{"id":"3c187eb2-bf58-4e18-a328-aed8bcdedac2","arxiv_id":"2507.02576","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A differentiable voxelization loss lets neural networks fit B-spline centerline-and-radius vessel models directly to segmentations, giving sparse editable meshes with Dice scores around 95, 86, and 82 percent on the three tested datasets.","lead":"The authors show that a blood vessel can be automatically turned into a smooth, editable model described by a center line and widths, using only a segmented scan as the target. This compact representation keeps the fit accuracy of standard segmentation methods while offering sparse, adjustable meshes for planning and simulation.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central 'end-to-end learning from segmentations' claim is not established: the differentiable voxelization loss is local and relies on an initial centerline from skeletonization and manual adjustment, yet no test isolates the voxelization loss's contribution.","rationale":"The paper's central claim is that shape parameters are learned from segmentations through a differentiable voxelization loss, without parametric ground truth. The reader's weakest assumption identifies the initial-centerline dependence; I agree and would sharpen it. Section 2.4 explicitly concedes that the voxelization loss is a local boundary-matching loss that cannot escape when the nearest boundary is on the wrong side of the object. Stage 1 therefore fits the centerline to an external skeletonization with manual endpoint adjustment (Section 3), and the pointwise loss L_cl is the only active loss. The subsequent stages freeze the backbone and refine radius and centerline. On MouseAneurysm, the authors themselves report that the centerline-correction stage does not improve the fit, which is consistent with the differentiable voxelization stage being a local refinement rather than the source of the geometric estimate. No experiment isolates the contribution of the differentiable voxelization loss: there is no initialization-perturbation study and no comparison against a classical B-spline fit to the same segmentation with a distance-transform objective. Because the central 'end-to-end learning' claim rests on this unisolated component, the concern is load-bearing. The correct verdict remains CONDITIONAL: the paper reports plausible fits for branch-free vessels, but the claimed mechanism is not demonstrated until this dependency is quantified. I do not see a need to reject the manuscript; the condition is a missing experiment rather than an observed contradiction.","tokens_in":10047,"tokens_out":7022,"duration_ms":77842,"concrete_test":"On Aorta24, rerun the full four-stage pipeline with initial centerlines displaced perpendicularly by 0, 2, 4, and 8 voxels from the paper's skeletonization-based centerline, holding all hyperparameters fixed, and record final Dice and centerline Chamfer distance. If Dice falls substantially (e.g., more than 2 points) with increasing displacement, then the method's success is dominated by the external initialization rather than by the differentiable voxelization loss, and the claimed end-to-end learning from segmentations is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assumption is that the differentiable voxelization loss actually drives the shape parameters to the correct vessel, so that the reported fits demonstrate the claimed learning of shape parameters from segmentations. Section 2.4 states the opposite for the core loss: 'the SDF-based voxelization loss acts on the object boundary, trying to match the boundary of the target to the nearest boundary. If the nearest boundary is on the wrong side of the object, the loss will be unable to escape this local minimum.' Consequently, Stage 1 fits the centerline to an external skeletonization (Scikit-image) with manual endpoint adjustment (Section 3), and the pointwise centerline loss L_cl is the only active loss in that stage. Section 5 reiterates the 'increased need for regularization, especially for centerline initialization.' On MouseAneurysm, the authors report that the centerline-correction stage does not improve fit, consistent with the differentiable voxelization loss being a local refinement rather than the source of the geometric estimate. There is no initialization-perturbation study and no comparison against a classical B-spline fit to the same segmentation using a distance-transform objective. Without such an ablation, the reported Aorta24, TopCoW, and MouseAneurysm fits may reflect the quality of the external centerline prior rather than the differentiable voxelization component, leaving the central claim unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a per-sample optimization framework that fits a parametric vessel model — a cubic B-spline centerline, a radius curve, and optional per-direction radial adjustments — to a reference segmentation. The parametric model is converted to a triangle mesh, which is then differentiably voxelized via a slice-wise SDF approximation, and the Dice loss between the soft voxelization and the reference segmentation supervises the fit. A neural network predicts the spline control points, and a four-stage training schedule first fits the centerline to an externally extracted skeleton, then the radius, then refines the centerline using the voxelization loss, and optionally adjusts radial directions. Experiments on Aorta24, TopCoW, and MouseAneurysm report Dice scores of 94.66, 82.22, and 86.43, respectively, with meshes of about 673 vertices and 1326 faces, comparing favorably to nnUNet and INR baselines on Aorta24 while being far sparser. The paper also demonstrates robustness to sparse annotations.","tokens_in":10284,"tokens_out":5074,"duration_ms":53668,"significance":"If the central claim is established, the framework offers a practical way to obtain sparse, editable, parametric vessel models directly from segmentations without parametric ground truth, which would be valuable for surgical planning, flow simulation, and interpretable vessel analysis. The differentiable voxelization is a nontrivial engineering contribution, the code is publicly available, and the multi-stage training recipe is described in enough detail to reproduce. The paper is also honest about its limitations, including the restriction to single non-branching vessels and the reliance on centerline initialization. However, the current evidence does not isolate the contribution of the differentiable voxelization from the external centerline prior, so the significance of the learning claim remains to be demonstrated.","major_comments":[{"comment":"The central claim that the method learns shape parameters from segmentations without the explicit need for ground-truth shape parameters is not yet fully supported. In Stage 1, the centerline is fit to an automatically extracted skeleton (Scikit-image) with manual endpoint adjustment (Section 3) using the pointwise loss L_cl, and the voxelization loss is not active until Stage 2. Section 2.4 states that the SDF-based voxelization loss acts on the object boundary and cannot escape local minima when the nearest boundary is on the wrong side of the object. Therefore, the reported Dice values may largely reflect the quality of the external centerline initialization rather than the differentiable voxelization component. Please add an ablation that isolates the voxelization loss: for example, fit the same parametric model with a classical distance-transform-based objective (without the differentiable voxelization) and report the resulting Dice, and perturb the initial centerline (translation, rotation, or noise) to measure the basin of convergence of the full pipeline.","section":"Section 2.4 and Section 3"},{"comment":"The centerline metrics (HD95, Chamfer) reported in Table 1 are computed against the same centerline extracted from the reference segmentation that is used to initialize the fit (Section 3). Because Stage 1 explicitly minimizes the pointwise distance to this centerline, the centerline metrics partly measure the network's ability to regress the initialization rather than the accuracy of the recovered centerline against an independent ground truth. Please state this explicitly in the evaluation section and, if possible, evaluate on an independent centerline annotation or on centerlines extracted by a different algorithm.","section":"Table 1 and Section 3"},{"comment":"The procedure for binarizing the soft voxelization output dVOX^soft for Dice computation is not described. Since the Dice score is the main quantitative claim, please specify the threshold (presumably 0.5) and report whether the same threshold is used for all datasets. Additionally, the comparison to baselines in Table 2 is only on Aorta24; please add at least one other dataset or justify why the comparison is limited to this dataset.","section":"Section 2.2 and Table 1"}],"minor_comments":[{"comment":"The INR* row reports an aspect ratio of 1e+26, which suggests that the remeshed INR mesh contains degenerate triangles; this should be noted or the baseline should be excluded, as it currently appears as an artifact that distorts the comparison.","section":"Table 2"},{"comment":"The notation sigma(SDF/tau) is confusing because the same symbol sigma is used for the sigmoid function and the soft voxelization output; please define the sigmoid explicitly and use a distinct symbol for the soft occupancy.","section":"Section 2.2, Eq. (1)"},{"comment":"Figure 2 is described as an overview of the network components and training stages, but the four stages are only listed in Section 2.4; a short pointer in the figure caption or in the text would improve readability.","section":"Figure 2"},{"comment":"The statement that 'the endpoints in this dataset are not as accurate' is vague; please quantify this claim or explain how it affects the reported Dice, since the paper later attributes the lower TopCoW Dice to endpoint quality.","section":"Section 3, TopCoW"},{"comment":"The paper says that the number of control points and cross-sections was adjusted to the dataset size and refers the reader to the codebase; please report these values for each dataset in the paper, as they are important hyperparameters for reproducibility.","section":"Implementation details"}],"recommendation":"major_revision","confidential_remarks":"The paper is well-organized and the code is available, which is a strength. The main issue is the missing ablation isolating the differentiable voxelization from the external centerline initialization; with that ablation, the paper could become acceptable. The reported INR* aspect ratio should be addressed. The paper fits the journal's scope, and I see no citation-pattern concerns."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a read if you work on vessel modeling or differentiable mesh/voxel pipelines. The genuinely new piece is the slice-wise SDF voxelization adapted from 2D polygon loss to 3D, with cycle detection and plane-alternating passes. That is a real engineering contribution, and the paper is honest about its memory cost. The B-spline centerline-plus-radius parameterization is clean, and the sparse-mesh comparison against remeshed nnUNet and INR outputs makes a fair point: at comparable vertex counts, their parametric mesh holds Dice better than decimated marching-cubes meshes. The 20x sparse annotation experiment is a nice practical result, even if the centerline is kept complete in that setup.\n\nThe soft spot is exactly where the stress-test lands. The voxelization loss is local — Section 2.4 says it cannot escape if the nearest boundary is on the wrong side — and the centerline is initialized from skeletonization with manual endpoint fixes. Stage 1 is pure centerline regression; the voxelization loss only enters after the centerline is already close. That means the reported Dice largely reflects the quality of the initial centerline plus a local refinement. There is no ablation that turns off the differentiable voxelization, no comparison to a classical distance-transform B-spline fit, no initialization-perturbation test. The MouseAneurysm note that stage 3 (centerline correction) does not improve fit further supports the view that the voxelization is a fine-tuner, not the primary driver. So the abstract's 'learn shape parameters from segmentations' is overstated for the general case; it is accurate for refining an already extracted centerline.\n\nOther gaps are real but secondary: TopCoW is restricted to direct-path vessels, branching is future work, and the final Dice threshold for the soft voxelization is not reported. The paper's own limitations section acknowledges the centerline initialization need, which I count in its favor.\n\nWho is this for? Someone building parametric vessel models or differentiable rasterization in 3D will get concrete value. The central claim needs an ablation before I would call it fully supported, but the method and the engineering are solid enough to deserve referee time.\n\nRecommendation: send it to review, with a request for an ablation isolating the voxelization loss and a classical baseline comparison. My own verdict would be conditional pending that.","headline":"A useful, well-engineered fitting pipeline whose core claim is softer than advertised: the differentiable voxelization is a local refinement over a centerline prior, not a standalone learner.","tokens_in":10914,"tokens_out":601,"would_cite":true,"duration_ms":8475,"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 parametric vessel model—centerline and radius as cubic B-splines—can be fitted to a segmentation end-to-end using a differentiable voxelization loss, without any ground-truth shape parameters.","keywords":["parametric vessel models","shape models","differentiable voxelization","3D vessels","centerline","mesh extraction","sparse annotation"],"falsifier":"On a synthetic tube with a known ground-truth centerline and radius, initialize the model from a centerline shifted by more than one voxel-radius and run the full four-stage fit; if the Dice score does not recover to the level reported for unperturbed initialization, the local-minimum limitation would be confirmed as a hard bound on the method's ability to learn shape from segmentation alone.","tokens_in":9753,"feed_emoji":"🫀","tokens_out":8331,"duration_ms":81215,"temperature":0.7,"pith_summary":"The paper proposes a way to turn a vessel segmentation into three linked representations—a parametric centerline-and-radius model, a triangle mesh, and a voxelized mask—connected by differentiable transformations. The central aim is to fit the shape parameters directly from the segmentation alone, without needing ground-truth centerlines or radii for supervision. Because the conversion from spline parameters to mesh to soft voxelization is differentiable, a neural network can adjust the parameters by backpropagating a Dice loss computed against the reference segmentation. On aortas, brain vessels, and mouse aortas with aneurysms, the fitted models achieve Dice scores of 94.66, 82.22, and 86.43 percent respectively while using meshes of only a few hundred vertices—over a hundredfold sparser than dense marching-cubes meshes. The practical payoff is a sparse, smooth, and editable vessel representation that retains the volumetric fidelity of dense segmentation.","feed_headline":"Segmentations alone yield editable spline vessel models","feed_subtitle":"A differentiable voxelization loss turns a mask into a sparse, smooth centerline-radius mesh without shape labels.","key_machinery":"The load-bearing mechanism is the differentiable voxelization loss: the parametric mesh is rasterized into a soft voxelized mask via a signed-distance field, and a Dice loss against the reference segmentation propagates gradients all the way back to the spline control points. To make this tractable in 3D, the signed-distance computation is sliced plane-by-plane: each slice is intersected with the mesh, the intersection graph is split into polygons by cycle detection, and occupancy and distance are computed with point-in-polygon tests. The parameters are cubic B-splines over centerline coordinates and radius, giving smoothness by construction, and a four-stage training scheme (centerline initialization, radius fit, centerline correction, radial adjustment) prevents the conflicting gradients that arise when the centerline and radius are optimized together.","core_discovery":"The central claim is that a parametric vessel model—a centerline and cross-sectional radii represented as cubic B-splines, together with optional per-radial-direction adjustments—can be fitted to a reference segmentation end-to-end by a neural network, with no ground-truth shape parameters. The fitting uses a differentiable voxelization of the mesh derived from the spline parameters; the voxelization is a soft signed-distance field, and a Dice loss between this soft field and the reference mask drives all parameter updates. The paper shows that this recipe works on real vessels: the fitted parametric models reproduce the volumetric shape of aortas, circle-of-Willis vessels, and aneurysmal mouse aortas at Dice scores of 94.66, 82.22, and 86.43 percent, while producing meshes that are over a hundredfold sparser than marching-cubes output at comparable fidelity. The paper also reports that the fitted centerline can correct a noisy reference centerline using only the shape supervision, and that the model remains accurate when supervision is reduced to 5 percent of the original segmentation slices.","pith_inferences":["The same fitting recipe should transfer to other tubular structures (e.g., airways, catheters, or neuronal processes) wherever a single non-branching centerline suffices; the branching case awaits a meshing step that handles bifurcations.","The decoupling of control-point count from sampling resolution suggests a multi-resolution capability: the same trained model could be evaluated at arbitrary mesh densities at inference time without retraining.","The locality of the signed-distance loss implies the method is best seen as a refinement stage; pairing it with a coarse, robust global initialization from any rough tube detector could make the pipeline fully automatic.","If the slice-wise signed-distance approximation were reimplemented directly on the GPU, the current minute-per-sample fitting cost could drop enough to make per-vessel online fitting practical in clinical workflows."],"forward_implications":["Vessel analysis can now use sparse, editable meshes of a few hundred vertices without giving up the volumetric fidelity of dense segmentation-based meshes.","The same differentiable pipeline lets a parametric model be fitted from very few annotated slices: using only 5% of the segmentation slices cost about 1% Dice, which could cut annotation effort for vessels.","Because the model is interpretable as centerline plus radius, it can be manipulated after fitting—for example, to adjust blood-flow cross-sections during surgical planning.","The end-to-end fitting removes the need for parametric ground truth, so any segmentation mask becomes a potential training signal for shape-model extraction.","The centerline-correction stage shows that noisy reference centerlines can be improved by shape evidence alone, pointing toward a fully automatic pipeline from image to parametric model."],"supporting_citations":[{"why":"supplies the differentiable polygonization loss that the 3D voxelization is built on.","marker":"[10]"},{"why":"provides the matrix formulation of cubic B-splines used to model centerline and radius.","marker":"[16]"},{"why":"gives the point-in-polygon test used to rasterize each slice in the signed-distance approximation.","marker":"[7]"},{"why":"defines the 3D network backbone that predicts the spline control points.","marker":"[6]"},{"why":"is the state-of-the-art segmentation baseline whose volumetric fit anchors the fidelity comparison.","marker":"[9]"},{"why":"is the marching-cubes baseline whose dense mesh is compared for sparsity and fit.","marker":"[11]"},{"why":"is the implicit-neural-representation baseline also compared for mesh quality and fidelity.","marker":"[18]"},{"why":"is the skeletonization tool that produces the initial centerline for the aorta dataset.","marker":"[20]"}],"fun_headline_variants":["Spline vessel models learned directly from segmentations","Differentiable voxelization turns masks into spline vessel meshes","No shape labels needed: learn spline vessels from segmentations","Editable spline vessel models from segmentations alone","Smooth vessel meshes learned without shape ground truth"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes a reasonably accurate initial centerline is already available, because the voxelization loss only moves the model toward the nearest boundary and cannot recover if the starting centerline is far from the target.","fun_headline_variants_meta":{"raw":{"variants":["Spline vessel models learned directly from segmentations","Differentiable voxelization turns masks into spline vessel meshes","No shape labels needed: learn spline vessels from segmentations","Editable spline vessel models from segmentations alone","Smooth vessel meshes learned without shape ground truth"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000705,"raw_usage":{"total_tokens":3175,"prompt_tokens":940,"completion_tokens":2235,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":556,"completion_tokens_details":{"reasoning_tokens":2155}},"tokens_in":556,"tokens_out":2235,"duration_ms":18463,"temperature":1.0,"reasoning_tokens":2155,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:26:34.125347+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a synthetic tube with a known ground-truth centerline and radius, initialize the model from a centerline shifted by more than one voxel-radius and run the full four-stage fit; if the Dice score does not recover to the level reported for unperturbed initialization, the local-minimum limitation would be confirmed as a hard bound on the method's ability to learn shape from segmentation alone.","supporting_citations":[{"cited_title":"In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (2022)","cited_arxiv_id":null,"evidence_quote":"supplies the differentiable polygonization loss that the 3D voxelization is built on."},{"cited_title":"Elsevier (2000)","cited_arxiv_id":null,"evidence_quote":"provides the matrix formulation of cubic B-splines used to model centerline and radius."},{"cited_title":"Web site: http://www","cited_arxiv_id":null,"evidence_quote":"gives the point-in-polygon test used to rasterize each slice in the signed-distance approximation."},{"cited_title":"In: Proceedings of the IEEE/CVF international conference on computer vision","cited_arxiv_id":null,"evidence_quote":"defines the 3D network backbone that predicts the spline control points."},{"cited_title":"In: International Conference on Medical Image Computing and Computer- Assisted Intervention (2024)","cited_arxiv_id":null,"evidence_quote":"is the state-of-the-art segmentation baseline whose volumetric fit anchors the fidelity comparison."},{"cited_title":"In: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH (1987)","cited_arxiv_id":null,"evidence_quote":"is the marching-cubes baseline whose dense mesh is compared for sparsity and fit."},{"cited_title":"PeerJ 2, e453 (2014)","cited_arxiv_id":null,"evidence_quote":"is the skeletonization tool that produces the initial centerline for the aorta dataset."}],"review_version":1}