QuacamFM: Quaternion-Constrained Flow Matching for Camera Pose Estimation

2026-09-26

AI Summary

This study addresses the limitation of existing sparse-view pose estimation methods that neglect the unit-norm constraint of quaternions, resulting in non-smooth trajectories and suboptimal performance. To overcome this, we propose a quaternion-constrained flow matching framework that deeply integrates flow matching with quaternion geometry for the first time. By strictly maintaining unit quaternion representations throughout the pipeline and leveraging spherical linear interpolation (Slerp) to optimize optimal transport paths, our approach overcomes the limitations of conventional unconstrained 4D vector generation. Extensive experiments on the CO3Dv2 dataset demonstrate that the proposed method surpasses mainstream diffusion models and classical Structure-from-Motion techniques in pose accuracy, while exhibiting strong generalization capabilities in both sparse-view and in-the-wild scenarios.

Abstract

Camera pose estimation from multi-view images remains a challenge in computer vision. Traditional methods often address this problem using Structure-from-Motion (SfM) with bundle adjustment. However, camera poses estimated from sparse views are inherently ambiguous due to insufficient geometric constraints. Recent work leverages probabilistic models, such as diffusion models, to generate multiple camera pose hypotheses and therefore capture this uncertainty better. Most of these methods represent camera rotations using unit quaternions, but treat them as unconstrained 4D vectors during the generative processes, thereby ignoring the unit-norm constraint of quaternions. Unconstrained quaternions create non-smooth and suboptimal generation trajectories. To this end, we propose *QuacamFM*, a quaternion-constrained flow matching framework for camera pose estimation that preserves unit quaternion representations throughout the entire flow trajectory. We design the optimal transport of the quaternion flows using smooth spherical linear interpolation. Experiments on CO3Dv2 demonstrate our method's advantage in camera pose accuracy over diffusion-based methods and classical SfM approaches. We further show that our quaternion-constrained formulation outperforms the naive application of standard flow matching to 4D quaternion vectors on sparse-view camera pose estimation. Finally, it is observed that QuacamFM generalizes well across datasets and in-the-wild examples.

Problem

• Camera Pose Estimation
• Sparse Views
• Unit Quaternion
• Flow Matching
• Ambiguity

Innovation

• Quaternion-Constrained Flow Matching
• Camera Pose Estimation
• Optimal Transport
• Spherical Linear Interpolation
• Sparse Views