{"id":"016657fa-104d-4cf4-9f6d-c4df0fa1562a","arxiv_id":"2506.21401","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A one-stage pipeline optimizes 3D parametric Bézier curves directly from multi-view edge maps by rendering curve-coupled Gaussians, outperforming two-stage curve reconstruction baselines.","lead":"This paper introduces CurveGaussian, a representation that couples 3D Bézier curves with Gaussian splats so parametric curves can be optimized directly against multi-view edge maps, skipping the usual two-stage point-cloud-then-fit pipeline. A reader in 3D vision should care because the method reports cleaner, more compact, and faster curve reconstruction on CAD and real-object benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The one-stage, edge-map-only claim is not cleanly tested on real scenes: curves are initialized from the COLMAP SfM point cloud and edge maps are custom-built, so the reported real-world superiority may depend on unstated 3D and preprocessing inputs.","rationale":"Good-faith reading: the core representation, coupling Bézier control points to rod-shaped Gaussians, is coherent, and the ABC-NEF DexiNed results do show that the full system is competitive with or better than EdgeGaussians and EMAP. The paper also honestly states the edge-map-quality limitation in Sec. 5. My concern is narrower: the experiments that would distinguish the one-stage claim from a two-stage pipeline are not clean. The real-world experiments add two inputs not present in Eq. 1, namely SfM point-cloud initialization and SAM2+normal edge extraction, and no ablation isolates either. Because the central narrative is that bypassing 3D edge point clouds removes error accumulation, a dependency on an SfM point cloud for initialization is directly relevant to the central claim, not merely a reproducibility detail. The concrete 2x2 test would settle whether the real-world gains survive without those extra inputs. If they do, the claim is supported within its stated limitations; if they do not, the abstract and conclusion overstate the one-stage, edge-map-only contribution. This does not change the reader's CONDITIONAL verdict, which already calls for scope corrections and reproducibility checks; it adds one specific missing ablation that should be reported before the claim is accepted at face value.","tokens_in":961,"tokens_out":1712,"duration_ms":170212,"concrete_test":"Run the MV2Cyl comparison (all six objects, per-object results) with a 2x2 design for both CurveGaussian and EdgeGaussians: initialization = random 3D grid (as on ABC-NEF) versus COLMAP SfM point cloud; edge maps = standard DexiNed versus the SAM2+normal-estimator pipeline. Also report ABC-NEF PiDiNet Accuracy/F5 with per-model variance. If removing the SfM initialization or using DexiNed edges removes CurveGaussian's advantage, the central claim must be restated as one-stage curve optimization given a good 3D initialization and clean custom edge maps, not as direct optimization from raw multi-view edge maps.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that CurveGaussian performs one-stage optimization of parametric curves directly from multi-view edge maps, bypassing explicit 3D reconstruction (Secs. 1 and 3.1). The real-world experiments do not instantiate that claim cleanly. Supplementary Sec. 6 states that for MV2Cyl the edge maps were not produced by the standard detectors used in Table 1; instead, SAM2 segmentation plus a monocular normal estimator were used, and NEF/EMAP are reported as failing. Supplementary Sec. 9 further states that for COLMAP-based datasets the midpoints of the Bézier curves were initialized using the SfM point cloud from COLMAP. Neither dependency appears in the problem definition Eq. 1, which lists only curve parameters, camera poses, and edge images. If the SfM point cloud places initial midpoints near true 3D edges, and if the custom SAM2+normal edge maps are substantially cleaner than the DexiNed maps supplied to baselines, then Table 3's large real-world gains (Acc 13.8→8.5, F10 56.7→73.1) and the one-stage, edge-map-only narrative are not yet established. The paper does not state whether EdgeGaussians received the same custom edge maps, and no ablation removes the SfM initialization. This is a load-bearing gap because the novelty and claimed superiority rest on being one-stage and directly driven by 2D edge evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes CurveGaussian, a hybrid representation that couples cubic and first-order Bézier curves with edge-oriented 3D Gaussian components, enabling one-stage optimization of parametric curves directly from multi-view edge maps through differentiable Gaussian splatting. The method introduces adaptive topology operations (linearization, merging, splitting, pruning) and several custom loss terms. On the ABC-NEF benchmark, the method reports improved accuracy, compactness, and training time over NEF, EMAP, and EdgeGaussians under the DexiNed edge detector; on MV2Cyl real objects it reports gains over EdgeGaussians; on Replica it shows qualitative results. The paper claims that the one-stage formulation bypasses the error accumulation and efficiency bottlenecks of two-stage pipelines.","tokens_in":16138,"tokens_out":8269,"duration_ms":77397,"significance":"If the central claims hold, the core idea is valuable: it demonstrates that parametric Bézier curves can be optimized directly through Gaussian splatting, removing the explicit two-stage edge-point-cloud fitting and potentially reducing error accumulation. The reported 70.5% reduction in curve count and 33% faster training on ABC-NEF are concrete, externally comparable improvements, and the authors commit to releasing code and data, which supports reproducibility. However, the strength of the real-world evidence is currently limited because the paper does not disclose in the main text that COLMAP-based scenes use SfM point clouds for initialization and that MV2Cyl uses custom SAM2-plus-normal edge maps, and the claim of outperforming all learning-based methods across all metrics is contradicted by the paper's own PiDiNet results. These issues are fixable but require additional experiments and corrections.","major_comments":[{"comment":"The claim that \"the proposed method outperforms all learning-based methods across all metrics\" is not supported by Table 1 when the PiDiNet edge detector is used. For example, EMAP (PiDiNet) has Accuracy 9.2 vs. Ours 10.8 (lower is better), and EdgeGaussians (PiDiNet) has Completeness 10.3 vs. Ours 12.3. The statement should be qualified to the DexiNed condition or to the specific metrics where the improvement holds, and the text should acknowledge that the relative performance depends on the edge detector.","section":"Section 4.2, Table 1"},{"comment":"The main text states in Section 3.3 that the optimization is initialized with \"random Bézier parameterized curves,\" but Supplementary Section 9 states that for COLMAP-based datasets the midpoints of the Bézier curves are initialized using the SfM point cloud. This is a direct contradiction and is load-bearing for the claimed one-stage, edge-map-only behavior. If SfM initialization places the initial curves near the true 3D edges, the reported real-world gains (e.g., Table 3) may be partly due to this extra 3D input. The paper must disclose this initialization in the main text, incorporate it into the problem formulation in Eq. (1), or justify its absence, and provide an ablation on at least one COLMAP scene with purely random initialization to quantify the contribution.","section":"Supplementary Section 9; main-text Section 3.3"},{"comment":"On MV2Cyl, the proposed method uses edge maps generated by SAM2 segmentation plus a monocular normal estimator, which the paper says are superior to standard detectors. The main-text comparison in Table 3 is only against EdgeGaussians, and the paper never states whether EdgeGaussians received the same custom edge maps. If EdgeGaussians used standard detector edge maps (e.g., DexiNed or PiDiNet), the comparison is confounded: the reported gains in accuracy and F-score could reflect the higher quality of the input edge maps rather than the one-stage optimization. The paper must specify the exact edge maps supplied to each method and, if feasible, run EdgeGaussians with the same SAM2-plus-normal edge maps.","section":"Supplementary Section 6; Section 4.2 (MV2Cyl)"},{"comment":"The adaptive topology operations depend on multiple hand-set thresholds (τ_l, τ_la, τ_ld, τ_b, θ_s, τ_m, τ_d, η, τ), but only a few values are reported in the supplementary (opacity below 0.05, bending angle above 20°, mask below 0.01, and the merge threshold taken from EMAP). For reproducibility and to assess sensitivity, the paper should list all threshold values in one place and include a brief analysis of how the results vary with a reasonable perturbation of these thresholds.","section":"Section 3.3; Supplementary Section 9"}],"minor_comments":[{"comment":"The metrics Accuracy, Completeness, Recall, Precision, and F-score are used in Table 1 without being defined in the main text; they are only defined in Supplementary Section 8. A one-sentence definition or a reference should be added in Section 4.1.","section":"Section 4.1"},{"comment":"The statement that \"NEF and EMAP fail to produce reasonable 3D edges in our experiments\" is made without supporting evidence. A qualitative figure or a brief explanation of the failure mode would strengthen the claim and allow readers to judge the comparison.","section":"Section 4.2 (MV2Cyl)"},{"comment":"The weighting in Eq. (8) is easy to misread: the first term over non-edge pixels N_I is weighted by |M_I|/|E_I|, and the second term over edge pixels M_I is weighted by |N_I|/|E_I|. A short explanatory sentence after the equation would clarify the intended balancing of the two classes.","section":"Equation (8)"},{"comment":"The so-called \"new metric, Curve Count\" is just the number of output curves and is not a novel metric in the conventional sense. Consider renaming it to \"output curve count\" to avoid overclaiming.","section":"Supplementary Section 8"},{"comment":"The notation for Gaussian indices is inconsistent (e.g., G_i^j in Section 3.2 versus v_j,i in Eq. (10)); please standardize the subscripts and superscripts.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The core idea is promising and the ABC-NEF results under DexiNed appear solid, but the undisclosed SfM initialization and the custom edge maps on MV2Cyl are serious confounds for the real-world claims. These issues are fixable with additional ablations and reporting, but they require a revision that goes beyond local edits. The PiDiNet inconsistency in Table 1 is a simpler factual correction that should be caught in the next version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: the core idea is real, the main synthetic evaluation is solid, and I'd send it to review. But the paper overstates its own numbers, and the real-world results lean on two extra inputs that don't appear in the problem formulation.\n\nWhat's new: the bi-directional coupling between Bézier control points and Gaussian primitives whose spatial attributes are analytic functions of curve parameters. That is a genuinely different mechanism from the two-stage NEF/EMAP/EdgeGaussians pipeline and from DiffVG-style rasterization of projected curves. Rendering losses flow directly to control points, topology is adjusted during training via linearize/merge/split/prune, and the representation is compact. The method section is clear, and the DexiNed rows in Table 1 show real improvement: Acc 8.2 vs 9.6 and 8.8 for EdgeGaussians and EMAP, F10 94.0 vs 93.7 and 88.9, and about 70% fewer curves than EdgeGaussians at similar runtime. The ablations are informative and mostly back the design choices.\n\nThe soft spots are real but fixable. First, the PiDiNet rows contradict the sentence that the method 'outperforms all learning-based methods across all metrics.' On PiDiNet, EMAP has better Acc, Comp, P5, and F5. The claim should be scoped to DexiNed or averaged fairly. Second, the real-world evaluation doesn't cleanly instantiate the one-stage, edge-map-only story. The supplement says MV2Cyl edge maps come from SAM2 segmentation plus a monocular normal estimator, and that COLMAP-based datasets initialize curve midpoints from the SfM point cloud. Neither dependency is in Eq. 1. If baselines didn't get the same custom edge maps, or if the SfM initialization is doing heavy lifting, the comparison isn't apples-to-apples. An ablation with and without that initialization would settle it. Third, there are no error bars and the code release isn't verified yet, so I'd want auditable code and settings before trusting the real-world numbers.\n\nBottom line: this is a solid contribution for the 3D curve reconstruction community, and the core mechanism deserves attention. It needs a more careful empirical write-up and an ablation that separates the extra inputs. Send it to peer review; I'd ask for major revision on the claims, not on the method.","headline":"Genuinely new one-stage curve reconstruction via curve-coupled Gaussians, with solid ABC results, but overclaimed baselines and real-world tests that depend on unstated SfM initialization and custom edge maps.","tokens_in":16714,"tokens_out":2898,"would_cite":true,"duration_ms":29571,"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":"A one-stage pipeline reconstructs 3D parametric curves directly from 2D edge maps via curve-aware Gaussian splatting, beating two-stage methods in accuracy, speed, and compactness.","keywords":["parametric curve reconstruction","Gaussian splatting","Bézier curves","multi-view edge maps","differentiable rendering","one-stage optimization","topology optimization","3D reconstruction"],"falsifier":"Take a CAD model with known ground-truth Bézier curves, render views, and corrupt the edge maps by deleting a controlled fraction of edge pixels and adding spurious edges; if the one-stage method's reconstruction error grows roughly with the corruption rate and never recovers the occluded portions (edges invisible in every view), that confirms the central premise. A sharper test: an edge that is present in only one view yet consistent with a wrong 3D line, which the multi-view photometric loss would not correct, showing that 2D edge quality, not reconstruction, is the limiting factor.","tokens_in":15557,"feed_emoji":"📐","tokens_out":5960,"duration_ms":63761,"temperature":0.7,"pith_summary":"The paper aims to show that 3D parametric curves—Bézier curves and line segments—can be optimized directly from multi-view 2D edge maps, bypassing the usual two-stage pipeline of first reconstructing an edge point cloud and then fitting curves. To make this possible, the paper couples each curve to a set of edge-oriented Gaussians whose positions, orientations, and scales are analytic functions of the curve's control points, so ordinary differentiable Gaussian splatting renders the curves and backpropagates loss gradients to the curve parameters. A training-time topology controller linearizes, merges, splits, and prunes curves to keep the reconstruction compact. On the ABC-NEF benchmark the method reports roughly 14.5% better reconstruction accuracy, 33% faster runtime, and 70.5% fewer output curves than a strong two-stage baseline. If correct, this shows that the intermediate 3D edge cloud is unnecessary and that its errors can be avoided, making curve reconstruction faster and cleaner for CAD-style objects.","feed_headline":"One-stage splatting rebuilds 3D curves directly from 2D edges","feed_subtitle":"Skipping the edge point cloud, it optimizes Bézier control points straight through rendering, gaining 14.5% accuracy and 33% speed.","key_machinery":"The load-bearing object is the CurveGaussian representation: a Bézier curve $c_j(t)$ spawns $N=12$ edge-oriented Gaussians through uniform sampling, with the $i$-th Gaussian's position $p_j(t_i)$, orientation (principal axis = curve tangent), and scale (axial length from neighboring sample distance, plus curve-specific thickness) all computed analytically from the control points. It carries the argument because it makes parametric curves renderable through standard splatting while keeping the curve itself the only optimizable entity, so photometric edge consistency and geometric curve regularization act on the same parameters. Around this core sit four adaptive operators—curve linearization (cubic to line when nearly straight), merging (lines and cubics), splitting (de Casteljau at abrupt tangent changes or low mask values), and pruning (low opacity or masked-out Gaussians)—that adjust topology during training.","core_discovery":"The central discovery is a bi-directional coupling between parametric curves and Gaussian primitives, called CurveGaussian. Each Bézier curve $c_j$ is sampled at $N$ evenly spaced parameters $t_i$, and the $i$-th Gaussian is anchored at the curve point $p(t_i)$, with its principal axis aligned to the curve tangent, its axial scale set to the inter-sample distance along with a curve thickness, and its opacity inherited from the curve. Because every Gaussian attribute is an analytic function of the control points, the rendering function $f$ in the optimization objective is exactly curve-aware Gaussian splatting, and multi-view rendering losses backpropagate straight to the control points, thicknesses, and opacities. The paper argues this eliminates the error accumulation of separate point-cloud reconstruction and RANSAC-style fitting, and empirically supports it with accuracy, completeness, precision, recall, runtime, and curve-count comparisons on ABC-NEF, MV2Cyl real objects, and Replica scenes.","pith_inferences":["If the claimed dependence on 2D edge quality is the binding constraint, pairing the method with learned edge detectors that fuse depth or normal cues (as the supplement does for MV2Cyl) could push the practical ceiling higher than the ABC-NEF results alone suggest; the paper gestures at this by proposing to lift 2D edge foundation models into 3D.","The bi-directional coupling is general: any parametric primitive whose sampling yields analytic Gaussian attributes (e.g., surfaces or open B-splines) could inherit the same one-stage optimization, a direction the paper does not explore.","A direct comparison against a two-stage pipeline that uses the same edge maps and the same Gaussian splatting backend would isolate exactly how much of the reported gain comes from removing the fitting stage versus from the curve-aware regularization; the paper compares against existing systems rather than this matched baseline."],"forward_implications":["Because the intermediate edge point cloud is eliminated, the method's output curve count drops (28.9 average versus 97.9 for the two-stage Gaussian baseline on ABC-NEF), so downstream CAD-style editing and rendering start from a much sparser representation.","Optimization variables are the curve control points rather than a dense set of per-Gaussian positional parameters, which is why the paper reports 33% shorter runtime at comparable or better accuracy.","The adaptive topology rules (linearize, merge, split, prune) let the number of curves shrink from a large random initialization to a compact set during training, so the method does not require knowing the curve count in advance.","Because rendering is standard splatting, the same machinery extends to any scene where edges can be extracted as 2D maps, including real-world captures and indoor scenes (shown on MV2Cyl and Replica)."],"supporting_citations":[{"why":"Supplies the standard 3D Gaussian splatting pipeline and rendering loss that CurveGaussian adapts for edge maps.","marker":"[15]"},{"why":"The two-stage Gaussian splatting baseline that the method must beat; provides the accuracy, runtime, and curve-count numbers for comparison.","marker":"[6]"},{"why":"The two-stage NeRF-based baseline whose evaluation protocol and metrics on ABC-NEF are adopted.","marker":"[19]"},{"why":"The original two-stage curve reconstruction framework and the source of the ABC-NEF dataset used for benchmarking.","marker":"[52]"},{"why":"Supplies the learnable importance mask mechanism that suppresses redundant Gaussian segments during optimization.","marker":"[18]"},{"why":"RANSAC is the greedy fitting primitive in the two-stage baselines that the one-stage optimization replaces.","marker":"[8]"}],"fun_headline_variants":["One-stage splatting turns 2D edges into 3D curves","CurveGaussian splatting fits curves end-to-end from edges","Direct 3D curve reconstruction from edge maps via splatting","One-stage splatting skips point cloud to fit 3D curves"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole optimization trusts that the input 2D edge maps correctly mark the target curves, so if edge detection is noisy, incomplete, or inconsistent across views, the one-stage optimizer has no independent signal to pull the curves back to the true geometry, and the paper's own conclusion and MV2Cyl experiments acknowledge this dependence.","fun_headline_variants_meta":{"raw":{"variants":["One-stage splatting turns 2D edges into 3D curves","CurveGaussian splatting fits curves end-to-end from edges","Direct 3D curve reconstruction from edge maps via splatting","One-stage splatting skips point cloud to fit 3D curves"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000706,"raw_usage":{"total_tokens":3204,"prompt_tokens":987,"completion_tokens":2217,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":2137}},"tokens_in":603,"tokens_out":2217,"duration_ms":18168,"temperature":1.0,"reasoning_tokens":2137,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T22:25:37.149721+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a CAD model with known ground-truth Bézier curves, render views, and corrupt the edge maps by deleting a controlled fraction of edge pixels and adding spurious edges; if the one-stage method's reconstruction error grows roughly with the corruption rate and never recovers the occluded portions (edges invisible in every view), that confirms the central premise. A sharper test: an edge that is present in only one view yet consistent with a wrong 3D line, which the multi-view photometric loss would not correct, showing that 2D edge quality, not reconstruction, is the limiting factor.","supporting_citations":[{"cited_title":"3d gaussian splatting for real-time radiance field rendering.ACM Transactions on Graphics, 42 (4), 2023","cited_arxiv_id":null,"evidence_quote":"Supplies the standard 3D Gaussian splatting pipeline and rendering loss that CurveGaussian adapts for edge maps."},{"cited_title":"EdgeGaussians -- 3D Edge Mapping via Gaussian Splatting","cited_arxiv_id":"2409.12886","evidence_quote":"The two-stage Gaussian splatting baseline that the method must beat; provides the accuracy, runtime, and curve-count numbers for comparison."},{"cited_title":"3d neural edge recon- struction","cited_arxiv_id":null,"evidence_quote":"The two-stage NeRF-based baseline whose evaluation protocol and metrics on ABC-NEF are adopted."},{"cited_title":"Nef: Neural edge fields for 3d parametric curve reconstruction from multi-view images","cited_arxiv_id":null,"evidence_quote":"The original two-stage curve reconstruction framework and the source of the ABC-NEF dataset used for benchmarking."},{"cited_title":"Compact 3d gaussian representation for radiance field","cited_arxiv_id":null,"evidence_quote":"Supplies the learnable importance mask mechanism that suppresses redundant Gaussian segments during optimization."},{"cited_title":"Fischler and Robert C","cited_arxiv_id":null,"evidence_quote":"RANSAC is the greedy fitting primitive in the two-stage baselines that the one-stage optimization replaces."}],"review_version":1}