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Computational Pathology Reading Roadmap

Writing study: Certifiably Optimal Anisotropic Rotation Averaging

← ICCV 2025 oral writing corpus

Carl Olsson, Yaroslava Lochman, Johan Malmport, Christopher Zach · Official ICCV 2025 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
≈ 8.05 page-equivalents
Main figures / tables
3 / 1
Attached appendix figures / tables
0 / 0
Attached appendix span
No boundary detected; not assumed zero
Before references / appendix: ≈ 80.5%References / intervening material: ≈ 19.5%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

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 headingStarts on PDF pageEstimated spanShare of entire PDF
1. Introduction1≈ 0.95 pp.9.5%
2. Related Work2≈ 0.48 pp.4.8%
3. Certifiably Optimal Rotation Averaging2≈ 0.58 pp.5.8%
4. Anisotropic Rotation Averaging3≈ 3.27 pp.32.7%
5. Experiments6≈ 1.24 pp.12.4%
6. Conclusions7≈ 1.21 pp.12.1%
References9≈ 1.95 pp.19.5%
All detected figure and table locations

Main text

Attached appendix

    No recognized caption labels.

    Argument and organization

    1. 1 Introduction; 2 Related Work; 3 Certifiably Optimal Rotation Averaging

      Introduces uncertainty-aware objectives against the standard chordal relaxation and rank-based certificate.

    2. 4 Anisotropic Rotation Averaging

      Derives the uncertainty objective, explains O(3) versus SO(3) failure and constructs a stronger convex relaxation.

    3. 5 Experiments; 6 Conclusions

      Crosses objective/relaxation choices on synthetic and real data, reporting rank, accuracy and solver cost.

    Problem, claim and contribution

    The obstacle is not simply adding anisotropic weights: dropping the determinant constraint changes which solutions a relaxation favors.

    Sections 1 and 4.2, physical pp.1–2,4–5 · Main paper

    Argument and section order

    A local uncertainty derivation leads to a failure theorem and then the replacement relaxation, creating a problem–counterexample–repair argument.

    Sections 4.1–4.3, pp.3–6 · Main paper

    Figures, captions and visual explanation

    The two-view illustration links axis-specific reprojection sensitivity to solid observed curves and dashed quadratic approximations.

    Figure 1, p.3 · Main paper

    Tables, comparisons and evidence

    The real-data table reports solution rank beside reconstruction error and runtime, and retains a Kronan non-win rather than conflating a certificate with best empirical accuracy.

    Table 1, p.8 · Main paper

    Appendix and reproducibility

    Alternative parameterizations, uncertainty propagation derivation and complementary synthetic/real comparisons are explicitly routed to supplements, not inspected here.

    Section 4.1 footnotes, pp.3–4; Section 5 footnote, p.6 · Main paper

    Clarity and writing conventions

    The conclusion frames solver efficiency as future work and distinguishes the modeling contribution from a dedicated fast implementation.

    Sections 6, pp.7–8 · Main paper

    What to reuse—and what not to infer

    Transferable lesson: When presenting certified optimization, show the certificate diagnostic next to task error and cost, and explain which modeling change breaks the old relaxation.

    Boundary: Global optimality concerns the specified approximate objective, not ground-truth camera accuracy. Local Laplace/Hessian assumptions and numerically estimated rank matter; the paper explicitly leaves full tightness analysis outside scope. This scan did not verify proofs or numerical certificates.

    Apply this lesson using the argument and evidence worksheet.

    Inspection record and sources

    Checked
    2026-10-07
    Reading status
    Writing-focused manuscript scan + selected visuals inspected
    Main text
    Writing-oriented scan across the main manuscript, physical PDF pp.1–8, covering framing, section progression, method explanations, captions, comparison protocols and concluding scope; reference boundary checked. Selected full-page rasters were inspected. Not exhaustive line-by-line reading, proof verification or experimental reproduction.
    Appendix / supplement
    Main-paper appendix/supplement references were checked. A separate supplementary source is linked in the inventory but was not retrieved or inspected; its contents are not included in the reading or visual-page counts.
    Visually inspected PDF pages
    3, 8

    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.