Motion Segmentation Using Locally Affine Atom Voting

Erez Posner; Rami Hagege

arxiv: 1907.06091 · v1 · pith:DDZUF2R2new · submitted 2019-07-13 · 💻 cs.CV

Motion Segmentation Using Locally Affine Atom Voting

Erez Posner , Rami Hagege This is my paper

Pith reviewed 2026-05-24 21:49 UTC · model grok-4.3

classification 💻 cs.CV

keywords motion segmentationlocally affine modelsfeature setsatom votingaffinity computationrandom votingvideo analysiscomputer vision

0 comments

The pith

Feature sets with local affine models replace pairwise affinities for motion segmentation.

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

The paper introduces LAAV as a pre-processing stage that groups image features into sets and computes affinities between those sets using local affine models. This replaces the usual calculation of affinities between every pair of individual features before feeding the results into a Random Voting step. The approach is presented as addressing challenges in complex scenes with multiple motions. If the method works as described, it reduces computational demands while producing segmentation accuracy that meets or exceeds other algorithms on clean data and holds up under noise. A reader would care because motion segmentation underpins video understanding tasks where full pairwise comparisons become prohibitive as the number of tracked points grows.

Core claim

LAAV segments motion for all features in a scene by replacing pairwise affinities with affinities between sets of features modeled as locally affine. The sets serve as atoms that vote after an initial grouping step, followed by a fine-tuned Random Voting procedure. Experiments show the method produces the highest accuracy among compared algorithms on standard tests and comparable results when measurement noise is added.

What carries the argument

Locally Affine Atom Voting, which computes motion affinities from groups of features that fit local affine models rather than from all individual feature pairs.

If this is right

Complex multi-body motion scenes become simpler to process because only set-to-set comparisons are needed.
Computational cost drops while accuracy is preserved or improved on the tested sequences.
The pipeline maintains performance levels comparable to existing methods when measurement noise is introduced.
All features receive a motion label through the atom-based voting process.

Where Pith is reading between the lines

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

The same set-based affinity idea could be tried on other vision grouping tasks that currently rely on dense pairwise matrices.
Scenes dominated by non-rigid or highly curved motions would form a natural test of where the local affine assumption begins to break.
Replacing hand-crafted features with learned descriptors inside the atom construction step might extend robustness without changing the overall voting structure.

Load-bearing premise

That local affine models fitted to feature sets capture motion relations well enough to stand in for pairwise affinities without missing critical distinctions between different motions.

What would settle it

A benchmark run on a dataset with ground-truth motion labels where LAAV's segmentation error rate exceeds that of a standard pairwise-affinity baseline by more than a few percent.

Figures

Figures reproduced from arXiv: 1907.06091 by Erez Posner, Rami Hagege.

**Figure 3.** Figure 3: Number Of Iteration for Accurate motion segmentation for σn ∈ {0,0.5,1,2} [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

read the original abstract

We present a novel method for motion segmentation called LAAV (Locally Affine Atom Voting). Our model's main novelty is using sets of features to segment motion for all features in the scene. LAAV acts as a pre-processing pipeline stage for features in the image, followed by a fine-tuned version of the state-of-the-art Random Voting (RV) method. Unlike standard approaches, LAAV segments motion using feature-set affinities instead of pair-wise affinities between all features; therefore, it significantly simplifies complex scenarios and reduces the computational cost without a loss of accuracy. We describe how the challenges encountered by using previously suggested approaches are addressed using our model. We then compare our algorithm with several state-of-the-art methods. Experiments shows that our approach achieves the most accurate motion segmentation results and, in the presence of measurement noise, achieves comparable results to the other algorithms.

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

LAAV adds a locally affine pre-processing stage to random voting and reports top accuracy on motion segmentation benchmarks.

read the letter

The paper's core move is to insert a locally affine atom voting step before a tuned random voting routine. Instead of computing affinities between every pair of features, it groups features into locally affine sets and works with those. The authors spell out how the atoms are built and how the voting integrates with the downstream RV stage. That shift is the actual novelty they put forward, and the full text shows the construction clearly enough to follow the steps without guessing. The experiments back the accuracy claim on the benchmarks they use and show the method stays competitive once noise is added, which is the kind of direct comparison that matters for this kind of algorithmic work. The gain appears to come from the combination of the new pre-step and the RV tuning, so the paper would be stronger if it isolated how much each piece contributes on its own. The affine assumption is reasonable for the rigid-motion cases in the tests, but it could be brittle in scenes with strong non-rigid deformation; the results do not explore that boundary much. Overall the argument holds together internally and the evaluation protocol is laid out without obvious gaps. This is useful reading for people already working on voting-based motion segmentation who want a practical pre-processing tweak. It is not a field-changing result, but the method is concrete and the numbers are presented plainly, so it deserves a serious referee rather than a desk reject.

Referee Report

0 major / 1 minor

Summary. The paper proposes LAAV (Locally Affine Atom Voting), a motion segmentation method that employs locally affine models on sets of features as a pre-processing stage before a fine-tuned Random Voting (RV) algorithm. It replaces standard pairwise feature affinities with feature-set affinities to simplify complex motion scenarios and reduce computational cost, while claiming to deliver the highest accuracy on motion segmentation benchmarks and performance comparable to other methods under measurement noise.

Significance. If the experimental claims hold, the shift to feature-set affinities based on local affine models offers a potentially simpler and more efficient route to motion segmentation without sacrificing accuracy, addressing challenges in complex scenes that pairwise methods struggle with.

minor comments (1)

[Abstract] Abstract: the sentence 'Experiments shows that our approach achieves the most accurate motion segmentation results' contains a subject-verb agreement error and should read 'Experiments show'.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their review and recommendation of minor revision. The report summarizes our contribution positively and does not list any specific major comments requiring response.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper is an algorithmic proposal for motion segmentation via LAAV (locally affine atom voting) as pre-processing before fine-tuned RV. Central claims rest on direct experimental comparisons to state-of-the-art methods on benchmarks, with reported accuracy and noise robustness. No derivation chain, fitted parameters presented as predictions, or load-bearing self-citations appear; the method construction and evaluation protocol are described explicitly and independently of the target results. The work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on parameters, axioms or entities.

pith-pipeline@v0.9.0 · 5668 in / 913 out tokens · 24315 ms · 2026-05-24T21:49:31.846906+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

atoms ... piecewise-smooth ... minimum cost multicut ... Sampson distance ... Random Voting

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages · 3 internal anchors

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Adaptive motion segmentation algorithm based on the principal angles conﬁguration

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[1] [1]

T. Brox, C. Bregler, and J. Malik. Large displacement optical ﬂow. In 2009 IEEE Conference on Computer Vision and Pattern Recognition , pages 41–48, June 2009. doi: 10.1109/CVPR.2009.5206697

work page doi:10.1109/cvpr.2009.5206697 2009

[2] [2]

Motion Segmentation by SCC on the Hopkins 155 Database

Guangliang Chen and Gilad Lerman. Motion segmentation by SCC on the hopkins 155 database. CoRR, abs/0909.1608, 2009. URL http://arxiv.org/abs/0909. 1608

work page internal anchor Pith review Pith/arXiv arXiv 2009

[3] [3]

A multibody factorization method for inde- pendently moving objects

João Paulo Costeira and Takeo Kanade. A multibody factorization method for inde- pendently moving objects. Int. J. Comput. Vision , 29(3):159–179, September 1998. ISSN 0920-5691. doi: 10.1023/A:1008000628999. URL http://dx.doi.org/ 10.1023/A:1008000628999

work page doi:10.1023/a:1008000628999 1998

[4] [4]

Dimitriou and A

N. Dimitriou and A. Delopoulos. Improved motion segmentation using locally sampled subspaces. In 2012 19th IEEE International Conference on Image Processing , pages 309–312, Sept 2012. doi: 10.1109/ICIP.2012.6466857

work page doi:10.1109/icip.2012.6466857 2012

[5] [5]

Ehsan Elhamifar and R. Vidal. Sparse subspace clustering: Algorithm, theory, and ap- plications. CoRR, abs/1203.1005, 2012. URL http://arxiv.org/abs/1203. 1005

work page internal anchor Pith review Pith/arXiv arXiv 2012

[6] [6]

Fischler and Robert C

Martin A. Fischler and Robert C. Bolles. Random sample consensus: A paradigm for model ﬁtting with applications to image analysis and automated cartography.Commun. ACM, 24(6):381–395, June 1981. ISSN 0001-0782. doi: 10.1145/358669.358692. URL http://doi.acm.org/10.1145/358669.358692

work page doi:10.1145/358669.358692 1981

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Fernando Flores-Mangas and Allan D. Jepson. Fast rigid motion segmentation via incrementally-complex local models. In CVPR, pages 2259–2266. IEEE Computer Society, 2013

work page 2013

[8] [8]

Two-view motion segmentation with model selection and outlier removal by ransac-enhanced dirichlet process mixture mod- els

Yong-Dian Jian and Chu-Song Chen. Two-view motion segmentation with model selection and outlier removal by ransac-enhanced dirichlet process mixture mod- els. International Journal of Computer Vision , 88(3):489–501, 2010. ISSN 1573-

work page 2010

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URL http://dx.doi.org/10.1007/ s11263-010-0317-y

doi: 10.1007/s11263-010-0317-y. URL http://dx.doi.org/10.1007/ s11263-010-0317-y

work page doi:10.1007/s11263-010-0317-y

[10] [10]

Rigid motion segmentation using ran- domized voting

Heechul Jung, Jeongwoo Ju, and Junmo Kim. Rigid motion segmentation using ran- domized voting. In Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on, June 2014. doi: 10.1109/CVPR.2014.158

work page doi:10.1109/cvpr.2014.158 2014

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Keuper, B

M. Keuper, B. Andres, and T. Brox. Motion trajectory segmentation via minimum cost multicuts. In IEEE International Conference on Computer Vi- sion (ICCV) , 2015. URL http://lmb.informatik.uni-freiburg.de/ /Publications/2015/KB15b. : 11

work page 2015

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Krause, M

J. Krause, M. Stark, J. Deng, and L. Fei-Fei. 3d object representations for ﬁne-grained categorization. In 2013 IEEE International Conference on Computer Vision Work- shops, pages 554–561, Dec 2013. doi: 10.1109/ICCVW.2013.77

work page doi:10.1109/iccvw.2013.77 2013

[13] [13]

PoseNet: A convolutional network for real-time 6-dof camera relocalization,

F. Lauer and C. Schnorr. Spectral clustering of linear subspaces for motion segmenta- tion. In 2009 IEEE 12th International Conference on Computer Vision, pages 678–685, Sept 2009. doi: 10.1109/ICCV .2009.5459173

work page doi:10.1109/iccv 2009

[14] [14]

H. Li. Two-view motion segmentation from linear programming relaxation. In 2007 IEEE Conference on Computer Vision and Pattern Recognition , pages 1–8, June 2007. doi: 10.1109/CVPR.2007.382975

work page doi:10.1109/cvpr.2007.382975 2007

[15] [15]

Latent low-rank representation for subspace seg- mentation and feature extraction

Guangcan Liu and Shuicheng Yan. Latent low-rank representation for subspace seg- mentation and feature extraction. In 2011 International Conference on Computer Vi- sion, pages 1615–1622. IEEE, 2011

work page 2011

[16] [16]

Faugeras

Quan-Tuan Luong and Olivier D. Faugeras. The fundamental matrix: Theory, al- gorithms, and stability analysis. International Journal of Computer Vision , 17(1): 43–75, Jan 1996. ISSN 1573-1405. doi: 10.1007/BF00127818. URL https: //doi.org/10.1007/BF00127818

work page doi:10.1007/bf00127818 1996

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Morel and G

J. Morel and G. Yu. Asift: A new framework for fully afﬁne invariant image com- parison. SIAM Journal on Imaging Sciences , 2(2):438–469, 2009. doi: 10.1137/ 080732730. URL https://doi.org/10.1137/080732730

work page doi:10.1137/080732730 2009

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Ng, Michael I

Andrew Y . Ng, Michael I. Jordan, and Yair Weiss. On spectral clustering: Analysis and an algorithm. In T. G. Dietterich, S. Becker, and Z. Ghahra- mani, editors, Advances in Neural Information Processing Systems 14 , pages 849–856. MIT Press, 2002. URL http://papers.nips.cc/paper/ 2092-on-spectral-clustering-analysis-and-an-algorithm. pdf

work page 2002

[19] [19]

A New Approach To Two-View Motion Segmentation Using Global Dimension Minimization

Bryan Poling and Gilad Lerman. A new approach to two-view motion segmentation using global dimension minimization. CoRR, abs/1304.2999, 2013. URL http:// arxiv.org/abs/1304.2999

work page internal anchor Pith review Pith/arXiv arXiv 2013

[20] [20]

S. R. Rao, R. Tron, R. Vidal, and Yi Ma. Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories. In 2008 IEEE Conference on Computer Vision and Pattern Recognition , pages 1–8, June 2008. doi: 10.1109/CVPR.2008.4587437

work page doi:10.1109/cvpr.2008.4587437 2008

[21] [21]

Normalized cuts and image segmentation

Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. , 22(8):888–905, August 2000. ISSN 0162-8828. doi: 10. 1109/34.868688. URL http://dx.doi.org/10.1109/34.868688

work page doi:10.1109/34.868688 2000

[22] [22]

P. H. Torr. Geometric motion segmentation and model selection [and discussion]. Philosophical Transactions: Mathematical, Physical and Engineering Sciences , 356 (1740):1321–1340, 1998. ISSN 1364503X. URL http://www.jstor.org/ stable/54848. 12 :

work page 1998

[23] [23]

Tron and R

R. Tron and R. Vidal. A benchmark for the comparison of 3-d motion segmentation algorithms. In 2007 IEEE Conference on Computer Vision and Pattern Recognition , pages 1–8, June 2007. doi: 10.1109/CVPR.2007.382974

work page doi:10.1109/cvpr.2007.382974 2007

[24] [24]

Vidal, Yi Ma, and S

R. Vidal, Yi Ma, and S. Sastry. Generalized principal component analysis (gpca).IEEE Transactions on Pattern Analysis and Machine Intelligence , 27(12):1945–1959, Dec

work page 1945

[25] [25]

doi: 10.1109/TPAMI.2005.244

ISSN 0162-8828. doi: 10.1109/TPAMI.2005.244

work page doi:10.1109/tpami.2005.244 2005

[26] [26]

Segmentation of dynamic scenes from the multibody fundamental matrix, 2002

Rene Vidal, Stefano Soatto, Yi Ma, and Shankar Sastry. Segmentation of dynamic scenes from the multibody fundamental matrix, 2002

work page 2002

[27] [27]

Adaptive motion segmentation algorithm based on the principal angles conﬁguration

Luca Zappella, Edoardo Provenzi, Xavier Lladó, and Joaquim Salvi. Adaptive motion segmentation algorithm based on the principal angles conﬁguration. In Asian Confer- ence on Computer Vision, pages 15–26. Springer, 2010

work page 2010

[28] [28]

Determining the epipolar geometry and its uncertainty: A review

Zhengyou Zhang. Determining the epipolar geometry and its uncertainty: A review. International Journal of Computer Vision, 27:161–195, 1996

work page 1996

[29] [29]

Fast and accurate motion segmentation using linear combination of views

Vasileios Zografos and Klas Nordberg. Fast and accurate motion segmentation using linear combination of views. In BMVC 2011 :, pages 12.1–12.11, 2011

work page 2011