A new preprint reports two geometric solvers that estimate where a camera is, how it is oriented and what its focal length is from a 3D reconstruction. The approach combines a known gravity direction from an inertial sensor with local geometric details in image features.
In the paper’s reported tests, the proposed solvers were faster than the listed P3.5Pf and P4Pf comparison methods and showed favorable results in synthetic experiments and visual-localization benchmarks. The findings are performance results from computer-vision evaluations, not evidence that the method reduces energy use in deployed devices.
A sparse geometric estimate
The method is designed for a query image that must be matched to a 3D reconstruction. UP1PfAC uses a single affine correspondence, while UP2PfORI uses two orientation-covariant correspondences. Both treat focal length as unknown and assume that the camera’s gravity direction is known.
For UP1PfAC, the reduced equations produce a quartic polynomial, meaning an equation that can yield four candidate solutions. The solver uses an additional constraint to choose the candidate with the smallest residual, or mismatch with the observed geometric information.
Strong results in controlled tests
The synthetic scenes randomized camera orientations and 3D points. The query camera was placed 2 units from the origin, and focal length was drawn uniformly between 200 and 1200.
In 5000 noise-free random configurations, most errors were below 10−12. UP1PfAC and UP2.5Pf were reported as the most numerically stable methods among the focal-length solvers.
When image noise was added, the authors reported better performance for the proposed methods, including when inertial-sensor noise was also present. The comparison used medians from 1000 random instances at each noise level, with one test setting using 1.2 pixels of image noise.
The reported median solver times were 2586 nanoseconds for UP1PfAC and 2149 nanoseconds for UP2PfORI, compared with 19,118 nanoseconds for P3.5Pf and 3179 nanoseconds for P4Pf. These timings came from one laptop, and the paper reports no measure of timing variability.
The proposed solvers were also tested in standard RANSAC. In scenes with 1000 correspondences, 1.2 pixels of image noise, 0.2 degrees of inertial-sensor noise and a 50% outlier ratio, both proposed methods showed advantageous performance across 100 synthetic problem instances.
Benchmark performance was more mixed
The real-data evaluations used the Cambridge Landmarks and Aachen Day-Night v1.1 benchmarks. Cambridge contributed five scenes with separate training and test data, while the Aachen evaluation used images from multiple devices and upright query images.
The localization pipeline used Graph-Cut-RANSAC with a direct-linear-transform initialization and 10 Levenberg–Marquardt refinement iterations. It also selected the top 20 database retrievals and top 10 query retrievals before estimating the camera pose.
On Cambridge, the authors reported lower errors and shorter times than other semi-calibrated solvers across all scenes and both feature pipelines. The proposed methods had better rotation results than calibrated methods, but worse translation results.
In one SuperPoint feature pipeline, the two proposed solvers were close on the GreatCourt and ShopFacade scenes. UP1PfAC reported median position, rotation, focal-length and time results of 57.7 centimetres, 0.13 degrees, 0.009 and 22.6 milliseconds on GreatCourt, and 10.6 centimetres, 0.26 degrees, 0.008 and 33.9 milliseconds on ShopFacade. UP2PfORI reported 57.9 centimetres, 0.13 degrees, 0.009 and 24.0 milliseconds on GreatCourt.
On Aachen, the proposed methods reached similar reported recall values in the SuperPoint evaluation. UP1PfAC’s daytime recalls were 48.5%, 70.8% and 97.9%, while its nighttime recalls were 60.2%, 80.1% and 97.4%. UP2PfORI recorded 48.4%, 71.2% and 98.2% by day, and 62.3%, 80.1% and 97.4% at night.
The reported focal-length error on Aachen was 0.009 for both proposed solvers with SuperPoint. Their times were 16.7 and 19.8 milliseconds; with SIFT features, both focal-length errors were 0.017 and the times were 28.0 and 30.8 milliseconds.
What the results leave open
The results assume usable gravity information and upright camera queries. They do not establish how the solvers perform when gravity is inaccurate or unavailable, when the camera is not upright, or when a fuller camera-intrinsic model is needed.
The study’s real-world validation covered two benchmarks and selected feature pipelines, while exact Aachen image and query counts were not reported. Most results were medians or histograms without confidence intervals or formal statistical tests, and the comparison methods did not all make the same focal-length assumption.
The solver timings do not measure the full cost of extracting and matching features, estimating 3D normals or handling mismatches and inertial-sensor errors. The paper therefore does not demonstrate lower end-to-end localization latency or reduced device energy consumption, and it does not establish universal superiority across hardware, environments or feature pipelines.
The document is an arXiv preprint, arXiv:2608.20056v1, dated 20 August 2026. The authors acknowledge grant JDC2024-055088-I, funded by MICIU/AEI/10.13039/501100011033 and the FSE+.
Paper data and sources
Original title: Gravity-aware partially calibrated absolute pose estimation from affine- or rotation-covariant features
Authors: Marcus Valtonen Örnhag, Alberto Jaenal, Stefan Adalbjörnsson
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: 10.1007/978-3-032-37211-6_19
Original paper · Full text