PC-CAC: Coronary Artery Completion

• PC-CAC is a point cloud completion task that restores incomplete coronary artery geometries by rejoining fractured segments with anatomical fidelity.
• The method employs a hybrid representation combining aortic surface and coronary centerline points from real CTA data to capture both global context and fine vessel details.
• TSRNet, designed for sparse tubular structures, uses progressive refinement and a global-to-local loss to achieve robust reconnection even with high point removals.

Searching arXiv for the benchmark paper and closely related coronary reconstruction/completion work to ground the article in current literature. Point Cloud-based Coronary Artery Completion (PC-CAC) denotes both a task formulation and a benchmark for restoring fractured coronary artery geometry directly in the point cloud domain from incomplete coronary CTA-derived anatomical representations. In the formulation introduced by "Rethinking the Detail-Preserved Completion of Complex Tubular Structures based on Point Cloud: a Dataset and a Benchmark" (Qi et al., 25 Aug 2025), the input is an incomplete point cloud $$\mathbf{P} = \{\mathbf{p}_i \mid i=1,\dots,N\} \in \mathbb{R}^{N\times 3}$$, where each point $\mathbf{p}_i$ stores 3D coordinates $(x,y,z)$, and the objective is to predict a completed point set that restores missing coronary segments and reconnects fractured branches while preserving anatomical plausibility and fine tubular geometry. The benchmark is motivated by clinically important failure modes in coronary analysis—stenosis, complete occlusion, and myocardial bridging—which can obscure vessels in CTA and induce discontinuities in downstream segmentation, thereby degrading visualization, lesion assessment, topology-dependent quantification, and generation of patient-specific vascular geometry for simulation (Qi et al., 25 Aug 2025).

1. Definition and clinical motivation

PC-CAC reframes tubular structure reconnection or completion as a point cloud completion problem specialized to vascular anatomy (Qi et al., 25 Aug 2025). The task is not generic shape densification. It is specifically the recovery of anatomically continuous vessel paths under missing local support, including cases in which branch segments are absent, terminal regions break, bifurcations disconnect, and tortuous curved segments fragment.

The formulation is tied to coronary CTA. In this setting, severe stenosis, blockage or occlusion, and myocardial bridging can make coronary segments blurry or missing in CT angiography, causing segmentation algorithms to produce discontinuous vessels (Qi et al., 25 Aug 2025). These discontinuities matter because downstream tasks depend on anatomically continuous vessel trees, especially visual inspection, lesion detection, quantification, and patient-specific physical or hemodynamic modeling.

The problem differs from generic point cloud completion in several respects. First, point distribution is highly imbalanced: the representation contains both the aorta and coronary arteries, while large regions such as the aortic surface dominate point counts and the clinically important coronary branches are thin, elongated, and sparsely represented (Qi et al., 25 Aug 2025). Second, global topology is substantially harder than in common object completion benchmarks because coronary trees are long, curvilinear, branching, and highly variable across patients. Third, reconnection is not merely surface completion; it requires continuity, curvature preservation, branch connectivity, and thin-structure fidelity.

This emphasis on continuity aligns PC-CAC with contemporaneous topology-preserving coronary extraction and vectorized reconstruction research. "A topology-preserving three-stage framework for fully-connected coronary artery extraction" (Qiu et al., 2 Apr 2025) treats coronary recovery as vessel segmentation, centerline reconnection, and missing vessel reconstruction, while "Segmentation and Vascular Vectorization for Coronary Artery by Geometry-based Cascaded Neural Network" (Yang et al., 2023) addresses fragmented coronary segmentation by learning continuous geometric representations. PC-CAC differs in that its primary representation and target are point clouds rather than voxel masks or meshes.

2. Dataset construction and benchmark protocol

PC-CAC is described as the first dedicated point-cloud benchmark for coronary artery completion or reconnection, derived from real clinical coronary artery data from 427 patients, yielding 3,416 cases in total (Qi et al., 25 Aug 2025). The CT images were scanned on a SOMATOM Definition Flash, with contrast media injected during scanning. Reported imaging properties are $0.25 \sim 0.57$ mm/voxel in $x/y$ resolution, $0.75 \sim 3$ mm/voxel slice thickness, $512$ voxels in $x/y$ image size, and $128 \sim 994$ voxels in the $z$-direction (Qi et al., 25 Aug 2025).

Preprocessing standardizes the image volumes before segmentation and point conversion. All images are resampled to $\mathbf{p}_i$0, grayscale values are thresholded to $\mathbf{p}_i$1, and intensities are normalized to $\mathbf{p}_i$2 (Qi et al., 25 Aug 2025). The manuscript prints a normalization expression,

$\mathbf{p}_i$3

but also states textually that thresholding is to $\mathbf{p}_i$4 followed by normalization to $\mathbf{p}_i$5; this indicates a reporting inconsistency in the printed formula rather than a change in the described preprocessing.

The dataset is not synthesized from generic CAD models. It is derived from real segmentation results from coronary CTA, explicitly preserving clinically realistic artifacts such as fractures, under-segmentation, and other imperfections (Qi et al., 25 Aug 2025). The paper states that input point clouds originate from real segmentation results using methods such as nnU-Net and the authors’ previous segmentation model. To make the benchmark more challenging and systematic, fractures are additionally simulated in damage-prone regions including bifurcations, tortuous structures, and random fracture locations, with noise also introduced (Qi et al., 25 Aug 2025). This combination of real segmentation failure patterns with controlled synthetic removal is central to the benchmark design.

The voxel-to-point-cloud conversion is distinctive. Cavities in coronary voxels are eliminated using morphological dilation and erosion with a spherical structuring element; a centerline point cloud is extracted for the coronary arteries; and a surface point cloud is extracted for the aorta using Marching Cubes followed by Farthest Point Sampling (FPS) (Qi et al., 25 Aug 2025). The final point cloud combines aortic surface points and coronary centerline points. The coronary main trunk is further extracted by removing irrelevant branches and computing shortest paths between endpoint pairs, then taking unions of these paths.

Ground truth $\mathbf{p}_i$6 is defined as the union of the complete aorta surface point cloud and the complete coronary trunk point cloud, whereas input $\mathbf{p}_i$7 is a fractured version in which points are removed from the coronary arteries while the aorta remains unchanged (Qi et al., 25 Aug 2025). Specifically, 10%–30% of the coronary artery points are removed and the aortic structure remains unchanged. Fracture simulation is constrained so that deletions actually induce disconnections.

The dataset split is fixed by patient:

Split	Patients	Cases
Training	300	2,400
Validation	40	320
Testing	87	696

Each patient generates 8 distinct input cases, giving $\mathbf{p}_i$8 total cases (Qi et al., 25 Aug 2025). Each point cloud contains 4,096 points in total: 3,072 for the aorta and 1,024 for the coronary arteries. The representation uses only 3D coordinates, without reported normals, radii, intensities, or branch labels, and coordinates are normalized to $\mathbf{p}_i$9 after centroid subtraction and scaling (Qi et al., 25 Aug 2025).

A key benchmark protocol choice is that evaluation is performed on the coronary arteries alone. The paper states that this is done to ignore inflated metrics caused by the high number of points in the aorta (Qi et al., 25 Aug 2025). This design makes the benchmark specifically sensitive to recovery of the sparse, thin, clinically relevant vessel component rather than the unchanged dominant structure.

3. Representation and task-specific challenges

The PC-CAC representation is hybrid: the aorta is modeled by surface geometry, whereas the coronary arteries are modeled by centerline geometry (Qi et al., 25 Aug 2025). This is not a full-surface coronary reconstruction benchmark. Instead, it encodes global cardiovascular context via the aorta and clinically important vessel paths via coronary centerlines.

This choice reflects a task-specific bias. Because the coronary completion target occupies only one quarter of the total points, the benchmark reproduces the imbalance that motivates specialized modeling (Qi et al., 25 Aug 2025). Generic point cloud completion methods may preferentially reconstruct large, easy structures, whereas the clinically relevant objective lies in sparse branches, distal segments, bifurcations, and curved regions.

The task therefore combines three technical requirements. One is density-aware feature extraction under severe imbalance. Another is preservation of long-range topology across elongated branching trees. The third is detail preservation in sparse regions where distal branches, thin vessels, and fracture-prone structures lie (Qi et al., 25 Aug 2025). This suggests that coronary completion is closer to structure-aware reconnection than to conventional object completion.

Related non-point-cloud research reinforces this interpretation. CorSegRec explicitly separates centerline reconnection from missing vessel reconstruction (Qiu et al., 2 Apr 2025), and the geometry-based cascaded network of Tang et al. emphasizes vectorized branch-wise surface generation to avoid fragmented voxel outputs (Yang et al., 2023). Earlier CTA-based reconstruction work also places centerlines at the center of coronary geometry recovery: "3D Reconstruction of Coronary Arteries and Atherosclerotic Plaques based on Computed Tomography Angiography Images" (Kigka et al., 2019) uses centerline extraction, shape-prior-constrained level sets, and Marching Cubes to recover lumen, outer wall, and calcified plaque surfaces. In PC-CAC, these neighboring lines of work function primarily as background on continuity, topology, and geometry generation rather than as direct methodological equivalents.

4. TSRNet architecture and optimization

The dedicated baseline proposed with PC-CAC is TSRNet, the Tubular Structure Reconnection Network, designed specifically for fractured tubular structures (Qi et al., 25 Aug 2025). Its architecture has two main stages—a Detail-preserved Feature Extractor and a Multiple Dense Refinement Strategy—trained jointly with a Global-to-Local Loss Function.

The network takes an incomplete point cloud

$(x,y,z)$0

A sparse but informative core point set is selected by the Core Points Selection module: $(x,y,z)$1 where $(x,y,z)$2 denotes dense-region points, $(x,y,z)$3 denotes sparse-region points, and $(x,y,z)$4 (Qi et al., 25 Aug 2025). CPS uses FPS as a base mechanism but imposes three constraints: simultaneous selection in separate dense and sparse regions, region-restricted point selection, and priority on end and isolated points. This modifies ordinary FPS to preserve sparse coronary structures and fracture-relevant endpoints.

Feature extraction is then performed by TransSA, which interleaves Set Abstraction (SA) for local grouping and aggregation with Transformer blocks for attention-based contextual modeling (Qi et al., 25 Aug 2025). The paper expresses the module as

$(x,y,z)$5

Despite formatting issues, the intended operations are explicit: local neighborhoods are built with K-Nearest Neighbors, local features are aggregated with PointNet, and Transformer self-attention captures longer-range dependencies (Qi et al., 25 Aug 2025). The best setting in ablation uses 2 stacked SA+Transformer blocks; 4 or 8 blocks degrade performance.

Refinement is progressive. TSRNet reconstructs $(x,y,z)$6 as a coarse output and then $(x,y,z)$7 as a dense or final output (Qi et al., 25 Aug 2025). Within each Refine Module, coordinates $(x,y,z)$8 are fused with feature $(x,y,z)$9, processed by an MLP, passed through three rounds of Self-Attention to produce $0.25 \sim 0.57$0, while $0.25 \sim 0.57$1 is processed in parallel by another MLP to produce $0.25 \sim 0.57$2; the two are concatenated and mapped by an MLP to the refined output $0.25 \sim 0.57$3 (Qi et al., 25 Aug 2025). The first refinement stage addresses major discontinuities and the second enhances detail in minute vascular structures.

Optimization is driven by a thresholded global-to-local loss. The global loss is

$0.25 \sim 0.57$4

The local sparse-region loss is

$0.25 \sim 0.57$5

The total objective is

$0.25 \sim 0.57$6

where $0.25 \sim 0.57$7 determines when the model transitions from purely global supervision to joint global and sparse-region supervision, and $0.25 \sim 0.57$8 balances the two terms (Qi et al., 25 Aug 2025).

This schedule makes early training globally driven and later training sparse-region-aware. In coronary completion, that is consequential because thin distal branches and fracture-prone structures are underrepresented in the raw point distribution. The implementation is in PyTorch, trained on GeForce RTX 2080 Ti GPUs with Adam and initial learning rate $0.25 \sim 0.57$9 (Qi et al., 25 Aug 2025). The paper reports $x/y$0 and $x/y$1 in the implementation details, but a hyperparameter table reports best results with $x/y$2, $x/y$3, and 2 SA+Transformer blocks, indicating a scale or reporting inconsistency in the manuscript (Qi et al., 25 Aug 2025).

5. Evaluation results and empirical profile

The PC-CAC evaluation compares TSRNet with generic or state-of-the-art point cloud completion methods—GRNet, PoinTr, SeedFormer, SnowflakeNet, AnchorFormer, PointAttN, and CRA-PCN—as well as voxel-based vascular reconstruction methods such as DRTT and VSR-Net (Qi et al., 25 Aug 2025). Reported metrics are $x/y$4 Chamfer Distance $x/y$5, F1-score, and Fidelity Error.

On PC-CAC, TSRNet achieves the best results across all reported metrics (Qi et al., 25 Aug 2025):

Method	$x/y$6	F1 (\%) $x/y$7	Fidelity $x/y$8
GRNet	32.683 ± 9.488	32.60 ± 4.95	52.549 ± 17.918
PoinTr	4.452 ± 0.896	87.98 ± 10.76	4.335 ± 1.634
SeedFormer	4.139 ± 1.286	93.41 ± 2.84	3.598 ± 1.368
SnowflakeNet	5.661 ± 1.661	88.11 ± 3.37	5.816 ± 2.365
AnchorFormer	6.747 ± 0.871	83.11 ± 7.32	6.178 ± 0.845
PointAttN	8.288 ± 1.348	67.22 ± 4.47	6.660 ± 2.488
CRA-PCN	5.869 ± 1.100	88.75 ± 3.87	6.245 ± 2.171
TSRNet	3.783 ± 1.456	94.58 ± 2.28	3.318 ± 1.768

Compared with the second-best point cloud baseline, SeedFormer, TSRNet improves $x/y$9 from 4.139 to 3.783, improves F1 from 93.41% to 94.58%, and improves Fidelity from 3.598 to 3.318 (Qi et al., 25 Aug 2025). The paper interprets these gains as evidence that tailoring architecture and loss design to sparse tubular structures matters.

Qualitative analysis emphasizes smoother and more complete reconnection of fractured coronary segments, better preservation of thin elongated branches, fewer structural distortions in curved or tortuous anatomy, and fewer false reconnections or new fractures in originally intact regions (Qi et al., 25 Aug 2025). PointAttN and CRA-PCN are reported to struggle with curved structures and may fracture intact regions, while PoinTr restores overall structure but does not focus enough on elongated tubular detail. SeedFormer, SnowflakeNet, and AnchorFormer are described as stronger but still prone to distortions, incomplete connections, or incorrect reconstructions.

Robustness under increasing fracture severity is a central benchmark result. On PC-CAC, the model is tested with 10%, 20%, and 30% removed coronary points (Qi et al., 25 Aug 2025). As severity increases, competing methods degrade substantially in $0.75 \sim 3$0, F1, and Fidelity, whereas TSRNet remains consistently best. The paper’s qualitative examples characterize 10% removal as a single fracture in a complex elongated region, 20% as multiple fractures at thin structures and bifurcations, and 30% as near-total fragmentation of the primary trunk, leaving scattered points. The reported behavior suggests that TSRNet’s advantage is most pronounced exactly where coronary completion is clinically fragile: bifurcations, distal terminals, and highly tortuous segments.

The paper also evaluates TSRNet on PC-ImageCAS and PC-PTR for cross-dataset context. PC-ImageCAS is derived from the public ImageCAS coronary artery segmentation dataset and contains 1,000 patients and 8,000 cases, while PC-PTR is derived from a pulmonary artery dataset with 799 patients, 6,392 cases, 8,192 points per sample, and simulated 5%–15% point removal (Qi et al., 25 Aug 2025). PC-CAC remains the only benchmark among them specifically designed as a point cloud coronary artery completion benchmark derived from real clinical data with realistic segmentation imperfections and explicit fracture simulation.

6. Relation to broader coronary reconstruction research

PC-CAC sits at the intersection of point cloud completion, topology-preserving vascular recovery, and coronary geometry reconstruction. Its closest direct contribution is the introduction of a point-cloud-native task and dataset (Qi et al., 25 Aug 2025). However, its conceptual background is broader.

CorSegRec (Qiu et al., 2 Apr 2025) addresses fully-connected coronary artery extraction from CTA through three stages: vessel segmentation, centerline reconnection, and missing vessel reconstruction. Its centerline reconnection stage uses a DPC walk that integrates a distance term, a centerline-probability term predicted by a classifier, and a directional cosine term. Its reconstruction stage applies an INR-based luminal contour extraction model and implicit extrusion surfaces to reconstruct missing vessel geometry (Qiu et al., 2 Apr 2025). Although the method is voxel- and image-driven rather than point-cloud-based, it establishes an explicit decomposition between topology repair and geometry reconstruction. A plausible implication is that PC-CAC methods may benefit from similar decoupling, especially when long-gap reconnection and local geometry recovery present different failure modes.

The geometry-based cascaded neural network of Tang et al. (Yang et al., 2023) addresses fragmented coronary segmentation through vascular vectorization. It reconstructs branch meshes using skeletonization, cubic B-spline centerlines sampled every 0.2 mm, cross-sectional ray sampling every $0.75 \sim 3$1, 1D Gaussian filtering of radii, and branch integration by mesh boolean union (Yang et al., 2023). The resulting vectorized geometry avoids adhesion between closely adjacent branches, reduces point dispersion in tiny branches, and achieves NoS $0.75 \sim 3$2 on both CCA-200 and ASOCA, where NoS counts the number of connected vessel components (Yang et al., 2023). This line of work is not completion in the strict PC-CAC sense, but it emphasizes that topology and smoothness are easier to preserve in vectorized geometry than in pure voxel occupancy.

Earlier CTA-based reconstruction methodology also informs the field. The semi-automated pipeline of (Kigka et al., 2019) reconstructs lumen, outer wall, and calcified plaque from CTA using vesselness filtering, centerline extraction by minimum cost path, level set segmentation with shape priors, and Marching Cubes. It reports a mean Dice coefficient of 0.749 and mean Hausdorff distance of 1.746 against expert manual annotations, and correlation coefficients of 0.79, 0.77, 0.75, 0.85, and 0.81 for DS1, DS2, plaque burden, MLA, and MLD, respectively, against IVUS-based reconstruction (Kigka et al., 2019). For PC-CAC, the importance of this work lies less in its direct applicability and more in its clinically meaningful geometric outputs and metrics, which could function as supervision or downstream validation targets.

Taken together, these neighboring approaches show that coronary completion can be interpreted at three levels: voxel extraction, centerline or topology repair, and geometric reconstruction. PC-CAC distinguishes itself by defining the problem natively in the point cloud domain and benchmarking completion directly on coronary geometry rather than on volumetric masks (Qi et al., 25 Aug 2025).

7. Strengths, limitations, and future directions

The principal contribution of PC-CAC is task redefinition. It formalizes coronary reconnection as a point cloud completion problem and provides a clinically grounded benchmark built from real coronary CTA data and real segmentation outputs while preserving authentic imperfections (Qi et al., 25 Aug 2025). Its representation combines aortic surface points with coronary centerline points, thereby encoding both global anatomical context and clinically relevant vessel paths. TSRNet further contributes an architecture whose components are explicitly aligned with the task’s failure modes: CPS for sparse-branch underrepresentation, coarse-to-fine dense refinement for reconnection, and global-to-local loss for sparse-region emphasis (Qi et al., 25 Aug 2025).

The paper does not present a separate limitations section, but several constraints are explicit or implied. It provides no hard graph or topology constraint, so there is no guarantee of anatomically correct connectivity even though continuity and structural integrity are targeted (Qi et al., 25 Aug 2025). Dataset construction depends on segmentation quality, cavity removal, centerline extraction, branch pruning, and normalization, so errors in the preprocessing pipeline may affect benchmark quality. The mixed aorta-surface and coronary-centerline representation is practical but does not make PC-CAC a full-surface coronary reconstruction benchmark. Some implementation details necessary for exact reproduction—such as KNN $0.75 \sim 3$3, feature widths, batch size, epochs, and training schedule—are omitted from the manuscript. Finally, although the data originate from real clinical cases, controlled point removal still plays a large role in generating incomplete inputs, which may not capture all real failure modes (Qi et al., 25 Aug 2025).

Common misconceptions arise at this point. PC-CAC is not a generic object completion benchmark applied to medical data, because its core challenge lies in sparse thin-branch preservation, bifurcation fidelity, and anatomically plausible long-gap reconnection (Qi et al., 25 Aug 2025). Nor is it equivalent to CTA segmentation. Segmentation seeks vessel occupancy in voxel space, whereas PC-CAC assumes a fractured point cloud representation and asks for restoration of continuous coronary geometry. It is also not synonymous with full coronary surface reconstruction, since the benchmark uses coronary centerline points rather than full coronary surface points.

The work points toward several research directions already implied in the paper. Future studies may investigate topology-aware completion, multimodal image-plus-point-cloud fusion, centerline-surface joint reconstruction, uncertainty-aware reconnection, and branch-consistent or graph-constrained generation (Qi et al., 25 Aug 2025). This suggests that the current benchmark functions not only as an evaluation protocol but also as a scaffold for integrating geometric priors from coronary extraction, vectorized reconstruction, and clinically grounded 3D modeling into point-cloud-native completion systems.

In its present form, PC-CAC establishes a reference setting for completion of fractured coronary anatomy in point cloud form, and TSRNet provides the baseline against which subsequent work can be measured. On PC-CAC, that reference performance is $0.75 \sim 3$4, F1 $0.75 \sim 3$5, and Fidelity $0.75 \sim 3$6 (Qi et al., 25 Aug 2025).