FLIGHT: Fibonacci Lattice-based Inference for Geometric Heading in real-Time

David Dirnfeld; Fabien Delattre; Pedro Miraldo; Erik Learned-Miller

cs.CVFeb 26, 2026

FLIGHT: Fibonacci Lattice-based Inference for Geometric Heading in real-Time

Authors: David Dirnfeld, Fabien Delattre, Pedro Miraldo, Erik Learned-Miller

Organizations: University of Massachusetts Amherst · Mitsubishi Electric Research Laboratories (MERL)

Abstract

Estimating camera motion from monocular video is a fundamental problem in computer vision, central to tasks such as SLAM, visual odometry, and structure-from-motion. Existing methods that recover the camera's heading under known rotation, whether from an IMU or an optimization algorithm, tend to perform well in low-noise, low-outlier conditions, but often decrease in accuracy or become computationally expensive as noise and outlier levels increase. To address these limitations, we propose a novel generalization of the Hough transform on the unit sphere (S(2)) to estimate the camera's heading. First, the method extracts correspondences between two frames and generates a great circle of directions compatible with each pair of correspondences. Then, by discretizing the unit sphere using a Fibonacci lattice as bin centers, each great circle casts votes for a range of directions, ensuring that features unaffected by noise or dynamic objects vote consistently for the correct motion direction. Experimental results on three datasets demonstrate that the proposed method is on the Pareto frontier of accuracy versus efficiency. Additionally, experiments on SLAM show that the proposed method reduces RMSE by correcting the heading during camera pose initialization.

Figures & tables

Figure 1: Left. A frame of a dynamic scene from the Sintel dataset. The blue vectors show translational flows compatible with the winning Fibonacci bin $\mathbf{s}_{j}$ as shown by the green point. Gray vectors show translational flows that do not agree on a direction. Right. The unit sphere of the possible directions a camera can move. The red points show a sparse sampling of the unit sphere (i.e., Fibonacci bins) with our hierarchical approach. The blue great circles (corresponding to the blue flow vectors in the frame) represent great circles that vote for a unique direction, whereas the gray great circles do not.

Figure 2: In the case of pure translation flow, two pairs of point correspondences are needed to obtain the direction of motion. On the left, we sample two flow vectors (indicated by the red and blue arrows). On the right, we show the great circles of translation directions compatible with these flow vectors. The points of intersection are the only directions compatible with both flow vectors.

Panel of Figure 3 — Figure 3: We employ a 2-stage voting scheme on the unit sphere $\mathcal{S}^{2}$ representation of the possible camera translation directions between two consecutive video frames using a Fibonacci lattice . Left: In the first stage, the red points represent a sparse Fibonacci lattice. The blue and gray arcs across the sphere are the great circles representing the camera motion directions compatible with a single pair of feature correspondences . Our goal is to find the point on the sphere compatible with the largest number of features. Right: In the second stage, the red points represent a dense sampling of the Fibonacci lattice in the winning region of step 1. The yellow dot shows the ground truth translation, and the purple point is the winning bin.

Panel of Figure 4 — Figure 4: The relationship of the angle $\theta_{i,j}$ between the normal $\mathbf{n}_{i}$ of a great circle $i$ and a Fibonacci bin center $\mathbf{s}_{j}$ . When $\theta_{i,j}$ is close to $\pi/2$ , the great circle intersects the region $\mathbf{s}_{j}$ defined by $r$ . Given the bin is approximately flat, we use the Pythagorean Theorem to solve for $b_{i,j}$ . The length $a_{i,j}$ of the intersection is therefore $2b_{i,j}$ and the amount the great circle $i$ votes for $\mathbf{s}_{j}$ .

	Method	mAA 2° $\uparrow$	mAA 5° $\uparrow$	Time (ms) $\downarrow$
Flow	FLIGHT	0.6193	0.8223	0.9472
	FOE [ 29 ]	0.6065	0.8169	3.8278
	BNB [ 25 ]	0.6013	0.81	35.7238
	PN [ 10 ]	0.5387	0.7796	0.0361
	PN*	0.5754	0.7986	0.8125
	2-Points	0.6141	0.8177	12.7976

Table 1: Quantitative results on KITTI dataset . We compare the mAA of translation error and the run time of our method with multiple other baselines. Bold text indicates the best and underlines as the second best. For each method, we report the mAA at 2° and mAA 5° and Time (ms) when using Flow, SIFT, and SURF.

	Method	mAA 5° $\uparrow$	mAA 10° $\uparrow$	Time (ms) $\downarrow$
Flow	FLIGHT	0.2731	0.4781	0.9149
	FOE [ 29 ]	0.2715	0.4795	43.4998
	BNB [ 25 ]	0.1578	0.2988	29.4898
	PN [ 10 ]	0.1139	0.2351	0.0375
	PN*	0.1284	0.2591	0.8601
	2-Points	0.2794	0.4819	11.4159

Table 2: Quantitative results on TUM RGB-D dataset . We compare the mAA of translation error and the run time of our method with multiple other baselines. Bold text indicates the best and underlines as the second best. For each method, we report the mAA at 5° and mAA at 10° and Time (ms) when using Flow, SIFT, and SURF.

	Method	mAA 5° $\uparrow$	mAA 10° $\uparrow$	Time (ms) $\downarrow$
Flow	FLIGHT	0.3591	0.4541	1.4428
	FOE [ 29 ]	0.3482	0.4429	132.2228
	BNB [ 25 ]	0.1728	0.2834	233.4138
	PN [ 10 ]	0.1358	0.1806	0.042
	PN*	0.1632	0.2127	0.8891
	2-Points	0.291	0.385	115.2381

Table 3: Quantitative results on Sintel dataset . We compare the mAA of translation error and the run time of our method with multiple other baselines. Bold text indicates the best and underlines as the second best. For each method, we report the mAA 5° and mAA at 10° and Time (ms) when using Flow, SIFT, and SURF.

	Method	RMSE $\downarrow$	STD $\downarrow$
KITTI	PySLAM	11.9354	4.2504
KITTI	PySLAM + FLIGHT	10.9056	2.5515
EuRoC	PySLAM	0.0895	0.0018
EuRoC	PySLAM + FLIGHT	0.0878	0.0005

Table 4: Quantitative results on PySLAM . We show an improvement in both error and STD when we use FLIGHT to refine the initial relative pose estimate in PySLAM. This improvement remains on monocular and stereo SLAM, with minimal computational overhead.

Figure 5: Results on synthetic data while varying the number of outliers. We plot time (ms) in log scale vs accuracy for probability of outlier $p\in[20\%,\cdots,80\%]$ and max 2px noise. FLIGHT remains consistent in time and has higher accuracy than the baselines.

Figure 6: The plot shows both mAA $5^{\circ}$ and time (log scale) in ms under varying rotation noise. The solid line shows the mAA, and the dashed lines show the time. Up to $.15^{\circ}$ rotation noise FLIGHT mAA remains above .9 while maintaining a near constant runtime.

Hierarchical	NLR	ES	mAA 5° $\uparrow$	mAA 10° $\uparrow$	Time (ms) $\downarrow$
			0.9087	0.9568	472.2631
		✓	0.9083	0.9565	127.6043
	✓		0.9123	0.9586	472.1992
	✓	✓	0.9122	0.9585	127.0941
✓			0.9073	0.9561	1.2672
✓		✓	0.9067	0.9558	0.8593

Table 5: Quantitative results on techniques to improve our base method to obtain our FLIGHT method. The experiments show that using the hierarchical approach with NLR and early stopping provided the best trade-off between speed and accuracy.

Panel of Figure 7 — Figure 7: Left: We compare the sample size $N$ vs. the runtime (ms) for FLIGHT for different values of $p\in[1\%,5\%,20\%,50\%,90\%]$ . Right: We plot sample size $N$ v.s. accuracy under the same conditions.

#Bins $\times 1000$	mAA 1° $\uparrow$	mAA 5° $\uparrow$	Time (ms) $\downarrow$
49	0.5765	0.9062	0.6432
54	0.5735	0.9050	0.6291
59	0.6020	0.9107	0.6726
64	0.6088	0.9123	0.6833
68	0.5926	0.9090	0.6697
102	0.5933	0.9092	0.7662

Table 6: The number of bins (in thousands) and their corresponding effect on accuracy vs speed. Using a Fibonacci lattice of

64k

provides a good balance of speed vs accuracy.

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PoseFM: Relative Camera Pose Estimation Through Flow Matching

Dominik Kuczkowski, Laura Ruotsalainen

Department of Computer Science University of Helsinki Finland

Relative Pose Estimation Camera Pose Estimation Visual Odometry

Open paper AskPDF arXiv

Monocular visual odometry (VO) is a fundamental computer vision problem with applications in autonomous navigation, augmented reality and more. While deep learning-based methods have recently shown superior accuracy compared to traditional geometric pipelines, particularly in environments where handcrafted features struggle due to poor structure or lighting conditions, most rely on deterministic regression, which lacks the uncertainty awareness required for robust applications. We propose PoseFM, the first framework to reformulate monocular frame-to-frame VO as a generative task using Flow Matching (FM). By leveraging FM, we model camera motion as a distribution rather than a point estimate, learning to transform noise into realistic pose predictions via continuous-time ODEs. This approach provides a principled mechanism for uncertainty estimation and enables robust motion inference under challenging visual conditions. In our evaluations, PoseFM achieves strong performance on TartanAir, KITTI and TUM-RGBD benchmarks, achieving the lowest absolute trajectory error (ATE) on some of the trajectories and overall being competitive with the best frame-to-frame monocular VO methods. Code and model checkpoints will be made available at https://github.com/helsinki-sda-group/posefm.

Abstract

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