Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

A Taxonomy of Structure from Motion Methods

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper proposes a three-way taxonomy of structure-from-motion methods based on which part of the problem a method focuses on—motion, structure, or both—and consolidates the theoretical conditions that make each formulation well posed.

desk verdict A useful, accurate conceptual survey of SfM whose organizing taxonomy is a helpful bookkeeping device rather than a deep new insight; worth publishing after minor fixes and a more candid treatment of boundary cases. read the letter →

arxiv 2505.15814 v1 pith:SVQHF77A submitted 2025-05-21 cs.CV

Federica Arrigoni This is my paper · ORCID
classification cs.CV
keywords StructurefromMotionMulti-viewGeometryCalibrated/UncalibratedCamerasViewingGraphProjectiveFactorizationRotationAveragingParallelRigiditySolvability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that the entire structure-from-motion literature can be organized by a simple question: which part of the problem—camera motion, scene structure, or both together—does a method put its attention on? Under this split, incremental SfM and projective factorization are joint methods, global SfM is motion-first, and distance-based structure recovery is structure-first. The author claims that this taxonomy highlights similarities between approaches that look different and, more importantly, it organizes the theoretical conditions that make each formulation well posed. A reader should care because the field largely lacks a unified conceptual map, and this survey supplies one together with a consolidated statement of known degeneracy conditions.

What carries the argument

The taxonomy is the organizing device, with three named categories: Structure and Motion (sequential/hierarchical SfM and projective factorization), Structure from Motion (global SfM on the viewing graph), and Structure without Motion (distance-based structure recovery). The viewing graph—nodes are cameras, edges are reliable two-view geometries—is the central object that carries the theoretical analysis, letting calibrated degeneracy be characterized by parallel rigidity and uncalibrated degeneracy by solvability. The spectral framework for rotations and the multi-view fundamental matrix are the main algebraic tools used to turn graph conditions into computable rank tests.

What would settle it

If a viewing graph passes the parallel rigidity test rank(S)=3n-4 for a random generic configuration yet still admits two distinct camera configurations with identical pairwise directional measurements, the equivalence between non-degeneracy and parallel rigidity for calibrated cameras would fail. Equivalently, an actual SfM method that cannot be placed in any of the three categories would falsify the taxonomy's exhaustiveness.

Watch

Extended reading notes

Core claim

The paper's central claim is that every SfM method can be meaningfully classified by the part of the problem it attends to: structure and motion simultaneously, motion alone, or structure alone. Within that frame it assembles the theoretical conditions that make each formulation well posed: the Generalized Projective Reconstruction Theorem for projective factorization, the condition rank(F)=6 with three positive and three negative eigenvalues for the multi-view fundamental matrix, rank(S)=3n-4 for parallel rigidity in calibrated translation recovery, and viewing graph solvability for uncalibrated cameras. It also notes that most practical pipelines never check these degeneracy conditions, and it calls for a better synergy between theory and practice as a future direction.

Load-bearing premise

The load-bearing premise is that the three-way split into joint, motion-first, and structure-first methods is exhaustive and that the few representative methods chosen for each category faithfully represent the whole field.

Editorial extensions

If this is right

  • A researcher can place a new SfM method into one of three families and immediately identify which theoretical well-posedness results apply to it.
  • A practitioner can check a viewing graph for degeneracy in advance, using the rank(S)=3n-4 test for calibrated cameras and finite-solvability tests for uncalibrated ones, before running a reconstruction.
  • The observation that most methods ignore degeneracy checks suggests that adding explicit checks to existing pipelines could reduce the number of failed or ambiguous reconstructions.
  • The taxonomy clarifies that the name 'structure from motion' properly applies only to the motion-first family; other families deserve their own names.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same three-way split could be applied to learning-based SfM systems, since the paper's own examples (VGGSfM and MASt3R-SfM) already map to the motion-first and structure-first categories, respectively; the taxonomy may help predict which theoretical guarantees such systems inherit.
  • The rank conditions reported here could be turned into certificate checks inside bundle adjustment, allowing an optimizer to know whether the current graph even admits a unique solution; the paper leaves this step implicit.
  • Because the paper notes that parallel rigidity is necessary but not sufficient for solvability, a natural extension would be a unified combinatorial invariant that predicts both calibrated and uncalibrated degeneracy from the graph alone.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a conceptual taxonomy for Structure from Motion (SfM) in which methods are grouped into three categories: (i) methods that estimate structure and motion jointly (sequential SfM and projective factorization), (ii) motion-first methods (calibrated and uncalibrated global SfM, represented via the viewing graph), and (iii) structure-without-motion methods (the distance-based approach of Li and recent deep-learning variants). The survey places particular emphasis on theoretical well-posedness conditions: the Generalized Projective Reconstruction Theorem, the rank-6 consistency condition for multi-view fundamental matrices, parallel rigidity of viewing graphs, and solvability conditions for projective SfM. It also reviews selected deep-learning SfM methods and lists open problems.

Significance. If the taxonomy is accepted as an organizing principle, the paper gives the community a useful way to compare SfM methods and a consolidated statement of many well-posedness conditions that are otherwise scattered across the literature. The paper's main strengths are its clear pedagogical structure, the consistent distinction between calibrated and uncalibrated settings, and the effort to include recent data-driven methods (VGGSfM, MASt3R-SfM, deep factorization) within the classical framework. The spot-checkable theoretical claims (essential-matrix decomposition, rank-4 factorization, depth-matrix degeneracies, multi-view fundamental matrix consistency) are, with the exception of the rotation-averaging hardness measure discussed below, transcribed accurately. The work does not contain new proofs or experiments, so its value rests on the fidelity of synthesis and on whether the proposed split is a genuinely clarifying classification rather than a bookkeeping device.

major comments (3)
  1. [Section II-D; Figure 1] The central claim that the taxonomy brings a new perspective and groups existing approaches is not fully operational, because the paper never defines a decision rule for what counts as 'focus' or 'simultaneous.' Several of the paper's own examples straddle the categories: sequential SfM (Section III-A) is labelled joint even though it initializes with two-view motion estimation and then alternates resection (motion-only) and intersection (structure-only); bundle adjustment (Section II-C), the most natural joint estimator, is deliberately placed outside the taxonomy as a refinement layer; and MASt3R-SfM (Remark 15) is treated as structure-without-motion even though it derives and uses relative poses. The author should either provide an explicit placement criterion (for example, which quantity is the primary output before the other, and whether the computation alternates or is a single optimization) and apply it to these boundary cases, or explicitly moderate the claim in the abstract from a grouping of 'existing approaches' to one possible expository perspective. As written, the taxonomy is not yet shown to be jointly exhaustive and disjoint, which weakens the paper's main contribution.
  2. [Remark 6, Eq. (24)] The hardness measure for rotation averaging is stated as λ2(L)/n, where λ2 is the second-smallest eigenvalue of the graph Laplacian. This is inconsistent with the sentence immediately following it: a complete graph has λ2 = n and hence λ2/n = 1, whereas a sparse cycle graph has λ2/n = O(n^{-3}), so the displayed ratio is large precisely in the easy, well-connected case and small in the hard, poorly-connected case. The source [86] relates problem difficulty to the inverse ratio n/λ2(L). The equation should be corrected, and the accompanying sentence should be made consistent with the source.
  3. [Section V, Remark 13] The statement that 3D points can be uniquely recovered from a subset of pairwise distances 'when the underlying graph is rigid in the classical sense' is imprecise: rigidity in the classical sense guarantees only finitely many embeddings, not uniqueness up to congruence. The correct sufficient notion for a unique recovery (up to rotation, translation, and reflection) is global rigidity, or rigidity together with generic position conditions. Since the cited reference [124] works with global rigidity, the terminology in the remark should be aligned with that notion.
minor comments (5)
  1. [Section I, penultimate paragraph] The sentence 'Section III describes the third category of approaches, that focus on structure instead' should refer to Section V; Section III is the first category.
  2. [Section III-B, after Eq. (14)] The phrase 'keeping only the fourth largest singular values' should read 'keeping only the four largest singular values'.
  3. [Section III-B, after Eq. (14)] The tilde notation is inconsistent: the text uses 'eU', 'eV T', and 'eΣ' for the SVD factors, and later writes 'S= eV T' without the tilde on V. The notation should be made uniform.
  4. [Remark 11] The phrase 'it is does not comply with the assumptions' contains a typo ('is does') and should read 'it does not comply'.
  5. [Section II-C] The description of Bundle Adjustment as 'a combination of Gradient Descent and Gauss-Newton' is acceptable informally, but it would be more precise to say that Levenberg-Marquardt interpolates between the two depending on the damping parameter.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the survey proposes an explicitly acknowledged taxonomy and cites external prior results, with no derivation that reduces to its own inputs.

full rationale

This is a conceptual survey, not a derivation, and none of its load-bearing claims reduce by construction to its inputs. The central contribution is the proposed three-category taxonomy (structure and motion, motion-first, structure-first). The paper explicitly presents this as an organizing choice rather than a forced consequence: Section II-D states "we group existing approaches into three main categories, according to which part of the problem they focus on," and immediately adds the footnote "Other taxonomies are possible as well." There is no fitted parameter being renamed as a prediction, and no uniqueness theorem is imported from the author's own work to forbid alternatives. The theoretical conditions reported in Section IV-D (rank(F)=6 in Eq. (32), rank(S)=3n-4 in Eq. (33), parallel rigidity, and viewing graph solvability) are cited to prior publications, several of which are authored or co-authored by the present author, but these are peer-reviewed external results that the survey summarizes rather than derives; the survey does not use them to justify the taxonomy itself. The paper also acknowledges its own limitations, such as the selective coverage in Section II-D ("citing all of them would be nearly impossible, therefore – for each category – we only describe a few representative approaches") and the admitted non-conformance of some recent methods (Remarks 11 and 15). These are coverage limitations, not circular steps. Therefore the paper is self-contained as a review and its central organizing claim is independent of any circular reduction.

Assumptions & free parameters 0 free parameters · 10 assumptions · 0 invented entities

The survey's narrative rests entirely on prior published theorems in multi-view geometry, graph theory, and optimization; each is cited to its source. The heaviest reliance is on the viewing graph solvability and parallel rigidity results in Section IV-D, several of which are co-authored by the present author ([112], [116], [118], [120], [122]), and on the projective factorization uniqueness results of [10]. All are peer-reviewed derivations, so they count as external grounding for the survey, though the author's own work shapes the emphasis.

assumptions (10)
  • domain assumption Two-view geometry: fundamental/essential matrix estimation, decomposition, and critical configurations for two cameras
    Invoked in Section III-A for initial pair reconstruction (Eqs. (8), (9)) and in Section III-C for two-view degeneracies; cited to [2], [20], [21].
  • domain assumption Classic Projective Reconstruction Theorem: non-zero projective depths imply uniqueness up to a projective transformation
    Invoked in Section III-C as the baseline that the Generalized Projective Reconstruction Theorem extends; cited to [2].
  • domain assumption Generalized Projective Reconstruction Theorem: depth matrix without zero rows/columns and not cross-shaped implies uniqueness up to projectivity
    Invoked in Section III-C to characterize degeneracies of projective factorization and to justify [7]; cited to [10].
  • domain assumption Triangulation and resection degeneracy classifications, including points on the baseline and the twisted cubic
    Invoked in Section III-C for the sequential pipeline's well-posedness; cited to [2] and [53].
  • domain assumption Multi-view fundamental matrix consistency: rank(F)=6 and 3 positive plus 3 negative eigenvalues, with the sign condition redundant
    Invoked in Section IV-C as the basis for spectral uncalibrated SfM and the triplet refinement of [14]; cited to [14] and [12].
  • standard math Rotation averaging spectral relaxation: the three leading eigenvectors of the matrix of relative rotations provide the global rotations
    Invoked in Section IV-B, Eqs. (20)-(22); combines the Rayleigh-Ritz theorem (standard linear algebra) with the synchronization analysis of [63] and [64].
  • domain assumption Parallel rigidity characterization: camera centers are uniquely recoverable from pairwise unit directions iff rank(S) equals 3n-4
    Invoked in Section IV-D for calibrated global SfM, Eq. (33), and used as the practical test for degenerate viewing graphs; cited to [92], [111], [112].
  • domain assumption Viewing graph solvability: uniqueness of uncalibrated cameras from fundamental matrices, checked via polynomial systems, with finite solvability as a rank test and the necessary conditions (11n-15)/7 edges, biconnectivity, and degree constraints
    Invoked in Section IV-D for uncalibrated SfM; cited to [54], [115], [116], [117], [120]. Several of these references are co-authored by the present author.
  • domain assumption Solvability implies parallel rigidity, and not conversely
    Invoked in Section IV-D to relate calibrated and uncalibrated cases and to interpret Figure 10; cited to [122], an author co-authored reference.
  • domain assumption Distance-based graph rigidity is necessary for unique 3D point recovery from pairwise distances
    Invoked in Remark 13 for the structure-without-motion category (MDS and rigidity theory); cited to [123], [124].

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Taxonomy of Structure from Motion Methods." pith.science (2026). https://pith.science/paper/SVQHF77A

@misc{pith2026250515814,
  author       = {Pith},
  title        = {Pith review of: A Taxonomy of Structure from Motion Methods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SVQHF77A}},
  note         = {Machine review of arXiv:2505.15814}
}
read the original abstract

Structure from Motion (SfM) refers to the problem of recovering both structure (i.e., 3D coordinates of points in the scene) and motion (i.e., camera matrices) starting from point correspondences in multiple images. It has attracted significant attention over the years, counting practical reconstruction pipelines as well as theoretical results. This paper is conceived as a conceptual review of SfM methods, which are grouped into three main categories, according to which part of the problem - between motion and structure - they focus on. The proposed taxonomy brings a new perspective on existing SfM approaches as well as insights into open problems and possible future research directions. Particular emphasis is given on identifying the theoretical conditions that make SfM well posed, which depend on the problem formulation that is being considered.

Figures

Figures reproduced from arXiv: 2505.15814 by the authors.

Figure 1
Figure 1. The goal of Structure from Motion (SfM) is to recover both camera [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The first category in the proposed SfM taxonomy recovers structure [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. There exist several ways to organize images in convenient abstract structures. In a sequence, images are consecutively captured, as happens (e.g.) in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: Projective factorization belongs to the first category in the proposed [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: The second category in the proposed SfM taxonomy first recovers [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: The second category in the proposed SfM taxonomy focuses on [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: The second category in the proposed SfM taxonomy focuses on the [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Examples of viewing graphs with six nodes. The graph on the left is [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: The third category in the proposed SfM taxonomy directly estimates [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. MAGiSt3R: Multi-Agent Feed-forward 3D Reconstruction from Monocular RGB Videos

    cs.CV 2026-07 conditional novelty 6.0 of 10

    MAGiSt3R is a multi-agent feed-forward 3D reconstruction system using a learned submap-merging model (MAGMA) and pose graph optimization to align local maps from multiple monocular RGB cameras into one consistent map ...

Reference graph

Works this paper leans on

132 extracted references · 79 canonical work pages · cited by 1 Pith paper

  1. [86]

    When is rotations averaging hard?

    K. Wilson, D. Bindel, and N. Snavely, “When is rotations averaging hard?” inProceedings of the European Conference on Computer Vision, 2016, pp. 255 – 270

    work page 2016

  2. [124]

    A theory of network localization,

    J. Aspnes, T. Eren, D. Goldenberg, A. Morse, W. Whiteley, Y . Yang, B. Anderson, and P. Belhumeur, “A theory of network localization,” IEEE Transactions on Mobile Computing, vol. 5, no. 12, pp. 1663 – 1678, 2006

    work page 2006

  3. [1]

    A survey of structure from motion,

    O. Ozyesil, V . V oroninski, R. Basri, and A. Singer, “A survey of structure from motion,”Acta Numerica, vol. 26, pp. 305 – 364, 2017

    2017

  4. [2]

    Hartley and A

    R. Hartley and A. Zisserman,Multiple View Geometry in Computer Vision, 2nd ed. Cambridge University Press, 2004

    2004

  5. [3]

    Discrete- continuous optimization for large-scale structure from motion,

    D. Crandall, A. Owens, N. Snavely, and D. P. Huttenlocher, “Discrete- continuous optimization for large-scale structure from motion,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2011, pp. 3001–3008

    2011

  6. [4]

    Efficient and robust large-scale rotation averaging,

    A. Chatterjee and V . M. Govindu, “Efficient and robust large-scale rotation averaging,” inProceedings of the International Conference on Computer Vision, 2013

    2013

  7. [5]

    Robust global translations with 1DSfM,

    K. Wilson and N. Snavely, “Robust global translations with 1DSfM,” inProceedings of the European Conference on Computer Vision, 2014, pp. 61–75

    2014

  8. [6]

    A new rank constraint on multi-view fundamental ma- trices, and its application to camera location recovery,

    S. Sengupta, T. Amir, M. Galun, T. Goldstein, D. W. Jacobs, A. Singer, and R. Basri, “A new rank constraint on multi-view fundamental ma- trices, and its application to camera location recovery,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017, pp. 2413–2421

    2017

Show all 132 references
  1. [7]

    Revisiting projective structure from motion: A robust and efficient incremental solution,

    L. Magerand and A. Del Bue, “Revisiting projective structure from motion: A robust and efficient incremental solution,”IEEE Transac- tions on Pattern Analysis and Machine Intelligence, vol. 42, no. 2, pp. 430–443, 2020

    2020

  2. [8]

    Pixel- perfect structure-from-motion with featuremetric refinement,

    P.-E. Sarlin, P. Lindenberger, V . Larsson, and M. Pollefeys, “Pixel- perfect structure-from-motion with featuremetric refinement,”IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023

    2023

  3. [9]

    Rotation averaging,

    R. I. Hartley, J. Trumpf, Y . Dai, and H. Li, “Rotation averaging,” International Journal of Computer Vision, 2013

    2013

  4. [10]

    A generalized projective reconstruction theorem and depth constraints for projective factoriza- tion,

    B. Nasihatkon, R. Hartley, and J. Trumpf, “A generalized projective reconstruction theorem and depth constraints for projective factoriza- tion,”International Journal of Computer Vision, vol. 115, pp. 87 – 115, 2015

    2015

  5. [11]

    On the distribution of minima in intrinsic- metric rotation averaging,

    K. Wilson and D. Bindel, “On the distribution of minima in intrinsic- metric rotation averaging,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2020, pp. 6030–6038

    2020

  6. [12]

    Compatibility of fundamental matrices for complete viewing graphs,

    M. Bratelund and F. Rydell, “Compatibility of fundamental matrices for complete viewing graphs,” inProceedings of the International Conference on Computer Vision, 2023, pp. 3305 – 3313

    2023

  7. [13]

    Sensitivity in translation averaging,

    L. Manam and V . M. Govindu, “Sensitivity in translation averaging,” inNeural Information Processing Systems (NeurIPS), 2023

    2023

  8. [14]

    GPSfM: Global projective SFM using algebraic constraints on multi-view fundamental matrices,

    Y . Kasten, A. Geifman, M. Galun, and R. Basri, “GPSfM: Global projective SFM using algebraic constraints on multi-view fundamental matrices,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019, pp. 3259–3267

    2019

  9. [15]

    Inside plato’s door: a tour in multi-view geometry,

    L. Magri and F. Arrigoni, “Inside plato’s door: a tour in multi-view geometry,” Tutorial – in conjunction with the Conference on Computer Vision and Pattern Recognition (CVPR), 2022, https://sites.google.com/ view/platomultiview/

    2022

  10. [16]

    Inside plato’s door: a tour in multi-view geometry,

    ——, “Inside plato’s door: a tour in multi-view geometry,” Tuto- rial – in conjunction with the European Conference on Computer Vision (ECCV), 2024, https://sites.google.com/view/platomultiview24/ home-page

    2024

  11. [17]

    Detector-free structure from motion,

    X. He, J. Sun, Y . Wang, S. Peng, Q. Huang, H. Bao, and X. Zhou, “Detector-free structure from motion,” in2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024, pp. 21 594–21 603

    2024

  12. [18]

    Visual SLAM and structure from motion in dynamic environments: A survey,

    M. R. U. Saputra, A. Markham, and N. Trigoni, “Visual SLAM and structure from motion in dynamic environments: A survey,”ACM Computing Surveys, vol. 51, no. 2, pp. 37:1–37:36, 2018

    2018

  13. [19]

    Single-view 3d reconstruction: A survey of deep learning methods,

    G. Fahim, K. Amin, and S. Zarif, “Single-view 3d reconstruction: A survey of deep learning methods,”Computers&Graphics, vol. 94, pp. 164–190, 2021

    2021

  14. [20]

    Critical configurations for two projective views, a new approach,

    M. Bratelund, “Critical configurations for two projective views, a new approach,”Journal of Symbolic Computation, vol. 120, 2024

    2024

  15. [21]

    Critical curves and surfaces for euclidean re- construction,

    F. Kahl and R. Hartley, “Critical curves and surfaces for euclidean re- construction,” inProceedings of the European Conference on Computer Vision. Springer Berlin Heidelberg, 2002, pp. 447–462

    2002

  16. [22]

    Snapshot of algebraic vision,

    J. Kileel and K. Kohn, “Snapshot of algebraic vision,”arXiv, no. 2210.11443, 2023

    2023 arXiv

  17. [23]

    Bundle adjustment - a modern synthesis,

    B. Triggs, P. F. McLauchlan, R. I. Hartley, and A. W. Fitzgibbon, “Bundle adjustment - a modern synthesis,” inProceedings of the International Workshop on Vision Algorithms. Springer-Verlag, 2000, pp. 298–372

    2000

  18. [24]

    Robust regression using iteratively reweighted least-squares,

    P. W. Holland and R. E. Welsch, “Robust regression using iteratively reweighted least-squares,”Communications in Statistics - Theory and Methods, vol. 6, no. 9, pp. 813–827, 1977

    1977

  19. [25]

    Distributed very large scale bundle adjustment by global camera consensus,

    R. Zhang, S. Zhu, T. Fang, and L. Quan, “Distributed very large scale bundle adjustment by global camera consensus,” in2017 IEEE International Conference on Computer Vision (ICCV), 2017, pp. 29–38

    2017

  20. [26]

    Stochastic bundle adjustment for efficient and scalable 3d reconstruction,

    L. Zhou, Z. Luo, M. Zhen, T. Shen, S. Li, Z. Huang, T. Fang, and L. Quan, “Stochastic bundle adjustment for efficient and scalable 3d reconstruction,” inComputer Vision – ECCV 2020, A. Vedaldi, H. Bischof, T. Brox, and J.-M. Frahm, Eds. Cham: Springer International Publishing,...

    2020

  21. [27]

    Megba: A gpu-based distributed library for large-scale bundle adjustment,

    J. Ren, W. Liang, R. Yan, L. Mai, S. Liu, and X. Liu, “Megba: A gpu-based distributed library for large-scale bundle adjustment,” in Computer Vision – ECCV 2022, S. Avidan, G. Brostow, M. Ciss´e, G. M. Farinella, and T. Hassner, Eds. Cham: Springer Nature Switzerland, 2022, pp...

    2022

  22. [28]

    Distributed bundle adjustment with block-based sparse matrix compression for super large scale datasets,

    M. Zheng, N. Chen, J. Zhu, X. Zeng, H. Qiu, Y . Jiang, X. Lu, and H. Qu, “Distributed bundle adjustment with block-based sparse matrix compression for super large scale datasets,” in2023 IEEE/CVF International Conference on Computer Vision (ICCV), 2023

    2023

  23. [29]

    Bundle adjustment on a graph processor,

    J. Ortiz, M. Pupilli, S. Leutenegger, and A. J. Davison, “Bundle adjustment on a graph processor,”2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2413–2422, 2020

    2020

  24. [30]

    Square root bundle adjustment for large-scale reconstruction,

    N. Demmel, C. Sommer, D. Cremers, and V . C. Usenko, “Square root bundle adjustment for large-scale reconstruction,”2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 11 718–11 727, 2021

    2021

  25. [31]

    Power bundle adjustment for large-scale 3d reconstruction,

    S. Weber, N. Demmel, T. C. Chan, and D. Cremers, “Power bundle adjustment for large-scale 3d reconstruction,” in2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023, pp. 281–289

    2023

  26. [32]

    Projective bundle adjustment from arbitrary initialization using the variable projection method,

    J. H. Hong, C. Zach, A. Fitzgibbon, and R. Cipolla, “Projective bundle adjustment from arbitrary initialization using the variable projection method,” inComputer Vision – ECCV 2016. Springer International Publishing, 2016, pp. 477–493

    2016

  27. [33]

    pose: Pseudo object space error for initialization-free bundle adjustment,

    C. Zach and J. H. Hong, “pose: Pseudo object space error for initialization-free bundle adjustment,” in2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018, pp. 1876–1885

    2018

  28. [34]

    expose: Accurate initialization-free projective factorization using exponential regulariza- tion,

    J. P. Iglesias, A. Nilsson, and C. Olsson, “expose: Accurate initialization-free projective factorization using exponential regulariza- tion,” in2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023, pp. 8959–8968

    2023

  29. [35]

    Power variable projection for initialization-free large-scale bundle adjustment,

    S. Weber, J. H. Hong, and D. Cremers, “Power variable projection for initialization-free large-scale bundle adjustment,” inComputer Vision – ECCV 2024. Cham: Springer Nature Switzerland, 2025, pp. 111–126

    2024

  30. [36]

    Photo tourism: exploring photo collections in 3D,

    N. Snavely, S. M. Seitz, and R. Szeliski, “Photo tourism: exploring photo collections in 3D,” inSIGGRAPH: International Conference on Computer Graphics and Interactive Techniques, 2006, pp. 835–846

    2006

  31. [37]

    Build- ing rome in a day,

    S. Agarwal, N. Snavely, I. Simon, S. M. Seitz, and R. Szeliski, “Build- ing rome in a day,” inIEEE International Conference on Computer Vision, 2009

    2009

  32. [38]

    Building Rome on a cloudless day,

    J.-M. Frahm, P. Fite-Georgel, D. Gallup, T. Johnson, R. Raguram, C. Wu, Y .-H. Jen, E. Dunn, B. Clipp, S. Lazebnik, and M. Pollefeys, 15 “Building Rome on a cloudless day,” inProceedings of the 11th European conference on Computer vision: Part IV, 2010, pp. 368–381

    2010

  33. [39]

    Towards linear-time incremental structure from motion,

    C. Wu, “Towards linear-time incremental structure from motion,” in Proceedings of the International Conference on 3D Vision (3DV). IEEE, 2013

    2013

  34. [40]

    Structure-from-motion revisited,

    J. L. Schonberger and J.-M. Frahm, “Structure-from-motion revisited,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016, pp. 4104 – 4113

    2016

  35. [41]

    Hierarchical structure-and-motion recovery from uncalibrated images,

    R. Toldo, R. Gherardi, M. Farenzena, and A. Fusiello, “Hierarchical structure-and-motion recovery from uncalibrated images,”Computer Vision and Image Understanding, 2015

    2015

  36. [42]

    Hypersfm,

    K. Ni and F. Dellaert, “Hypersfm,” inProceedings of the Joint 3DIM/3DPVT Conference: 3D Imaging, Modeling, Processing, Visu- alization and Transmission, 2012, pp. 144–151

    2012

  37. [43]

    A method for registration of 3-D shapes,

    P. Besl and N. McKay, “A method for registration of 3-D shapes,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239–256, February 1992

    1992

  38. [44]

    A factorization based algorithm for multi- image projective structure and motion,

    P. Sturm and B. Triggs, “A factorization based algorithm for multi- image projective structure and motion,” inProceedings of the European Conference on Computer Vision, 1996, pp. 709–720

    1996

  39. [45]

    Iterative extensions of the sturm/triggs algorithm: Convergence and nonconvergence,

    J. Oliensis and R. I. Hartley, “Iterative extensions of the sturm/triggs algorithm: Convergence and nonconvergence,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 12, pp. 2217– 2233, 2007

    2007

  40. [46]

    3d reconstruction by fitting low-rank ma- trices with missing data,

    D. Martinec and T. Pajdla, “3d reconstruction by fitting low-rank ma- trices with missing data,” in2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005

    2005

  41. [47]

    Low-rank matrix fitting based on subspace perturbation analysis with applications to structure from motion,

    H. Jia and A. M. Martinez, “Low-rank matrix fitting based on subspace perturbation analysis with applications to structure from motion,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 5, pp. 841–854, 2009

    2009

  42. [48]

    Projective multiview structure and motion from element-wise factorization,

    Y . Dai, H. Li, and M. He, “Projective multiview structure and motion from element-wise factorization,”IEEE Transactions on Pattern Anal- ysis and Machine Intelligence, vol. 35, no. 9, pp. 2238–2251, 2013

    2013

  43. [49]

    Low-rank matrix completion: A contemporary survey,

    L. T. Nguyen, J. Kim, and B. Shim, “Low-rank matrix completion: A contemporary survey,”IEEE Access, vol. 7, pp. 94 215–94 237, 2019

    2019

  44. [50]

    Deep permutation equivariant structure from motion,

    D. Moran, H. Koslowsky, Y . Kasten, H. Maron, M. Galun, and R. Basri, “Deep permutation equivariant structure from motion,” inProceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021, pp. 5976–5986

    2021

  45. [51]

    Resfm: Robust deep equivariant structure from motion,

    F. Khatib1, Y . Kasten, D. Moran, M. Galun, and R. Basri, “Resfm: Robust deep equivariant structure from motion,” inInternational Con- ference on Learning Representations (ICLR), 2025

    2025

  46. [52]

    Learning structure- from-motion with graph attention networks,

    L. Brynte, J. P. Iglesias, C. Olsson, and F. Kahl, “Learning structure- from-motion with graph attention networks,” in2024 IEEE/CVF Con- ference on Computer Vision and Pattern Recognition (CVPR), 2024, pp. 4808–4817

    2024

  47. [53]

    Space resection: Failure cases,

    E. Thompson, “Space resection: Failure cases,”Photogrammetric Record, vol. X, no. 27, pp. 201–204, 1966

    1966

  48. [54]

    The viewing graph,

    N. Levi and M. Werman, “The viewing graph,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2003, pp. 518 – 522

    2003

  49. [55]

    Graph-based consistent matching for structure-from-motion,

    T. Shen, S. Zhu, T. Fang, R. Zhang, and L. Quan, “Graph-based consistent matching for structure-from-motion,” inProceedings of the European Conference on Computer Vision, 2016, pp. 139 – 155

    2016

  50. [56]

    View-graph selection frame- work for sfm,

    R. Shah, V . Chari, and P. J. Narayanan, “View-graph selection frame- work for sfm,” inComputer Vision – ECCV 2018. Springer Interna- tional Publishing, 2018, pp. 553–568

    2018

  51. [57]

    Graphmatch: Efficient large-scale graph construction for structure from motion

    Q. Cui, V . Fragoso, C. Sweeney, and P. Sen, “Graphmatch: Efficient large-scale graph construction for structure from motion.” inInterna- tional Conference on 3D Vision (3DV). IEEE Computer Society, 2017, pp. 165–174

    2017

  52. [58]

    Efficient detection of long consistent cycles and its application to distributed synchronization,

    S. Li, Y . Shi, and G. Lerman, “Efficient detection of long consistent cycles and its application to distributed synchronization,” in2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024, pp. 5260–5269

    2024

  53. [59]

    Robustness in motion averaging,

    V . M. Govindu, “Robustness in motion averaging,” inProceedings of the Asian Conference on Computer Vision, 2006, pp. 457–466

    2006

  54. [60]

    Disambiguating visual re- lations using loop constraints,

    C. Zach, M. Klopschitz, and M. Pollefeys, “Disambiguating visual re- lations using loop constraints,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2010, pp. 1426 – 1433

    2010

  55. [61]

    Global motion estimation from relative measurements in the presence of outliers,

    G. Bourmaud, R. Megret, A. Giremus, and Y . Berthoumieu, “Global motion estimation from relative measurements in the presence of outliers,” inProceedings of the Asian Conference on Computer Vision, 2014

    2014

  56. [62]

    Leveraging camera triplets for efficient and accurate structure-from-motion,

    L. Manam and V . M. Govindu, “Leveraging camera triplets for efficient and accurate structure-from-motion,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2024

    2024

  57. [63]

    Angular synchronization by eigenvectors and semidefi- nite programming,

    A. Singer, “Angular synchronization by eigenvectors and semidefi- nite programming,”Applied and Computational Harmonic Analysis, vol. 30, no. 1, pp. 20 – 36, 2011

    2011

  58. [64]

    Global motion estimation from point matches,

    M. Arie-Nachimson, S. Z. Kovalsky, I. Kemelmacher-Shlizerman, A. Singer, and R. Basri, “Global motion estimation from point matches,”Proceedings of the Joint 3DIM/3DPVT Conference: 3D Imaging, Modeling, Processing, Visualization and Transmission, 2012

    2012

  59. [65]

    Robust rotation and translation estimation in multiview reconstruction,

    D. Martinec and T. Pajdla, “Robust rotation and translation estimation in multiview reconstruction,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2007

    2007

  60. [66]

    Spectral synchronization of multiple views in SE(3),

    F. Arrigoni, B. Rossi, and A. Fusiello, “Spectral synchronization of multiple views in SE(3),”SIAM Journal on Imaging Sciences, vol. 9, no. 4, pp. 1963 – 1990, 2016

    1963

  61. [67]

    Robust syn- chronization in SO(3) and SE(3) via low-rank and sparse matrix decomposition,

    F. Arrigoni, B. Rossi, P. Fragneto, and A. Fusiello, “Robust syn- chronization in SO(3) and SE(3) via low-rank and sparse matrix decomposition,”Computer Vision and Image Understanding, vol. 174, pp. 95–113, 2018

    2018

  62. [68]

    Rotation synchronization via deep matrix factorization,

    G. Tejus, G. Zara, P. Rota, A. Fusiello, E. Ricci, and F. Arrigoni, “Rotation synchronization via deep matrix factorization,” in2023 IEEE International Conference on Robotics and Automation (ICRA), 2023

    2023

  63. [69]

    Combining two-view constraints for motion estima- tion,

    V . M. Govindu, “Combining two-view constraints for motion estima- tion,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2001

    2001

  64. [70]

    Message passing least squares framework and its application to rotation synchronization,

    Y . Shi and G. Lerman, “Message passing least squares framework and its application to rotation synchronization,” inProceedings of the 37th International Conference on Machine Learning, ser. Proceedings of Machine Learning Research, vol. 119. PMLR, 2020, pp. 8796–8806

    2020

  65. [71]

    Rotation averaging and strong duality,

    A. Eriksson, C. Olsson, F. Kahl, and T.-J. Chin, “Rotation averaging and strong duality,” inProceedings of the IEEE Conference on Com- puter Vision and Pattern Recognition, 2018, pp. 127–135

    2018

  66. [72]

    Shonan rotation averaging: Global optimality by surfingso(p) n,

    F. Dellaert, D. M. Rosen, J. Wu, R. Mahony, and L. Carlone, “Shonan rotation averaging: Global optimality by surfingso(p) n,” inComputer Vision – ECCV 2020. Springer International Publishing, 2020, pp. 292–308

    2020

  67. [73]

    Rotation coordinate descent for fast globally optimal rotation averaging,

    A. Parra, S.-F. Chng, T.-J. Chin, A. Eriksson, and I. Reid, “Rotation coordinate descent for fast globally optimal rotation averaging,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021, pp. 4298–4307

    2021

  68. [74]

    Rotation averaging in a split second: A primal-dual method and a closed-form for cycle graphs,

    G. Moreira, M. Marques, and J. a. P. Costeira, “Rotation averaging in a split second: A primal-dual method and a closed-form for cycle graphs,” inProceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021, pp. 5452–5460

    2021

  69. [75]

    Synchronizing probability measures on rotations via optimal transport,

    T. Birdal, M. Arbel, U. Simsekli, and L. J. Guibas, “Synchronizing probability measures on rotations via optimal transport,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2020, pp. 1566–1576

    2020

  70. [76]

    Revisiting rotation averaging: Uncertainties and robust losses,

    G. Zhang, V . Larsson, and D. Barath, “Revisiting rotation averaging: Uncertainties and robust losses,” inProceedings of the IEEE Confer- ence on Computer Vision and Pattern Recognition, 2023

    2023

  71. [77]

    Gravity-aligned rotation aver- aging with circular regression,

    L. Pan, M. Pollefeys, and D. Bar ´ath, “Gravity-aligned rotation aver- aging with circular regression,” inComputer Vision – ECCV 2024. Cham: Springer Nature Switzerland, 2025, pp. 97–116

    2024

  72. [78]

    Hara: A hierarchical approach for robust rotation averaging,

    S. H. Lee and J. Civera, “Hara: A hierarchical approach for robust rotation averaging,” in2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022

    2022

  73. [79]

    Neurora: Neural robust rotation averaging,

    P. Purkait, T.-J. Chin, and I. Reid, “Neurora: Neural robust rotation averaging,” inComputer Vision – ECCV 2020. Springer International Publishing, 2020, pp. 137–154

    2020

  74. [80]

    End-to-end rotation averaging with multi-source propagation,

    L. Yang, H. Li, J. A. Rahim, Z. Cui, and P. Tan, “End-to-end rotation averaging with multi-source propagation,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2021, pp. 11 774–11 783

    2021

  75. [81]

    Pogo-net: Pose graph optimization with graph neural networks,

    X. Li and H. Ling, “Pogo-net: Pose graph optimization with graph neural networks,” inProceedings of the IEEE/CVF International Con- ference on Computer Vision (ICCV), October 2021, pp. 5895–5905

    2021

  76. [82]

    Rago: Recurrent graph optimizer for multiple rotation averaging,

    H. Li, Z. Cui, S. Liu, and P. Tan, “Rago: Recurrent graph optimizer for multiple rotation averaging,” in2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022

    2022

  77. [83]

    L1 rotation averaging using the Weiszfeld algorithm,

    R. Hartley, K. Aftab, and J. Trumpf, “L1 rotation averaging using the Weiszfeld algorithm,”Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3041–3048, 2011

    2011

  78. [84]

    A survey on rotation optimization in structure from motion,

    R. Tron, X. Zhou, and K. Daniilidis, “A survey on rotation optimization in structure from motion,” inComputer Vision and Pattern Recognition Workshops (CVPRW), 2016. 16

    2016

  79. [85]

    Cramer-Rao bounds for synchronization of rotations,

    N. Boumal, A. Singer, P. A. Absil, and V . D. Blondel, “Cramer-Rao bounds for synchronization of rotations,”Information and Inference: A Journal of the IMA, vol. 3, no. 1, pp. 1 – 39, 2014

    2014

  80. [87]

    Divide and conquer: Efficient large-scale structure from motion using graph partitioning,

    B. Bhowmick, S. Patra, A. Chatterjee, V . M. Govindu, and S. Banerjee, “Divide and conquer: Efficient large-scale structure from motion using graph partitioning,” in12th Asian Conference on Computer Vision (ACCV 2014), 2014

    2014

  81. [88]

    Synchronization of group-labelled multi-graphs,

    A. Porfiri Dal Cin, L. Magri, F. Arrigoni, A. Fusiello, and G. Boracchi, “Synchronization of group-labelled multi-graphs,” inProceedings of the International Conference on Computer Vision, 2021

    2021

  82. [89]

    Very large-scale global sfm by distributed motion averaging,

    S. Zhu, R. Zhang, L. Zhou, T. Shen, T. Fang, P. Tan, and L. Quan, “Very large-scale global sfm by distributed motion averaging,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018, pp. 4568–4577

    2018

  83. [90]

    Spectral solution of large- scale extrinsic camera calibration as a graph embedding problem,

    M. Brand, M. Antone, and S. Teller, “Spectral solution of large- scale extrinsic camera calibration as a graph embedding problem,” in Proceedings of the European Conference on Computer Vision, 2004

    2004

  84. [91]

    Stable camera motion estimation using convex programming,

    O. Ozyesil, A. Singer, and R. Basri, “Stable camera motion estimation using convex programming,”SIAM Journal on Imaging Sciences, vol. 8, no. 2, pp. 1220 – 1262, 2015

    2015

  85. [92]

    Robust camera location estimation by convex programming,

    O. Ozyesil and A. Singer, “Robust camera location estimation by convex programming,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2015, pp. 2674 – 2683

    2015

  86. [93]

    A robust translation synchronization algorithm,

    Z. He, H. Ruan, and Q. Huang, “A robust translation synchronization algorithm,” inProceedings of the International Conference on 3D Vision (3DV), 2025

    2025

  87. [94]

    Baseline desensitizing in translation averaging,

    B. Zhuang, L.-F. Cheong, and G. H. Lee, “Baseline desensitizing in translation averaging,” in2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018, pp. 4539–4547

    2018

  88. [95]

    A global linear method for camera pose registration,

    N. Jiang, Z. Cui, and P. Tan, “A global linear method for camera pose registration,” inProceedings of the International Conference on Computer Vision, 2013

    2013

  89. [96]

    Global fusion of relative motions for robust, accurate and scalable structure from motion,

    P. Moulon, P. Monasse, and R. Marlet, “Global fusion of relative motions for robust, accurate and scalable structure from motion,” in Proceedings of the International Conference on Computer Vision, 2013, pp. 3248–3255

    2013

  90. [97]

    Distributed 3-D localization of camera sensor networks from 2-D image measurements,

    R. Tron and R. Vidal, “Distributed 3-D localization of camera sensor networks from 2-D image measurements,”IEEE Transactions on Automatic Control, vol. 59, no. 12, pp. 3325–3340, 2014

    2014

  91. [98]

    ShapeFit and ShapeKick for robust, scalable structure from motion,

    T. Goldstein, P. Hand, C. Lee, V . V oroninski, and S. Soatto, “ShapeFit and ShapeKick for robust, scalable structure from motion,” inProceed- ings of the European Conference on Computer Vision, 2016, pp. 289 – 304

    2016

  92. [99]

    Adaptive annealing for robust aver- aging,

    S. Chitturi and V . M. Govindu, “Adaptive annealing for robust aver- aging,” inComputer Vision – ECCV 2024. Cham: Springer Nature Switzerland, 2025, pp. 53–69

    2024

  93. [100]

    Correspondence reweighted translation averaging,

    L. Manam and V . M. Govindu, “Correspondence reweighted translation averaging,” inComputer Vision – ECCV 2022. Cham: Springer Nature Switzerland, 2022, pp. 56–72

    2022

  94. [101]

    Estimation of camera locations in highly corrupted scenarios: All about that base, no shape trouble,

    Y . Shi and G. Lerman, “Estimation of camera locations in highly corrupted scenarios: All about that base, no shape trouble,” in2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018, pp. 2868–2876

    2018

  95. [102]

    On computing the translations norm in the epipolar graph,

    F. Arrigoni, A. Fusiello, and B. Rossi, “On computing the translations norm in the epipolar graph,” inProceedings of the International Conference on 3D Vision (3DV), 2015, pp. 300–308

    2015

  96. [103]

    Algebraic char- acterization of essential matrices and their averaging in multiview settings,

    Y . Kasten, A. Geifman, M. Galun, and R. Basri, “Algebraic char- acterization of essential matrices and their averaging in multiview settings,” in2019 IEEE/CVF International Conference on Computer Vision (ICCV), 2019, pp. 5894–5902

    2019

  97. [104]

    Revisiting global translation estimation with feature tracks,

    P. Tao, H. Cui, M. Rong, and S. Shen, “Revisiting global translation estimation with feature tracks,” in2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024, pp. 20 686– 20 696

    2024

  98. [105]

    Global structure-from-motion revisited,

    L. Pan, D. Barath, M. Pollefeys, and J. L. Schonberger, “Global structure-from-motion revisited,” inProceedings of the European Con- ference on Computer Vision, 2024

    2024

  99. [106]

    Vggsfm: Visual geometry grounded deep structure from motion,

    J. Wang, N. Karaev, C. Rupprecht, and D. Novotny, “Vggsfm: Visual geometry grounded deep structure from motion,” in2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024, pp. 21 686–21 697

    2024

  100. [107]

    Synchronization of pro- jective transformations,

    R. Madhavan, A. Fusiello, and F. Arrigoni, “Synchronization of pro- jective transformations,” inProceedings of the European Conference on Computer Vision, 2024

    2024

  101. [108]

    Camera network calibration from dynamic silhouettes,

    S. Sinha, M. Pollefeys, and L. McMillan, “Camera network calibration from dynamic silhouettes,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2004, pp. I–I

    2004

  102. [109]

    A closed form solution for viewing graph construction in uncalibrated vision,

    C. Colombo and M. Fanfani, “A closed form solution for viewing graph construction in uncalibrated vision,” in2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW), 2021

    2021

  103. [110]

    Harary,Graph Theory

    F. Harary,Graph Theory. Addison-Wesley, 1972

    1972

  104. [111]

    Localizability and distributed protocols for bearing-based network localization in arbitrary dimensions,

    S. Zhao and D. Zelazo, “Localizability and distributed protocols for bearing-based network localization in arbitrary dimensions,”Automat- ica, vol. 69, pp. 334 – 341, 2016

    2016

  105. [112]

    Bearing-based network localizability: A unifying view,

    F. Arrigoni and A. Fusiello, “Bearing-based network localizability: A unifying view,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 41, no. 9, pp. 2049 – 2069, 2019

    2019

  106. [113]

    Rigid components identification and rigidity enforcement in bearing-only localization using the graph cycle basis,

    R. Tron, L. Carlone, F. Dellaert, and K. Daniilidis, “Rigid components identification and rigidity enforcement in bearing-only localization using the graph cycle basis,” inIEEE American Control Conference, 2015, pp. 3911–3918

    2015

  107. [114]

    Identifying maximal rigid components in bearing-based localization,

    R. Kennedy, K. Daniilidis, O. Naroditsky, and C. J. Taylor, “Identifying maximal rigid components in bearing-based localization,” inProceed- ings of the International Conference on Intelligent Robots and Systems, 2012, pp. 194 – 201

    2012

  108. [115]

    The joint image handbook,

    M. Trager, M. Hebert, and J. Ponce, “The joint image handbook,” in Proceedings of the International Conference on Computer Vision, 2015, pp. 909–917

    2015

  109. [116]

    A direct approach to viewing graph solvability,

    F. Arrigoni, A. Fusiello, and T. Pajdla, “A direct approach to viewing graph solvability,” inProceedings of the European Conference on Computer Vision, 2024

    2024

  110. [117]

    On the solvability of viewing graphs,

    M. Trager, B. Osserman, and J. Ponce, “On the solvability of viewing graphs,” inProceedings of the European Conference on Computer Vision, 2018, pp. 335–350

    2018

  111. [118]

    Viewing graph solvability via cycle consistency,

    F. Arrigoni, A. Fusiello, E. Ricci, and T. Pajdla, “Viewing graph solvability via cycle consistency,” inProceedings of the International Conference on Computer Vision, 2021, pp. 5540 – 5549

    2021

  112. [119]

    The structure of polynomial ideals and Gr ¨obner bases,

    T. W. Dub ´e, “The structure of polynomial ideals and Gr ¨obner bases,” SIAM Journal on Computing, vol. 19, no. 4, pp. 750 – 773, 1990

    1990

  113. [120]

    Viewing graph solvability in practice,

    F. Arrigoni, T. Pajdla, and A. Fusiello, “Viewing graph solvability in practice,” inProceedings of the International Conference on Computer Vision, 2023, pp. 8147–8155

    2023

  114. [121]

    Linear solvability in the viewing graph,

    A. Rudi, M. Pizzoli, and F. Pirri, “Linear solvability in the viewing graph,” inProceedings of the Asian Conference on Computer Vision, 2011, pp. 369–381

    2011

  115. [122]

    Revisit- ing viewing graph solvability: an effective approach based on cycle consistency,

    F. Arrigoni, A. Fusiello, R. Rizzi, E. Ricci, and T. Pajdla, “Revisit- ing viewing graph solvability: an effective approach based on cycle consistency,”IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 1–14, 2022

    2022

  116. [123]

    Multi-view structure computation without explicitly estimating motion,

    H. Li, “Multi-view structure computation without explicitly estimating motion,” in2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2010, pp. 2777–2784

    2010

  117. [125]

    Direct structure estimation for 3d reconstruction,

    N. Jiang, W.-Y . Lin, M. N. Do, and J. Lu, “Direct structure estimation for 3d reconstruction,” in2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 2655–2663

    2015

  118. [126]

    Angle independent bundle adjustment refinement,

    J. Zhang, D. G. Aliaga, M. Boutin, and R. Insley, “Angle independent bundle adjustment refinement,” inThird International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT’06), 2006, pp. 1108–1116

    2006

  119. [127]

    Simplifying the reconstruc- tion of 3d models using parameter elimination,

    D. G. Aliaga, J. Zhang, and M. Boutin, “Simplifying the reconstruc- tion of 3d models using parameter elimination,” in2007 IEEE 11th International Conference on Computer Vision, 2007

    2007

  120. [128]

    Mast3r-sfm: a fully-integrated solution for unconstrained structure-from-motion,

    B. P. Duisterhof, L. Zust, P. Weinzaepfel, V . Leroy, Y . Cabon, and J. Revaud, “Mast3r-sfm: a fully-integrated solution for unconstrained structure-from-motion,” inInternational Conference on 3D Vision (3DV), 2025

    2025

  121. [129]

    Probabilistic structure from motion with objects (psfmo),

    P. Gay, C. Rubino, V . Bansal, and A. Del Bue, “Probabilistic structure from motion with objects (psfmo),” inProceedings of the IEEE International Conference on Computer Vision (ICCV), Oct 2017

    2017

  122. [130]

    Robust incremental structure-from-motion with hybrid features,

    S. Liu, Y . Gao, T. Zhang, R. Pautrat, J. L. Sch ¨onberger, V . Larsson, and M. Pollefeys, “Robust incremental structure-from-motion with hybrid features,” inComputer Vision – ECCV 2024. Cham: Springer Nature Switzerland, 2025, pp. 249–269

    2024

  123. [131]

    Privacy preserving structure-from-motion,

    M. Geppert, V . Larsson, P. Speciale, J. L. Sch ¨onberger, and M. Polle- feys, “Privacy preserving structure-from-motion,” inComputer Vision – ECCV 2020. Cham: Springer International Publishing, 2020, pp. 333–350. 17

    2020

  124. [132]

    Multibody structure- from-motion in practice,

    K. E. Ozden, K. Schindler, and L. Van Gool, “Multibody structure- from-motion in practice,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 6, pp. 1134–1141, 2010

    2010

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.