arxiv: 2605.01552 · v1 · submitted 2026-05-02 · 💻 cs.CV

Recognition: unknown

Robust Fundamental Matrix Estimation from Single Image Motion Blur

Bao-Long Tran , Per-Erik Forss\'en , Fredrik Viksten

Authors on Pith no claims yet

Pith reviewed 2026-05-09 14:15 UTC · model grok-4.3

classification 💻 cs.CV

keywords motion blurfundamental matrixcamera motionpoint correspondencesrobust estimationepipolar geometrymotion segmentation

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The pith

A fundamental matrix summarizing 3D camera motion during exposure can be recovered from point correspondences along smear paths in one motion-blurred image.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a single motion-blurred photograph contains enough information to compute a fundamental matrix describing the camera's 3D trajectory across the exposure interval. Smear paths supply the raw material for locating the same scene points at two different instants inside that interval, even though the forward or backward direction along each path remains unknown. The authors replace the standard eight-point algorithm with a version that tolerates this transpose ambiguity and weights samples by the reliability of the predicted smear. When the approach succeeds, motion information becomes extractable from individual frames instead of requiring pairs of sharp images or video sequences. Downstream experiments show the resulting matrix supports motion segmentation on both synthetic and real blurred data.

Core claim

We demonstrate the feasibility of establishing correspondences between two time instances within the camera exposure window, and that these can be used to robustly infer a fundamental matrix, which summarizes the motion of the camera during the exposure time. The inferred fundamental matrix is unique up to a transpose, corresponding to an ambiguity of the direction of time. Due to this per-smear ambiguity, classic methods such as the 8-point algorithm are no longer usable. The proposed method modifies the estimation to work on time-direction ambiguous correspondences and incorporates an uncertainty measurement in smear pattern prediction.

What carries the argument

A robust sampler that draws candidate correspondences from predicted smear paths while explicitly handling time-direction ambiguity and weighting each sample by its prediction uncertainty.

If this is right

Camera motion during exposure can be summarized by a single fundamental matrix without requiring multiple sharp frames.
The matrix supports direct motion segmentation on blurred images as a downstream task.
Standard robust estimators must be altered to tolerate transpose ambiguity in the correspondences.
Incorporating per-correspondence uncertainty from blur prediction improves sampling reliability over unweighted methods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Existing deblurring pipelines could use the recovered matrix as an additional motion constraint to reduce artifacts.
Single-frame motion analysis might extend to higher-order trajectory models if the smear representation is generalized beyond linear paths.
Structure-from-motion pipelines could treat blurred frames as usable observations rather than discarding them.

Load-bearing premise

Smear paths must supply enough distinct, repeatable features to form reliable point matches across different moments inside the exposure despite noise and the unknown time direction.

What would settle it

Generate synthetic blurred images from known 3D camera trajectories, run the estimator, and check whether the recovered matrices satisfy the epipolar constraint on held-out points with error comparable to standard methods on sharp pairs; systematic failure above that threshold would disprove the claim.

Figures

Figures reproduced from arXiv: 2605.01552 by Bao-Long Tran, Fredrik Viksten, Per-Erik Forss\'en.

**Figure 1.** Figure 1: Epipolar lines computed from the estimated fundamental matrix for a real view at source ↗

**Figure 2.** Figure 2: Example of data generation. (a), (b) Two consecutive sharp images. (c) view at source ↗

**Figure 3.** Figure 3: Double angle-based representation for smear paths in the motion-blurred view at source ↗

**Figure 4.** Figure 4: Example of Top-50% best predicted smears from a single motion-blurred input. This shows that our model focuses on reliable blurry patterns while disregarding occlusion motion regions (e.g., the image border and the monkey’s moving arm) by assigning higher variance σ. From left to right: Input blurry image, Top-50% predicted smears, smear path annotation, σ distribution view at source ↗

**Figure 5.** Figure 5: (a) Sparsification plot of different smear estimation approaches on Monkaa view at source ↗

**Figure 6.** Figure 6: Examples of fundamental matrix estimations. Columns: 1 view at source ↗

**Figure 7.** Figure 7: Example results on the downstream task of local motion segmentation, view at source ↗

**Figure 8.** Figure 8: Failure to estimate the fundamental matrix in a dynamic scene with view at source ↗

**Figure 9.** Figure 9: Comparison of synthetic blur using convolution and frame averaging. The view at source ↗

**Figure 10.** Figure 10: Examples of smear path estimation. 1 st column is the input blurry image, 2 nd column is the generated ground truth smear paths, 3 rd column is the Top50% output of the smear-path prediction network, with column 1 as input. demonstrates Top-50% best smear predictions ranked by the uncertainty measure σ. Accurate smear-path predictions are well distributed across the image, implying that geometry estimat… view at source ↗

**Figure 11.** Figure 11: Additional quantitative examples in real scenes, similar to Fig. 6. First view at source ↗

**Figure 12.** Figure 12: More examples of failure cases. 1 st row: Dynamic scene. 2 nd row: Dominant plane scene. 3 rd row: Only camera rotation scene view at source ↗

read the original abstract

In this paper, we introduce a challenging task: extracting a fundamental matrix from a single motion blurred image. For a camera moving in 3D during exposure, the smear paths in the blurry image contain cues and constraints on this motion. We demonstrate the feasibility of establishing correspondences between two time instances within the camera exposure window, and that these can be used to robustly infer a fundamental matrix, which summarizes the motion of the camera during the exposure time. The inferred fundamental matrix is unique up to a transpose, corresponding to an ambiguity of the direction of time. Due to this per-smear ambiguity, classic methods, such as the 8-point algorithm, are no longer usable. The proposed method modifies the estimation to work on time-direction ambiguous correspondences. To improve the robustness of the fundamental matrix estimation, we also propose to incorporate an uncertainty measurement in smear pattern prediction and use it in the sampling process of the estimator. Experiments on synthetic and real-world motion-blur datasets demonstrate that our approach is able to estimate the fundamental matrix encoding the 3D camera motion, from single frames. Practical applicability is demonstrated on the downstream task of motion segmentation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper defines a new task of recovering a fundamental matrix from smear paths inside one motion-blurred image and adapts the 8-point algorithm for the per-pair time-flip ambiguity.

read the letter

The central claim is that smear paths in a single blurred frame give enough point pairs to estimate the camera motion during exposure, with the matrix unique only up to transpose. They replace the usual 8-point solver with a version that tries both directions per pair and weights samples by an uncertainty score taken from the smear predictor. That modification is simple and directly addresses the ambiguity the abstract flags. Experiments on synthetic and real blurred data plus a motion-segmentation example show the pipeline can run end to end. The idea is absent from the cited prior work, so the task itself counts as new. A reader who already works on structure-from-motion with real-world blur will see immediate practical value in skipping a separate deblurring step. The soft spot is the one the stress-test note highlights: localizing two distinct points on each smear and treating them as a correspondence still has to survive real-image noise and the flip choice. The abstract gives no error numbers, no baseline comparisons, and no count of usable smears per frame, so the robustness claim rests on details that are not visible here. If the full paper supplies those numbers and they are reasonable, the method becomes more convincing; if the errors stay large, the downstream utility shrinks. This is aimed at geometric-vision groups that handle degraded video or SfM pipelines. It is coherent on its own terms and engages the right literature, so it deserves a serious referee to check the quantitative support and the uncertainty model. I would send it out for review rather than desk-reject.

Referee Report

2 major / 2 minor

Summary. The paper introduces the task of estimating a fundamental matrix from a single motion-blurred image. It establishes point correspondences along smear paths that represent camera motion at two distinct times within the exposure window, modifies the 8-point algorithm to handle the resulting time-direction ambiguity (yielding F unique up to transpose), and incorporates an uncertainty measure from smear prediction into the sampling process. Experiments on synthetic and real-world motion-blur datasets are reported to demonstrate feasibility, with an additional demonstration on a downstream motion-segmentation task.

Significance. If the central claim holds, the work would be significant for enabling 3D motion recovery from individual blurred frames in computer vision pipelines where sharp images are unavailable. The paper is credited for formulating a novel problem, explicitly addressing the per-smear ambiguity, and showing a practical downstream application to motion segmentation. The approach avoids circularity in its derivation and introduces an uncertainty-weighted sampler, which are positive technical contributions.

major comments (2)

[Experiments section] Experiments section: The abstract and experiments claim that the method successfully estimates the fundamental matrix on synthetic and real-world motion-blur datasets and supports motion segmentation, yet no quantitative error metrics (e.g., mean epipolar distance, inlier ratios), baseline comparisons (standard 8-point algorithm or deblurring-based alternatives), or ablation results on the uncertainty threshold are reported. This absence directly undermines assessment of whether localization noise and time ambiguity are handled robustly enough for the central feasibility claim.
[Method description] Method description (smear correspondence and sampling): The claim that smear paths yield usable correspondences despite per-path time ambiguity requires that localization error remains small enough for the epipolar constraint to produce a stable F. The paper provides no quantitative breakdown of correspondence precision, fraction of usable smears, or sensitivity analysis to the free parameter 'uncertainty threshold for smear prediction', which is load-bearing for the robustness assertion.

minor comments (2)

[Abstract] The abstract states that the inferred fundamental matrix is 'unique up to a transpose' but does not clarify in the main text whether this ambiguity is resolved or propagated in the downstream motion-segmentation task.
Notation for the uncertainty measurement and its integration into the modified sampler could be presented with an explicit equation or pseudocode for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the novelty of the problem formulation, the handling of time-direction ambiguity, and the downstream application. We address each major comment below and will revise the manuscript to incorporate the requested quantitative evaluations.

read point-by-point responses

Referee: [Experiments section] Experiments section: The abstract and experiments claim that the method successfully estimates the fundamental matrix on synthetic and real-world motion-blur datasets and supports motion segmentation, yet no quantitative error metrics (e.g., mean epipolar distance, inlier ratios), baseline comparisons (standard 8-point algorithm or deblurring-based alternatives), or ablation results on the uncertainty threshold are reported. This absence directly undermines assessment of whether localization noise and time ambiguity are handled robustly enough for the central feasibility claim.

Authors: We agree that the current experiments focus on qualitative demonstration and a downstream task, which limits rigorous assessment. In the revised manuscript we will add mean epipolar distances and inlier ratios on both the synthetic and real-world datasets. We will also include direct comparisons to the standard 8-point algorithm (applied to the ambiguous correspondences) and to deblurring-based alternatives where feasible, together with an ablation on the uncertainty threshold to quantify its contribution to robustness. revision: yes
Referee: [Method description] Method description (smear correspondence and sampling): The claim that smear paths yield usable correspondences despite per-path time ambiguity requires that localization error remains small enough for the epipolar constraint to produce a stable F. The paper provides no quantitative breakdown of correspondence precision, fraction of usable smears, or sensitivity analysis to the free parameter 'uncertainty threshold for smear prediction', which is load-bearing for the robustness assertion.

Authors: We concur that a quantitative characterization of correspondence quality is necessary to support the robustness claim. The revised paper will report measured localization precision along the extracted smear paths, the fraction of smears retained after uncertainty filtering, and a sensitivity analysis that varies the uncertainty threshold and shows its effect on the stability and accuracy of the recovered fundamental matrix. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method modifies standard 8-point algorithm without reducing outputs to fitted inputs or self-citations

full rationale

The paper's core contribution is a modified RANSAC-style estimator that handles per-smear time-direction ambiguity by allowing flipped correspondences and weighting by an uncertainty measure derived from smear prediction. This is an algorithmic adaptation of the classic 8-point algorithm rather than a derivation that reduces by construction to the same data or parameters. No equations are shown to equate the output fundamental matrix to a fitted quantity defined from the identical inputs, and no load-bearing uniqueness theorems or ansatzes are imported via self-citation. The approach remains self-contained against external benchmarks such as the standard fundamental matrix estimation literature.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The method rests on the classical epipolar geometry relation and the domain assumption that smear paths encode valid inter-time point matches; one practical free parameter (uncertainty threshold) is introduced for sampling.

free parameters (1)

uncertainty threshold for smear prediction
Used to weight or filter correspondences during RANSAC-style sampling; value is chosen for robustness but not derived from first principles.

axioms (2)

standard math The fundamental matrix can be estimated from point correspondences via the 8-point algorithm
Invoked when adapting the estimator to time-ambiguous matches.
domain assumption Smear paths provide geometrically valid point matches at different instants during exposure
Central premise stated in the abstract as the source of constraints on camera motion.

pith-pipeline@v0.9.0 · 5501 in / 1355 out tokens · 73562 ms · 2026-05-09T14:15:34.416891+00:00 · methodology

discussion (0)

Reference graph

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