Writing study: QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition
← CVPR 2026 oral writing corpus
Daniel Miao, Gilad Lerman, Joe Kileel · Official CVPR 2026 oral record
Figure, table and section ledger
Editorial contribution type: Theory & formal analysis (primary).
Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.
- Canonical PDF
- 10 physical pages
- Before references / appendix
- ≈ 8.16 page-equivalents
- Main figures / tables
- 3 / 0
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- Separate file recorded below; not in this PDF total
Extraction notes: No attached appendix boundary detected. Zero means no recognized caption, not independently verified absence.
Section-by-section lengths and source pages
The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.
| Top-level heading | Starts on PDF page | Estimated span | Share of entire PDF |
|---|---|---|---|
| 1. Introduction | 1 | ≈ 0.77 pp. | 7.7% |
| 2. We develop the first global synchronization algorithm for | 2 | ≈ 0.02 pp. | 0.2% |
| 3. We demonstrate the promise of our algorithms through nu- | 2 | ≈ 2.18 pp. | 21.8% |
| 4. The blocks where two of the indices are the same and the | 4 | ≈ 2.15 pp. | 21.5% |
| 5. Experiments | 6 | ≈ 2.34 pp. | 23.4% |
| 6. Conclusion | 8 | ≈ 0.41 pp. | 4.1% |
| References | 9 | ≈ 1.84 pp. | 18.4% |
All detected figure and table locations
Attached appendix
No recognized caption labels.
Separate source files—excluded from canonical-PDF totals
A separate author version may repeat main text and references. Whole-file lengths and counts are not extra appendix material and are never added to the canonical PDF totals. Read the study's source scope for which sections received substantive reading versus layout inspection.
Additional source 1
Separate PDF (or ZIP containing it): whole-file layout of 13 physical pages; 3 detected figures and 7 tables. These may include overlapping main-text material.
Located appendix only: starts on physical p.1; ≈ 12.91 page-equivalents, 3 figure labels and 7 table labels. This interval is distinct from the whole file.
Argument and organization
- Algebraic characterization
Define quadrifocal tensors and Tucker decomposition before stating block-tensor rank and scale results.
- From theorem to optimizer
Translate the characterization into IRLS–ADMM schemes and joint optimization, then test practical and collinear cases.
Problem, claim and contribution
The introduction confronts the perception that quadrifocal tensors are only theoretical, making the bridge from algebra to usable SfM algorithms the central story.
Introduction and contributions · Main paper · Additional source 2
Argument and section order
Definitions, theorems and propositions appear before optimization; the method uses explicit numbered objectives and separately described outer/inner updates.
Sections 2–4, PDF pp. 2–6 · Main paper · Additional source 2
Figures, captions and visual explanation
The two dataset-level bar plots use logarithmic location-error axes and consistent method colors, making several orders of magnitude and per-scene exceptions visible.
Figures 1–2, PDF p. 7 · Main paper · Additional source 2
Tables, comparisons and evidence
The evaluation includes near-collinear camera recovery in addition to conventional scene comparisons, testing the geometric regime that motivates higher-order information.
Section 5.4 and Figure 3, PDF pp. 7–8 · Main paper · Additional source 2
Appendix and reproducibility
Numbered theorem proofs precede executable-style algorithm blocks; later tables provide completion rates, runtimes and detailed rotation/location errors.
Supplement Sections 8–11, pp. 1–13 · Main paper · Additional source 2
Clarity and writing conventions
Named remarks state estimation noise and nonconvex initialization caveats directly beside the practical procedure, rather than saving all qualifications for the conclusion.
Remarks 4–5, PDF p. 7 · Main paper · Additional source 2
What to reuse—and what not to infer
Transferable lesson: For theory-plus-algorithm work, make definitions, guarantees, optimization and diagnostic geometric cases form one traceable chain.
Boundary: The dense grouped bars and terse captions require careful legend/axis reading; absent bars or failed completion must be checked against full tables, not interpreted as zero error.
Apply this lesson using the argument and evidence worksheet.
Inspection record and sources
- Checked
- 2026-09-26
- Reading status
- Writing-focused manuscript scan + selected visuals inspected
- Main text
- Manuscript-wide writing scan of main PDF pp. 1–8: framing, section structure, method exposition, figure/table captions, evaluation organization and conclusions; not an exhaustive technical proof audit or reproduction.
- Appendix / supplement
- Separate supplement pp. 1–13 scanned: background, theorem/proposition proofs, two full algorithms, randomized/collinear/distributed tests and complete numerical tables.
- Visually inspected PDF pages
- 4, 7
This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.