P1AC: Revisiting Absolute Pose From a Single Affine Correspondence

TL;DR

This work presents P1AC, the first general solution to absolute camera pose estimation from a single affine correspondence (AC) given an oriented 3D point and a locally planar scene. By deriving AC-induced constraints and reformulating the problem as a $3Q3$ minimal solver via a Cayley-parameterized rotation, the authors obtain up to eight candidate poses and recover the translation, achieving robust performance with a single correspondence. Compared to $P3P$, this approach reduces combinatorics in RANSAC and, on standard localization benchmarks (Cambridge and Aachen), yields higher accuracy and recall while maintaining competitive runtimes within robust pipelines such as GC-RANSAC. The method is validated on synthetic data for stability under noise and on real-world datasets, and it is complemented by reasonable baselines (DPR, IPPE) to contextualize performance. The authors provide code for reproducibility, demonstrating practical impact for large-scale image-based localization tasks.

Abstract

Affine correspondences have traditionally been used to improve feature matching over wide baselines. While recent work has successfully used affine correspondences to solve various relative camera pose estimation problems, less attention has been given to their use in absolute pose estimation. We introduce the first general solution to the problem of estimating the pose of a calibrated camera given a single observation of an oriented point and an affine correspondence. The advantage of our approach (P1AC) is that it requires only a single correspondence, in comparison to the traditional point-based approach (P3P), significantly reducing the combinatorics in robust estimation. P1AC provides a general solution that removes restrictive assumptions made in prior work and is applicable to large-scale image-based localization. We propose a minimal solution to the P1AC problem and evaluate our novel solver on synthetic data, showing its numerical stability and performance under various types of noise. On standard image-based localization benchmarks we show that P1AC achieves more accurate results than the widely used P3P algorithm. Code for our method is available at https://github.com/jonathanventura/P1AC/ .

Figures (4)

• Figure 1: Overview of the perspective-one-affine-correspondence (P1AC) problem. Our goal is to estimate the pose of a query image based on a single 2D observation of a known oriented 3D point and an affine correspondence to a reference image with known pose.
• Figure 2: Results of synthetic data experiments. (a) Analysis of numerical stability with zero noise added to observations. The plots are estimates of the distribution produced by Gaussian kernel-density estimation. Top: Log rotation error; Bottom: Log position error. (b) Analysis of error with respect to various types and levels of noise. Left: Error of P1AC solver w.r.t. affine and point noise, with normal noise fixed to 1$^\circ$. Center: Error of P1AC solver w.r.t. normal and point noise, with affine noise fixed to 4%. Right: Error of P3P solver w.r.t. affine and point noise. Note that the P3P solver does not use the affine transformation or normal vector and thus is unaffected by affine and normal noise.
• Figure 3: Rotation accuracy versus skew in the affine transformation, over 1M random problem instances. The accuracy of the DPR solver degrades as perspective distortion increases, whereas our P1AC solver is stable.
• Figure 4: Average timing for each robust estimation method across a range of outlier ratios.