{"id":"8c852a24-f1c7-425e-82ac-313387553a6e","arxiv_id":"2412.04120","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"CrossSDF learns a 3D signed distance field from planar cross-sections using a symmetric difference loss, adaptive sampling, and hybrid encoding, improving reconstruction of thin structures.","lead":"CrossSDF turns 2D slices of an object into a 3D shape by training a neural field to match the inside/outside labels on each slice while staying smooth in between. It improves reconstruction of thin structures like blood vessels, where earlier methods produce gaps or artifacts.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table 1's connected-component counts contradict the topological-continuity claim: CrossSDF outputs 6–176 components where ground truth is 1–3, so the central claim needs qualification.","rationale":"The reader's weakest assumption focuses on Eikonal regularization in unsampled regions, which is a reasonable general concern. However, the most load-bearing and concrete problem is in the paper's own evaluation table: the connected-component metric, used to support topological fidelity, shows CrossSDF producing 6–176 components where ground truth has 1–3. This is an internal tension between the reported numbers and the central claim, not just a question of generalization or inductive bias. The concern is therefore different from the reader's stated weak assumption, though the two are related: topological fragmentation likely arises from underdetermined regions between slices, but the explicit evidence is the CC metric. A robust re-evaluation of topology, as proposed, would settle whether the claim is salvageable with thresholding or whether it should be softened. The verdict remains CONDITIONAL because the method may still be a strong improvement on other axes, but the topological claim must be either re-established with more careful analysis or explicitly qualified.","tokens_in":14410,"tokens_out":4449,"duration_ms":52534,"concrete_test":"Re-extract CrossSDF meshes from the authors' checkpoints (or retrain) at 512^3 and 1024^3 with several iso-values around 0, then count connected components after removing components smaller than 0.1% of the total volume. If Heart and Alveolis still yield more than 5 components where ground truth is 1, the topological-continuity claim fails. Additionally, compute persistent homology (Betti numbers) of the implicit SDF's sublevel sets to separate mesh-extraction artifacts from genuine topological errors.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central contribution is reconstructing thin structures 'without breakages' and while preserving 'topological continuity.' Yet the CC metric, which the paper itself introduces to confirm 'structural integrity,' shows CrossSDF's extracted meshes are far more fragmented than the ground truth: in Table 1, Heart aligned has 68 components vs. ground-truth 1, Heart non-aligned has 176 vs. 1, Alveolis non-aligned has 33 vs. 1, and Coronaries non-aligned has 35 vs. 3. These are not small deviations; they indicate spurious disconnected components or genuine breaks in the reconstructed vessel trees. The paper does not discuss this discrepancy or attribute it to marching-cubes threshold sensitivity. Since the headline claim 'faithfully reconstructs the full 3D shape' and 'preserves topological continuity' is directly supported by this metric, the reported numbers undercut the claim. The qualitative point about avoiding interpolation artifacts and over-smoothing may still hold, but the strong topological claim is not supported as stated.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces CrossSDF, a neural signed distance field (SDF) method for reconstructing 3D geometry from planar cross-sections. The input is a set of 2D contours, from which 2D SDFs are derived. The method combines per-contour adaptive sampling, a hybrid hash-grid and random Fourier feature encoding, and a symmetric difference loss that supervises the network only where the predicted and target interior/exterior classifications disagree, together with Eikonal and minimum-surface regularization. The authors evaluate on synthetic thin and thick structures and on real CT scans, comparing against OReX, Neural-IMLS, POCO, and Screened Poisson Reconstruction, reporting Chamfer distance, Hausdorff distance, connected-component count, and volume IoU. The claimed contributions are high-fidelity reconstruction of thin structures, preservation of topological continuity, and avoidance of interpolation artifacts.","tokens_in":14688,"tokens_out":5050,"duration_ms":53097,"significance":"The method is clearly specified and each component is motivated by a specific artifact (laddering, grid interpolation, under-sampled thin contours). The ablations in Table 4 and Figure 8 show that each proposed component contributes to the quantitative and qualitative results. The problem setting, reconstruction from arbitrary planar cross-sections, is practically important, particularly for medical imaging of vessels. If the claims hold, CrossSDF would be a valuable advance over the current state of the art. The introduction of a benchmark for thin-structure cross-section reconstruction is potentially useful, although no code or dataset is released in the manuscript. The main weakness is that the paper's central claim of preserving topological continuity is directly contradicted by the connected-component counts reported in Table 1, and the evaluation lacks statistical rigor (no error bars, self-defined benchmark).","major_comments":[{"comment":"The paper claims in the Abstract and Section 4.1 that CrossSDF preserves topological continuity and reconstructs thin structures 'without breakages.' However, the connected-component (CC) counts in Table 1 show that CrossSDF's extracted meshes are far more fragmented than the ground truth: e.g., Heart aligned 68 vs. 1, Heart non-aligned 176 vs. 1, Alveolis non-aligned 33 vs. 1, and Coronaries non-aligned 35 vs. 3. Since the paper itself introduces CC as a metric that 'confirms correct segmentation and topological consistency,' these numbers directly undercut the central claim. The authors do not discuss this discrepancy or attribute it to marching-cubes threshold sensitivity, spurious tiny components, or mesh post-processing. This issue must be addressed by either analyzing the components (e.g., size filtering, main-component connectivity, or alternative topology metrics) or substantially qualifying the topological-continuity claim.","section":"Table 1 and Section 4.1"},{"comment":"All quantitative results are reported as single numbers without error bars, multiple seeds, or any variance analysis. Training is stochastic (random initialization, sampling, and optimization), and the evaluation is performed on a self-defined benchmark. Consequently, the assertion of 'significant improvement over existing methods' is not statistically supported. The authors should report mean and standard deviation over at least three runs, or otherwise justify why the variance is negligible.","section":"Tables 1, 2, 3, 4, 5, A1, A2"}],"minor_comments":[{"comment":"The column header 'Coro (75)' is ambiguous; it likely denotes a separate coronary structure but is not named in the text. Please clarify the naming.","section":"Table 1"},{"comment":"The inset figure illustrating the adaptive sampling issue is not numbered or referenced clearly; it would help to include it as a formal figure or explicitly describe the depicted situation in the text.","section":"Section 3.2"},{"comment":"The definition of Ωon as the set where f2D(x) = 0 is technically measure-zero for continuous functions; in practice on-contour samples are used. The text should state that these are the discretized on-contour samples.","section":"Section 3.4, Eq. (4)"},{"comment":"The description of withholding '≈ 10% of the slices' is inconsistent with the example: keeping every 61//10 = 6th slice removes about 17% of the data. Please correct the explanation of the split procedure.","section":"Appendix B.2"},{"comment":"The definitions of Chamfer distance and Hausdorff distance are attributed to [30] (UniSurf), which is not the standard source; consider citing a more appropriate reference for these metrics.","section":"References"},{"comment":"The paper does not mention whether code and the new benchmark dataset will be released; for reproducibility, please state availability or provide a link.","section":"Overall"}],"recommendation":"major_revision","confidential_remarks":"The connected-component discrepancy is the most serious issue: the numbers in Table 1 conflict with the paper's headline claim. If the authors can convincingly explain or fix this (e.g., by filtering spurious components or replacing CC with a more appropriate topology metric), the paper may be acceptable. The lack of error bars and the self-defined benchmark make the 'significant improvement' claim less robust. Please also ensure the benchmark is described with enough detail for others to replicate."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I read the CrossSDF paper. Bottom line: the method is real and worth taking seriously, but the paper's own connected-component numbers cut against its headline claim.\n\nWhat's genuinely new: the symmetric difference loss in Sec 3.4 is a clever way to keep the network from locking onto the 2D SDFs inside the slices, and the adaptive per-contour sampling fixes a concrete weakness in OReX. The hybrid hash-plus-Fourier encoding is a sensible combination of known pieces, and the ablations actually show each component pulling its weight. The new thin-structure benchmark is also a useful addition—there isn't a good public benchmark for this problem, and the medical CT results are promising.\n\nWhat's soft, in proportion: the central claim needs qualification. The paper says \"without breakages\" and \"preserving topological continuity,\" but Table 1's CC counts tell a different story. CrossSDF gets 6 to 176 components where ground truth has 1 to 3. Heart non-aligned is 176 vs 1; Coronaries non-aligned is 35 vs 3. Those aren't rounding errors. The paper never discusses this discrepancy. It dismisses Neural-IMLS's artificially good CC score because that method just produces a blob, which is fair, but it doesn't apply the same scrutiny to its own numbers. If the field is fragmented on the metric they themselves chose to measure structural integrity, the \"no breakages\" claim is too strong as stated.\n\nOther weaknesses are more standard: no error bars anywhere, baselines may not have been tuned to the same degree, and the benchmark is self-defined. Those are fixable with more careful experiments. The method also relies on the Eikonal regularizer to define the field in the large unsampled regions between planes; that's a reasonable assumption for a fitting method and it's backed by empirical results, but it's worth stating explicitly.\n\nThe paper is honest about some limits—the limitations section admits sparse slices and the need for data-driven priors. The citation pattern is clean; self-citations to OReX and Deep Medial Fields are appropriate.\n\nOverall, this deserves a serious referee. The method is novel, the experiments are thorough in scope if not in rigor, and the problem matters. But the CC discrepancy has to be addressed head-on, either by discussing marching-cubes threshold sensitivity or by revising the topological claim. With that fixed, I'd be happy to see it in a good venue.\n\nRecommendation: send it to review, with a clear note that the topological-continuity claim needs substantial revision.","headline":"CrossSDF is a genuinely novel and well-engineered method, but its own connected-component numbers contradict the 'no breakages' headline and need to be addressed before publication.","tokens_in":15178,"tokens_out":2521,"would_cite":true,"duration_ms":24523,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"CrossSDF reconstructs thin 3D structures from planar cross-sections by training a neural signed distance field with a symmetric-difference loss, avoiding the interpolation artifacts and over-smoothing of prior methods.","keywords":["neural signed distance fields","cross-section reconstruction","thin structures","symmetric difference loss","hash encoding","Fourier features","CT scan reconstruction","implicit neural representations"],"falsifier":"Slice a ground-truth thin branching mesh into 25 parallel planes, run CrossSDF, and check the result in two ways: count the connected components of the extracted zero set against the mesh, and measure the angle between the learned field's gradient at points midway between planes and the slice-plane normal. If thin branches fragment into multiple components or the gradients align with the slicing direction, the symmetric-difference and Eikonal supervision has not produced a genuine 3D signed distance field.","tokens_in":14266,"feed_emoji":"🩻","tokens_out":11934,"duration_ms":104198,"temperature":0.7,"pith_summary":"CrossSDF sets out to reconstruct a complete 3D shape from a sparse set of planar cross-sections, where the geometry is known only as 2D contours on arbitrarily oriented planes. The paper argues that fitting a neural signed distance field directly to the in-plane 2D distances produces laddering artifacts because the field is forced to match distance values that are only meaningful inside each slice. Its fix is to supervise the field only on the contour itself and on the symmetric difference between the predicted and target inside/outside classification, leaving the rest of each plane free to behave as a genuine 3D distance field. Combined with per-contour adaptive sampling and a hybrid hash-plus-Fourier encoding, the method claims accurate reconstructions of thin branching structures such as blood vessels, where point-cloud baselines break and prior bespoke methods over-smooth. If true, this would give slice-based domains such as medical imaging a way to recover fine topology from sparse scans without interpolation artifacts.","feed_headline":"Thin 3D structures rebuilt from sparse 2D slices","feed_subtitle":"Keeps thin branches intact by supervising only where inside/outside labels clash, avoiding laddering artifacts.","key_machinery":"The central object is the symmetric-difference loss. Given planar samples with known 2D distance values, define $\\Omega_{on} = \\{x : f_{2D}(x) = 0\\}$ and $\\Omega_{off} = \\{x : f_{2D}(x) \\neq 0 \\text{ and } \\operatorname{sign}(f(x;\\theta)) \\neq \\operatorname{sign}(f_{2D}(x))\\}$. The loss is $\\mathcal{L}_{on} = \\mathbb{E}_{x\\in\\Omega_{on}} |f(x;\\theta) - f_{2D}(x)|$ plus $\\mathcal{L}_{off} = \\mathbb{E}_{x\\in\\Omega_{off}} (f(x;\\theta) - f_{2D}(x))^2$, so the network receives distance supervision only on the contour and where the predicted and target interiors disagree. This region shrinks to zero as the predicted surface aligns with the target contour, freeing the field to be a true 3D SDF between planes. Two auxiliary mechanisms carry much of the practical performance: the hybrid encoding $z = M_{hash}(\\gamma_{hash}(x)) + \\alpha M_{RF}(\\gamma_{RF}(x))$, concatenated with $x$, which adds Fourier-feature smoothness to hash-grid detail; and adaptive sampling that keeps sampling inside every contour until a threshold, so small cross-sectional areas are not ignored.","core_discovery":"CrossSDF learns a neural signed distance function $f(x;\\theta)$ whose zero set is the reconstructed surface. The training signal comes from planar signed distance fields $f_{2D}$ computed on each input slice. On-contour samples $\\Omega_{on}$ regress $f$ to the 2D distance value, while off-contour samples $\\Omega_{off}$ enter the loss only when the sign of $f$ and $f_{2D}$ disagree, so supervision is applied exactly where the predicted interior/exterior differs from the target. This symmetric-difference scheme forces the zero set to match the input contours without forcing $f$ to be a 2D distance field inside the plane, which is what the paper identifies as the cause of laddering. Eikonal and minimum-surface regularization in 3D keep $f$ a valid signed distance field and suppress spurious surfaces, while per-contour adaptive sampling and a hybrid hash-plus-random-Fourier encoding preserve thin features and remove grid creases. On synthetic thin and thick datasets the paper reports lower Chamfer and Hausdorff distances than OReX, Neural-IMLS, POCO, and Screened Poisson, and higher held-out-slice IoU on real CT vessel scans.","pith_inferences":["The symmetric-difference principle could generalize to any sparse supervision that provides inside/outside labels, such as sparse LiDAR returns or partial segmentations, without fitting a proxy function in unsampled regions.","The hash-plus-Fourier blend could reduce grid-boundary creases in other hash-based neural fields trained from sparse observations, such as multi-view reconstruction with few views.","A natural extension would replace the fixed per-contour sample threshold with an analytic criterion based on contour area or local feature size, which could further improve extreme thin structures.","If the held-out CT results hold in practice, standard 5 mm-slice scans could be reconstructed into vessel trees usable for pre-surgical planning without dense follow-up imaging."],"forward_implications":["Reconstructions from sparse arbitrary-orientation slices can be meshed directly with marching cubes, with no slice-interpolation step and no smoothing post-process.","Thin branching topology, such as vessel trees spanning only a few CT slices, is preserved better than with indicator-field or point-cloud methods.","Halving the number of slices (for example, from 75 to 50) degrades quality only mildly, and even 25 slices remain usable for some structures, so acquisition could be sparser.","Each component contributes a specific property: the symmetric-difference loss removes staircase and laddering artifacts, the adaptive sampler rescues thin contours, and the hybrid encoding removes grid creases while retaining detail."],"supporting_citations":[{"why":"Bespoke cross-section reconstruction baseline whose indicator-field representation and sampling scheme CrossSDF targets and adapts.","marker":"[33]"},{"why":"Point-cloud reconstruction baseline that over-smooths and fails to converge on thin medical structures.","marker":"[40]"},{"why":"Data-driven point-cloud baseline that struggles with out-of-distribution sparse cross-sections.","marker":"[11]"},{"why":"Classical screened Poisson baseline that exhibits ridging artifacts and fragmented topology.","marker":"[19]"},{"why":"Multi-resolution hash encoding that supplies fine detail and is the source of the grid interpolation artifacts the hybrid encoder addresses.","marker":"[29]"},{"why":"Random Fourier features used in the hybrid encoding to add smoothness and suppress hash-grid creases.","marker":"[38]"},{"why":"Eikonal regularization used to make the predicted field a 3D signed distance function in unsampled regions.","marker":"[17]"},{"why":"Minimum-surface regularizer used to suppress spurious surfaces ('floaters') in unsampled regions.","marker":"[32]"},{"why":"Source of six patient-specific thin anatomical meshes used as the thin-structure benchmark.","marker":"[41]"},{"why":"Real CT dataset used, with held-out slices, to evaluate 2D IoU on vessel structures.","marker":"[4]"}],"fun_headline_variants":["CrossSDF: Thin 3D structures from sparse cross-sections","Supervise only where signs clash: thin 3D from 2D slices","CrossSDF: Rebuild thin vessels without laddering artifacts","Neural SDF from cross-sections: only sign-clash supervision","CrossSDF: Clash-only supervision recovers thin 3D from slices"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that Eikonal regularization on uniformly sampled 3D points, together with the network's inductive bias, is enough to define a correct, artifact-free signed distance field in the large unsampled regions between cross-section planes, where there is no direct distance supervision.","fun_headline_variants_meta":{"raw":{"variants":["CrossSDF: Thin 3D structures from sparse cross-sections","Supervise only where signs clash: thin 3D from 2D slices","CrossSDF: Rebuild thin vessels without laddering artifacts","Neural SDF from cross-sections: only sign-clash supervision","CrossSDF: Clash-only supervision recovers thin 3D from slices"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000532,"raw_usage":{"total_tokens":2562,"prompt_tokens":945,"completion_tokens":1617,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":561,"completion_tokens_details":{"reasoning_tokens":1518}},"tokens_in":561,"tokens_out":1617,"duration_ms":12160,"temperature":1.0,"reasoning_tokens":1518,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:43:48.177368+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Slice a ground-truth thin branching mesh into 25 parallel planes, run CrossSDF, and check the result in two ways: count the connected components of the extracted zero set against the mesh, and measure the angle between the learned field's gradient at points midway between planes and the slice-plane normal. If thin branches fragment into multiple components or the gradients align with the slicing direction, the symmetric-difference and Eikonal supervision has not produced a genuine 3D signed distance field.","supporting_citations":[{"cited_title":"Neural-imls: Self-supervised im- plicit moving least-squares network for surface reconstruc- tion","cited_arxiv_id":null,"evidence_quote":"Point-cloud reconstruction baseline that over-smooths and fails to converge on thin medical structures."},{"cited_title":"Orex: Object reconstruction from planar cross-sections us- ing neural fields","cited_arxiv_id":null,"evidence_quote":"Bespoke cross-section reconstruction baseline whose indicator-field representation and sampling scheme CrossSDF targets and adapts."},{"cited_title":"Poco: Point convo- lution for surface reconstruction","cited_arxiv_id":null,"evidence_quote":"Data-driven point-cloud baseline that struggles with out-of-distribution sparse cross-sections."},{"cited_title":"Screened poisson sur- face reconstruction","cited_arxiv_id":null,"evidence_quote":"Classical screened Poisson baseline that exhibits ridging artifacts and fragmented topology."},{"cited_title":"Fourier features let networks learn high frequency functions in low dimen- sional domains","cited_arxiv_id":null,"evidence_quote":"Random Fourier features used in the hybrid encoding to add smoothness and suppress hash-grid creases."},{"cited_title":"Implicit geometric regularization for learning shapes","cited_arxiv_id":null,"evidence_quote":"Eikonal regularization used to make the predicted field a 3D signed distance function in unsampled regions."},{"cited_title":"The vascular model repository: a public resource of medi- cal imaging data and blood flow simulation results","cited_arxiv_id":null,"evidence_quote":"Source of six patient-specific thin anatomical meshes used as the thin-structure benchmark."},{"cited_title":"The medical segmentation decathlon.Nature communications, 2022","cited_arxiv_id":null,"evidence_quote":"Real CT dataset used, with held-out slices, to evaluate 2D IoU on vessel structures."}],"review_version":1}