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arxiv: 2606.09139 · v2 · pith:M2XUBBGVnew · submitted 2026-06-08 · 💻 cs.CV

A Geometric Framework for Absolute Pose and Velocity Estimation with Event Cameras

Zibin Liu , Shunkun Liang , Banglei Guan , Yang Shang , Qifeng Yu , Ji Zhao This is my paper

Pith reviewed 2026-06-27 17:15 UTC · model grok-4.3

classification 💻 cs.CV
keywords event camerasabsolute pose estimationvelocity estimationgeometric constraints3D linesevent-based vision
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0 comments X

The pith

Absolute pose and velocity from event cameras are recoverable from three line correspondences via two geometric constraints.

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

The paper establishes a geometric framework that recovers both absolute 6-DoF pose and velocities from event camera streams by associating events with 3D lines in the scene. It relies on the orthogonality between each 3D line and the normal to its event plane together with the collinearity between an event and the projection of its line. These constraints yield linear solvers for both pose and velocity as well as a polynomial solver for globally optimal rotation. A reader would care because the approach works with a minimal number of correspondences and addresses the previously open problem of joint pose-velocity recovery.

Core claim

The central claim is a geometric framework for absolute pose and velocity estimation that uses two constraints: the orthogonality between a 3D line and the normal vector of its corresponding event plane, and the collinearity of an event with the 2D projection of its associated line. Based on these, linear and polynomial solvers are derived for pose estimation and linear plus optimization solvers for velocity, all requiring only a minimum of three event-line correspondences to determine the 6-DoF quantities independently.

What carries the argument

The two geometric constraints of line-event plane orthogonality and event-line projection collinearity, which enable closed-form solvers from three correspondences.

If this is right

  • Linear solvers enable efficient absolute pose computation from events.
  • A polynomial solver yields a globally optimal rotation estimate.
  • Both angular and linear velocities are recoverable by a linear solver or an optimization-based one.
  • The 6-DoF pose or velocities can be determined independently with three correspondences.

Where Pith is reading between the lines

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

  • The same constraints might support fusion with inertial measurements to handle brief periods without detectable lines.
  • Extension to rolling-shutter or multi-camera event rigs would require only re-deriving the projection collinearity term.
  • In scenes where line detection is unreliable, the framework predicts graceful degradation rather than total failure if at least three good matches remain.

Load-bearing premise

Reliable correspondences can be established between 3D lines and the events they trigger, and the scene must contain enough lines to produce detectable events.

What would settle it

Generate synthetic event streams from known 3D lines and a ground-truth trajectory; if the solvers using exactly three correspondences produce pose or velocity errors larger than sensor noise, the framework does not hold.

Figures

Figures reproduced from arXiv: 2606.09139 by Banglei Guan, Ji Zhao, Qifeng Yu, Shunkun Liang, Yang Shang, Zibin Liu.

Figure 1
Figure 1. Figure 1: Illustration of joint absolute pose and velocity estimation for event [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the geometric constraints for absolute pose estimation. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of velocity estimation. The camera motion between two [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Error analysis of absolute pose and velocity estimation under various conditions. Plots (a)-(d) sequentially illustrate the impact of event count, number [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The proposed method maintains a success rate above [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: Robustness analysis to outlier correspondences. We evaluate the min [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Experimental setup for event simulation. We visualize the data [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Reprojection results on the E-POSE dataset. Object models are reprojected onto the event accumulation images (for visualization purposes only) using [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Initial pose estimation results on the LOPET dataset. (a) Visual comparison of reprojected 3D lines from different methods. (b) Mean reprojection [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Reprojection results on the LOPET dataset. 3D lines of Objects are reprojected onto the event accumulation images (for visualization purposes only) [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
read the original abstract

Despite the rapid advancements in event-based motion estimation, current geometric methods primarily focus on velocity estimation. However, absolute pose estimation, which is equally crucial for key applications such as robotic navigation and augmented reality, remains relatively underexplored. Consequently, the simultaneous recovery of absolute pose and velocity from event streams remains an open and challenging problem. To address this gap, we propose a geometric framework for absolute pose and velocity estimation by leveraging 3D lines in the scene and the events they trigger. At the core of the framework lie two key geometric constraints: the orthogonality between a 3D line and the normal vector of its corresponding event plane, and the collinearity of an event with the 2D projection of its associated line. Based on these constraints, we present both linear and polynomial solvers for absolute pose estimation. The former enables efficient computation, while the latter provides a globally optimal solution for rotation. For velocity estimation, we develop an efficient linear solver and a more accurate optimization-based solver to recover both angular and linear velocities. Notably, our methods require a minimum of three event-line correspondences to determine the 6-DoF absolute pose or velocities independently. Extensive experiments in simulation and on real-world datasets demonstrate that our methods achieve state-of-the-art performance, with significant improvements in accuracy and computational efficiency compared to existing methods. The demo code is publicly available at https://github.com/Zibin6/EventPoseVelocity.

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.

Referee Report

2 major / 2 minor

Summary. The paper proposes a geometric framework for absolute pose and velocity estimation from event cameras by using 3D lines in the scene. It introduces two constraints per event-line correspondence (orthogonality of the 3D line to the event-plane normal, and collinearity of the event with the projected line) and derives linear and polynomial solvers for 6-DoF pose plus linear and optimization-based solvers for 6-DoF velocity, all requiring a minimum of three correspondences. Experiments on simulated and real data are reported to achieve SOTA accuracy and efficiency, with public code released.

Significance. If the correspondence assumption holds and the algebraic derivations are correct, the work addresses an underexplored problem in event-based vision by enabling absolute pose recovery (previously focused mainly on velocity) with minimal correspondences. The parameter-free geometric approach and public code are strengths that could support reproducibility and further development in robotics and AR applications.

major comments (2)
  1. [Abstract and geometric-constraints section] Abstract and geometric-constraints section: the claim that three event-line correspondences suffice for independent 6-DoF pose or velocity recovery is load-bearing, yet the manuscript provides no mechanism, algorithm, or validation procedure for establishing or verifying those correspondences under realistic event noise, partial occlusions, or line sparsity; without this, both the linear and polynomial solvers are inapplicable regardless of their algebraic correctness.
  2. [Solver derivations and experiments] Solver derivations and experiments: no error-propagation analysis, degeneracy characterization, or data-exclusion rules are supplied for the minimum-three-correspondence case, making it impossible to assess whether the reported SOTA improvements are robust or contingent on favorable matching conditions.
minor comments (2)
  1. [Geometric constraints] Notation for the event plane and its normal should be defined explicitly before the orthogonality constraint is stated.
  2. [Experiments] Figure captions for the real-world dataset results should include the number of event-line correspondences used per frame.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address each of the major comments below.

read point-by-point responses

  1. Referee: [Abstract and geometric-constraints section] Abstract and geometric-constraints section: the claim that three event-line correspondences suffice for independent 6-DoF pose or velocity recovery is load-bearing, yet the manuscript provides no mechanism, algorithm, or validation procedure for establishing or verifying those correspondences under realistic event noise, partial occlusions, or line sparsity; without this, both the linear and polynomial solvers are inapplicable regardless of their algebraic correctness.

    Authors: The manuscript focuses on developing a geometric framework and minimal solvers assuming that event-line correspondences are given, which is a common practice in the development of geometric computer vision algorithms (e.g., essential matrix estimation or PnP solvers). The algebraic derivations are independent of how correspondences are obtained. We will revise the paper to make this assumption explicit in the abstract and introduction, and to briefly discuss related work on event-based feature detection and matching that could be used to obtain such correspondences in practice. This clarification will help readers understand the scope of the contribution. revision: partial

  2. Referee: [Solver derivations and experiments] Solver derivations and experiments: no error-propagation analysis, degeneracy characterization, or data-exclusion rules are supplied for the minimum-three-correspondence case, making it impossible to assess whether the reported SOTA improvements are robust or contingent on favorable matching conditions.

    Authors: We acknowledge the value of including an analysis of error propagation, degeneracies, and rules for handling unreliable correspondences in the minimal case. In the revised version, we will add a subsection discussing potential degenerate cases for the three-correspondence solvers (e.g., when lines are parallel or the configuration leads to singular matrices) and provide an empirical sensitivity analysis using the simulated data with varying noise levels. We will also suggest simple data-exclusion criteria based on the reprojection residuals or the condition number of the design matrix in the linear solvers. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation follows from standard projective geometry constraints

full rationale

The framework defines two geometric constraints (orthogonality of 3D line to event-plane normal; collinearity of event with projected line) from the event camera model and scene lines, then algebraically solves for 6-DoF pose or velocity using a minimum of three correspondences. These steps are direct consequences of the input geometry and degrees-of-freedom counting; no parameter is fitted to data and renamed as a prediction, no self-citation chain justifies a uniqueness claim, and no ansatz is smuggled in. The derivation is self-contained against external projective geometry benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Framework rests on domain assumptions about line-event correspondences and scene structure; no free parameters or invented entities named in abstract.

axioms (1)
  • domain assumption 3D lines exist in the scene and generate detectable events that can be corresponded to the lines
    Stated as core of the framework in abstract

pith-pipeline@v0.9.1-grok · 5799 in / 1123 out tokens · 16798 ms · 2026-06-27T17:15:52.493490+00:00 · methodology

discussion (0)

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