cs.CVSep 26, 2026

QuacamFM: Quaternion-Constrained Flow Matching for Camera Pose Estimation

Authors: Bao-Long Tran, Cuong Le, Tahereh Dehdarirad, Fredrik Viksten, Per-Erik Forssén

Organizations: Linköping University, Sweden

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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.

Figures & tables

Figure 1: Camera generation trajectory of QuacamFM vs. QuacamFM- lerp and PoseDiffusion during inference, from starting step t=0t=0 to ending step t=1t=1 . Lighter shades indicate earlier flow steps, and darker shades indicate later steps. QuacamFM produces smoothest trajectories, yielding better camera pose estimation accuracy.
Figure 2: QuacamFM overview . We present a flow-matching-based method to predict camera poses given an image sequence. The camera rotation is estimated via quaternion-constrained flows, where the optimal transport path is constructed using slerp , preserving the unit-quaternion constraint. The quaternion trajectory is integrated using the quaternion differential equation, while the translation uses a standard normalizing flow. The rightmost picture shows the camera trajectory during inference, lighter shades indicate earlier flow steps, and darker shades indicate later steps.
Figure 3: Qualitative results on CO3Dv2 . Camera pose estimations from input images (top row). Our QuacamFM and baseline results are shown in below rows. Camera frustum colors correspond to input-image borders. Solid frustums are camera estimations and dash frustums are camera ground-truths. The first four examples are from seen categories, and last three from held out (unseen) categories. Missing cameras indicate non-convergence.
Figure 4: Camera pose accuracy on CO3Dv2 . Quantitative metrics ( yy -axis, higher-better) at different thresholds and numbers of input images ( xx -axis). RelPose does not predict camera translation and hence is omitted in the respective metrics.
MethodRTA@30 ↑\uparrowRRA@30 ↑\uparrowAUC@30 ↑\uparrowRTA@15 ↑\uparrowRRA@15 ↑\uparrowAUC@15 ↑\uparrows\mathrm{s}
PixSfM40.438.630.132.933.728.320.2
COLMAP + SPSG28.244.425.127.331.621.13.26
PoseReg61.365.545.549.153.235.70.03
RelPose †-72.7--57.2-29.5
RelPose++ †84.388.766.574.284.545.14.49
PoseDiffusion †79.986.766.579.880.547.58.83
Table 1: Results on CO3Dv2 . Quantitative evaluation of camera pose estimation with 10-frame input. Bold denotes the best and underline the second best. The inference time is measured in seconds (s)(\mathrm{s}) . † Methods that require correspondences or post optimization.
Table 6
Figure 5: Optimal transport ablation . Comparison of rotation accuracy between quaternion-constrained flows (QuacamFM), vanilla normalizing flows (QuacamFM- lerp ), and diffusion-based methods (PoseDiffusion and PoseDiffusion w/o GGS). Experiments conducted on CO3Dv2 test set.
Figure 6: Camera pose estimations on in-the-wild examples . QuacamFM generalizes well to images outside of the distribution of CO3Dv2 training categories, and can recover plausible camera poses even on self-captures that contain varying distances from the camera and in-plane rotations.
Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Qualitative results of QuacamFM on RealEstate10K.
Table 10
Method5 images10 images20 images
PoseDiffusion6.3448.83420.61
PoseDiffusion w/o GGS0.3420.3930.825
RelPose++2.8544.49111.32
QuacamFM0.3520.4650.735
Appendix
Table 6: Inference time of methods with multi-image inputs. The inference time is measured in second s\mathrm{s} .
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