AEP$n$P: A Less-constrained EP$n$P Solver for Pose Estimation with Anisotropic Scaling

TL;DR

AEP$n$P addresses pose estimation when full 3D models are unavailable by extending EP$n$P to jointly estimate the camera pose and unknown anisotropic scaling factors. By algebraic manipulation and a suitable reference frame, the problem reduces to a linear null-space solution followed by scale-aware point registration, yielding the rotation $R$, translation $t$, and axis scales embedded in $S$. The method is integrated with RANSAC to handle outliers and optional non-linear refinement to improve accuracy. Experiments on synthetic data and real datasets (NYU-RGBD, MegaDepth) demonstrate robustness to noise and outliers and show that reliable pose and anisotropic scaling can be recovered even with limited 2D-3D correspondences, including sparse keypoints. This broadens practical applicability of pose estimation when precise 3D models are not available.

Abstract

Perspective-$n$-Point (P$n$P) stands as a fundamental algorithm for pose estimation in various applications. In this paper, we present a new approach to the P$n$P problem with relaxed constraints, eliminating the need for precise 3D coordinates, which is especially suitable for object pose estimation where corresponding object models may not be available in practice. Built upon the classical EP$n$P solver, we refer to it as AEP$n$P due to its ability to handle unknown anisotropic scaling factors in addition to the common 6D transformation. Through a few algebraic manipulations and a well-chosen frame of reference, this new problem can be boiled down to a simple linear null-space problem followed by point registration-based identification of a similarity transformation. Experimental results on both simulated and real datasets demonstrate the effectiveness of AEP$n$P as a flexible and practical solution to object pose estimation. Code: https://github.com/goldoak/AEPnP.

Figures (6)

• Figure 1: Illustration of one practical case in object pose estimation which can be well handled by our proposed AEP$n$P solver. Specifically, it can simultaneously estimate anisotropic scaling factors as well as the 6D pose.
• Figure 2: Statistical plot of different metrics with respect to Gaussian image noise (#corrspondences=1024). Lines with markers represent the median errors of different methods while the corresponding shaded area indicates IQR, the difference between the 75th and 25th percentiles of the data.
• Figure 3: Statistical plot of different metrics with respect to the number of correspondences (noise=2px). Lines with markers represent the median errors of different methods while the corresponding shaded area indicates IQR, the difference between the 75th and 25th percentiles of the data.
• Figure 4: Computational time analysis with respect to the number of correspondences.
• Figure 5: Different metrics with respect to outlier ratios on two real datasets.