rotation averaging into projective invariant framework

Existing camera pose estimation methods suffer from low initial pose accuracy, reliance on task-specific descriptors, or the need for network fine-tuning or scene reconstruction. To address these limitations, we propose GS-SMC—the first lightweight pose optimization framework based on 3D Gaussian Splatting (3DGS). GS-SMC leverages a pre-trained 3DGS model to render multi-view images, establishes 2D–2D correspondences via feature matching, and iteratively refines poses using epipolar geometry constraints—without requiring network adaptation or scene re-reconstruction. Its modular architecture enables flexible substitution of feature extraction and matching components, eliminating dependence on specialized descriptors or networks. Evaluated on the 7-Scenes and Cambridge Landmarks benchmarks, GS-SMC reduces translational error by 53.3% and 40.7%, and rotational error by 56.9% and 53.2%, respectively—outperforming state-of-the-art approaches significantly.

Establishing epipolar constraints between query and rendered imagesOvercoming limitations of descriptor-dependent or geometry-lacking methodsRefining camera poses using 3D Gaussian Splatting without retraining

This work addresses the computational inefficiency of conventional bundle adjustment in multi-camera systems, which jointly optimizes camera poses and 3D points. By leveraging the generalized camera model, the authors introduce, for the first time, a purely pose-based geometric constraint that implicitly encodes 3D points through two reference observations and their associated poses, thereby entirely eliminating 3D point parameters from the optimization. The resulting formulation optimizes only camera poses, significantly enhancing computational efficiency while maintaining or even improving pose estimation accuracy. Experimental results on both synthetic and real-world datasets demonstrate that the proposed method consistently outperforms traditional bundle adjustment in terms of speed and accuracy.

bundle adjustmentcomputational efficiencyfeature redundancy

Practical solutions to the relative pose of three calibrated cameras

Mar 28, 2023
CT
C. Tzamos
🏛️ Czech Technical University in Prague | ETH Zürich

This paper addresses the relative pose estimation problem for three calibrated cameras given only four correspondences across all views. To overcome limitations of conventional methods—namely, their reliance on more correspondences or insufficient robustness—we propose a novel strategy that approximates a fifth correspondence using the centroid of the four observed points. We further introduce the first joint three-view pose estimation framework integrating a 4-point affine fundamental matrix solver, a standard 5-point relative pose solver, and a P3P solver. Geometric modeling enhances robustness against noise and outliers, while local optimization refines accuracy. Evaluated on real-world datasets, our method achieves state-of-the-art performance: the centroid-based strategy significantly outperforms pure affine approaches, striking a superior balance among accuracy, robustness, and computational efficiency, with straightforward implementation.

Estimating relative pose of three calibrated camerasImproving robustness with approximate mean-point correspondencesUsing four point correspondences for efficient solutions

JOGS: Joint Optimization of Pose Estimation and 3D Gaussian Splatting

Oct 30, 2025
YL
Yuxuan Li
🏛️ Beijing Jiaotong University

Traditional novel view synthesis relies on external Structure-from-Motion (SfM) tools (e.g., COLMAP), which introduce pose estimation errors and computational bottlenecks. To address this, we propose the first end-to-end framework that jointly optimizes 3D Gaussian splatting radiance fields and camera poses. Our method decouples optimization into two alternating stages—Gaussian parameter refinement and pose fine-tuning—guided by differentiable rendering and a geometric-photometric consistency constraint enforced via 3D optical flow. This design significantly suppresses projection errors, especially under large parallax and sparse-texture conditions. Evaluated on multiple standard benchmarks, our approach not only substantially outperforms existing COLMAP-free methods but also surpasses the COLMAP+3DGS baseline across both reconstruction quality and camera pose accuracy.

Eliminates dependency on external pose estimation tools like COLMAPImproves scene reconstruction and pose accuracy in challenging scenariosJointly optimizes 3D Gaussian points and camera poses without pre-calibration

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This work proposes a ray-based camera calibration framework tailored for 3D reconstruction, addressing the limitations of traditional reprojection error–based methods that rely on 2D calibration boards and inadequately reflect 3D geometric accuracy. Instead of reprojection error, the approach introduces reconstruction error and intersection error as more representative metrics. It employs a novel icosahedral 3D calibration target and a ring-shaped feature detector, integrated with a generalized distortion model and bootstrapping to refine both intrinsic and extrinsic parameter estimates. Experimental results on synthetic data demonstrate that the proposed method reduces average intersection error by approximately 40%, significantly enhances calibration stability, and validates that ray-level metrics provide a more faithful assessment of 3D reconstruction fidelity compared to conventional approaches.

3D reconstruction3D targetscalibration accuracy

This work addresses the inherent scale ambiguity in feed-forward 3D reconstruction models, which hinders their ability to recover metrically accurate geometry and limits applicability in scenarios requiring metric understanding. To resolve this, the authors propose the first end-to-end trainable feed-forward framework that leverages readily available unlabeled satellite imagery as a global metric prior. By integrating satellite image retrieval, bidirectional cross-view feature interaction, and scale consistency constraints, the model recovers absolute scene scale, refines geometric structure, and estimates camera poses in a metric coordinate system—even with only coarse initial pose estimates. Evaluated on KITTI, nuScenes, and Oxford RobotCar, the method significantly improves metric depth estimation, multi-view point cloud reconstruction, and cross-view localization accuracy, while demonstrating strong generalization across datasets and geographic regions.

3D reconstructionfeed-forward modelsmetric reconstruction

This study addresses the degradation in 3D Gaussian Splatting (3DGS) reconstruction quality caused by illumination variations and insufficient geometric accuracy in multi-temporal, high-resolution satellite imagery with small convergence angles. To overcome these challenges, this work introduces 2D Gaussian Splatting (2DGS) into satellite photogrammetry for the first time. The proposed method integrates an affine camera model with online camera refinement based on sparse observations, while jointly incorporating geometric shadow mapping and per-camera color correction to effectively mitigate time-varying illumination and shadow artifacts. Evaluated on the DFC2019 and IARPA2016 datasets, the approach significantly outperforms existing 3DGS-based methods, achieving an 11.93% reduction in mean absolute error and a 31% decrease in peak GPU memory consumption.

3D reconstructiongeometric accuracyillumination variation

This study addresses the challenge of unreliable manual feature matching in traditional RPC bundle adjustment for multi-temporal satellite imagery, which suffers from seasonal variations, illumination changes, and surface cover dynamics that degrade uncontrolled geometric positioning accuracy. To overcome this limitation, the authors propose an appearance-aware RPC refinement method that, for the first time, jointly leverages learned local features and global image descriptors to robustly extract season-invariant correspondences. Furthermore, the approach employs visual compatibility metrics to select optimal image pairs, thereby enhancing the match graph structure. Evaluated on a multi-season WorldView-3 dataset, the method significantly outperforms open-source baselines, achieving notably reduced geometric consistency errors and substantially improved matching efficiency across image blocks of 39–42 scenes.

feature matchinggeolocation accuracymulti-date satellite imagery

This work proposes a novel method for establishing point correspondences across image sequences in real time under unknown 3D scene structure and imaging geometry. The approach introduces a channel-vector-based uncertainty density model and employs an online optimization mechanism driven by Neyman chi-square divergence to iteratively learn mappings between image point sets. By representing channel vectors with basis functions and integrating a density divergence criterion, the algorithm achieves rapid convergence and high-accuracy correspondence estimation under general imaging geometries. Experimental results demonstrate that the proposed method outperforms state-of-the-art techniques across multiple metrics, offering a compelling combination of real-time performance, robustness, and accuracy.

3D surfacesimage sequencesonline learning

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