PPCAR-Net: Projection-Refined Parametric 3D Coronary Artery Reconstruction from Sparse X-ray Angiographic Views

Yu Ren; Hwee Kuan Lee; Tat-Jen Cham; Jonathan Yap; Khung Keong Yeo

cs.CVOct 7, 2026

PPCAR-Net: Projection-Refined Parametric 3D Coronary Artery Reconstruction from Sparse X-ray Angiographic Views

Authors: Yu Ren, Hwee Kuan Lee, Tat-Jen Cham, Jonathan Yap, Khung Keong Yeo

Organizations: Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR) · College of Computing and Data Science, Nanyang Technological University · National Heart Centre Singapore

Abstract

Sparse-view 3D coronary reconstruction commonly relies on cross-view correspondence and triangulation, which are vulnerable to vessel overlap and foreshortening, or on volumetric prediction followed by vascular-graph extraction, which does not directly provide centrelines and radii. We introduce PPCAR-Net, a projection-refined parametric coronary artery reconstruction network that directly predicts a branch-structured centreline-and-radius representation without explicit point matching, triangulation, or an intermediate volume. Given a variable number of segmented views, a coarse predictor combines frozen VGGT features with learned branch queries to estimate branch presence, B-spline centreline trajectories, and dense radius profiles. Projection-guided geometry and radius refiners then sample local evidence from the input views and apply residual corrections learned with 3D supervision. We evaluate representation fidelity and sparse-view reconstruction quantitatively and qualitatively. On simulated angiographic masks generated from CT-derived coronary anatomy, PPCAR-Net produces better connected artery reconstructions and achieves strong centreline accuracy, particularly for RCA, while maintaining competitive volumetric overlap. Coarse-to-fine inference takes 121 ms, enabling real-time reconstruction.

Figures & tables

Method	Number of input views	Output representation	Output			Per-case runtime $\downarrow$
			3D volume	Connected centreline	Radius
Iyer et al. (2023)	2 or 3	Dense centreline points and radii	$\bm{\checkmark}$	$\bm{\checkmark}$	$\bm{\checkmark}$	–
NeRF-CA ( Maas et al., 2025 )	$\geq 4$	Novel 2D views	$\bm{\times}$	$\bm{\times}$	$\bm{\times}$	–
NerT-CA ( Maas et al., 2026 )	$\geq 3$	Novel 2D views	$\bm{\times}$	$\bm{\times}$	$\bm{\times}$	–
SDF-CAR ( Reda et al., 2026 )	2	3D implicit SDF field	$\bm{\checkmark}$	$\bm{\times}$	$\bm{\times}$	45 min
3DGR-CAR ( Fu et al., 2024 )	$\geq 2$	3D Gaussian primitives	$\bm{\checkmark}$	$\bm{\times}$	$\bm{\times}$	63.7 s

Table 1: Comparison of learning-based coronary artery reconstruction methods. Per-case runtime is the complete time required to reconstruct one 3D artery from two input views, including vascular-graph extraction when applicable.

Figure 1: Coronary trees and vessel code representation. (A) Schematic RCA tree showing the right coronary artery (RCA), posterolateral branch (PLB), posterior descending artery (PDA), and acute marginal branch (AM); (B) Schematic LCA tree showing the left main (LM), left anterior descending (LAD), and left circumflex (LCX) arteries; (C) Dense centreline $\bm{c}_{m,n}$ and radius $r_{m,n}$ representation of a branch; (D) B-spline representation of the centreline of branch $m$ with dark-blue points denoting B-spline control points $\bm{p}_{m,j}$ and the light-blue centreline that they define.

Figure 2: Flexible-view coarse parametric predictor in PPCAR-Net: (A) Frozen VGGT features are concatenated ( $\oplus$ ) with encoded acquisition directions to form the multiview memory $\bm{E}_{\mathrm{view}}$ . (B) Trainable branch queries cross-attend to this memory, and the existence, control-point, and radius heads produce the coarse vessel code $\hat{\bm{V}}^{(0)}$ . Fire and snowflake symbols denote trainable and frozen modules, respectively.

Figure 3: Recursive projection-guided refinement in PPCAR-Net. The B-spline geometry refiner uses local multiview evidence to predict residual updates to the coarse control points. With the refined centreline fixed, the dense-radius refiner then updates the pointwise radii. The two refiners are trained sequentially and separately, using $\mathcal{L}_{\mathrm{geom\text{-}ref}}$ and $\mathcal{L}_{\mathrm{rad\text{-}ref}}$ , respectively.

Method	One view				Two views				Four views
	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$
3DGR-CAR ( Fu et al., 2024 )	$\underline{22.18}$ [-0.2ex] $(\pm 0.65)$	$\underline{22.35}$ [-0.2ex] $(\pm 0.73)$	$\underline{10.11}$ [-0.2ex] $(\pm 0.44)$	$72.77$ [-0.2ex] $(\pm 12.08)$	$37.32$ [-0.2ex] $(\pm 0.91)$	$39.47$ [-0.2ex] $(\pm 1.09)$	$7.72$ [-0.2ex] $(\pm 0.48)$	$159.62$ [-0.2ex] $(\pm 16.84)$	$\underline{44.33}$ [-0.2ex] $(\pm 1.12)$	$\underline{46.54}$ [-0.2ex] $(\pm 1.31)$	$\underline{7.37}$ [-0.2ex] $(\pm 0.49)$	$216.25$ [-0.2ex] $(\pm 17.95)$
AutoCAR ( Zhu et al., 2025 )	–	–	–	–	$\mathbf{68.76}$ [-0.2ex] $(\pm 0.70)$	$\underline{79.13}$ [-0.2ex] $(\pm 1.37)$	$\underline{3.24}$ [-0.2ex] $(\pm 0.27)$	$3.35$ [-0.2ex] $(\pm 0.31)$	–	–	–	–
DeepCA ( Wang et al., 2025b )	–	–	–	–	$63.49$ [-0.2ex] $(\pm 1.56)$	$78.00$ [-0.2ex] $(\pm 1.73)$	$3.78$ [-0.2ex] $(\pm 0.51)$	$4.41$ [-0.2ex] $(\pm 0.60)$	–	–	–	–
PPCAR-Net (coarse)	$15.73$ [-0.2ex] $(\pm 1.46)$	$16.43$ [-0.2ex] $(\pm 1.84)$	$11.86$ [-0.2ex] $(\pm 0.59)$	$\underline{1.324}$ [-0.2ex] $(\pm 0.072)$	$19.47$ [-0.2ex] $(\pm 1.12)$	$20.40$ [-0.2ex] $(\pm 1.56)$	$9.70$ [-0.2ex] $(\pm 0.41)$	$\underline{1.324}$ [-0.2ex] $(\pm 0.064)$	$21.45$ [-0.2ex] $(\pm 1.26)$	$22.88$ [-0.2ex] $(\pm 1.70)$	$9.16$ [-0.2ex] $(\pm 0.36)$	$\underline{1.284}$ [-0.2ex] $(\pm 0.059)$
PPCAR-Net (refined)	$\mathbf{27.37}$ [-0.2ex] $(\pm 1.86)$	$\mathbf{32.38}$ [-0.2ex] $(\pm 2.56)$	$\mathbf{9.39}$ [-0.2ex] $(\pm 0.55)$	$\mathbf{1.081}$ [-0.2ex] $(\pm 0.032)$	$\underline{66.92}$ [-0.2ex] $(\pm 1.50)$	$\mathbf{80.62}$ [-0.2ex] $(\pm 1.92)$	$\mathbf{3.16}$ [-0.2ex] $(\pm 0.27)$	$\mathbf{1.054}$ [-0.2ex] $(\pm 0.026)$	$\mathbf{73.05}$ [-0.2ex] $(\pm 1.25)$	$\mathbf{88.54}$ [-0.2ex] $(\pm 1.45)$	$\mathbf{2.12}$ [-0.2ex] $(\pm 0.19)$	$\mathbf{1.014}$ [-0.2ex] $(\pm 0.014)$

Table 2: RCA reconstruction from one, two, and four input views. CD denotes Chamfer distance, and CC count denotes connected-component count. Values are mean

\pm

standard error. The best result is shown in bold and the second-best result is underlined . – denotes a view-count setting that is not reported in the corresponding paper.

Method	One view				Two views				Four views
	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$
3DGR-CAR ( Fu et al., 2024 )	$\mathbf{26.51}$ [-0.2ex] $(\pm 0.51)$	$\mathbf{26.48}$ [-0.2ex] $(\pm 0.56)$	$\mathbf{8.25}$ [-0.2ex] $(\pm 0.17)$	$46.43$ [-0.2ex] $(\pm 3.54)$	$35.05$ [-0.2ex] $(\pm 0.48)$	$37.16$ [-0.2ex] $(\pm 0.54)$	$\mathbf{5.87}$ [-0.2ex] $(\pm 0.11)$	$76.10$ [-0.2ex] $(\pm 8.06)$	$\underline{43.64}$ [-0.2ex] $(\pm 0.66)$	$\underline{47.81}$ [-0.2ex] $(\pm 0.75)$	$\mathbf{4.94}$ [-0.2ex] $(\pm 0.20)$	$100.88$ [-0.2ex] $(\pm 11.59)$
AutoCAR ( Zhu et al., 2025 )	–	–	–	–	$46.89$ [-0.2ex] $(\pm 1.29)$	$\underline{63.00}$ [-0.2ex] $(\pm 1.59)$	$6.13$ [-0.2ex] $(\pm 0.38)$	$11.36$ [-0.2ex] $(\pm 0.78)$	–	–	–	–
DeepCA ( Wang et al., 2025b )	–	–	–	–	$\mathbf{56.56}$ [-0.2ex] $(\pm 0.81)$	$\mathbf{71.20}$ [-0.2ex] $(\pm 1.11)$	$6.66$ [-0.2ex] $(\pm 0.24)$	$9.97$ [-0.2ex] $(\pm 0.32)$	–	–	–	–
PPCAR-Net (coarse)	$11.15$ [-0.2ex] $(\pm 0.76)$	$10.10$ [-0.2ex] $(\pm 0.81)$	$14.08$ [-0.2ex] $(\pm 0.51)$	$\underline{1.829}$ [-0.2ex] $(\pm 0.118)$	$14.92$ [-0.2ex] $(\pm 0.77)$	$13.94$ [-0.2ex] $(\pm 0.90)$	$12.37$ [-0.2ex] $(\pm 0.51)$	$\underline{1.605}$ [-0.2ex] $(\pm 0.097)$	$14.59$ [-0.2ex] $(\pm 0.73)$	$14.05$ [-0.2ex] $(\pm 0.93)$	$12.46$ [-0.2ex] $(\pm 0.49)$	$\underline{1.618}$ [-0.2ex] $(\pm 0.095)$
PPCAR-Net (refined)	$\underline{19.73}$ [-0.2ex] $(\pm 1.00)$	$\underline{21.36}$ [-0.2ex] $(\pm 1.19)$	$\underline{11.31}$ [-0.2ex] $(\pm 0.45)$	$\mathbf{1.197}$ [-0.2ex] $(\pm 0.050)$	$\underline{49.45}$ [-0.2ex] $(\pm 1.32)$	$61.30$ [-0.2ex] $(\pm 1.93)$	$\underline{5.98}$ [-0.2ex] $(\pm 0.47)$	$\mathbf{1.053}$ [-0.2ex] $(\pm 0.026)$	$\mathbf{53.45}$ [-0.2ex] $(\pm 1.28)$	$\mathbf{67.43}$ [-0.2ex] $(\pm 1.93)$	$\underline{5.30}$ [-0.2ex] $(\pm 0.42)$	$\mathbf{1.039}$ [-0.2ex] $(\pm 0.022)$

Table 3: LCA reconstruction from one, two, and four input views. CD denotes Chamfer distance, and CC count denotes connected-component count. Values are mean

\pm

standard error. The best result is shown in bold and the second-best result is underlined . – denotes a view-count setting that is not reported in the corresponding paper.

Reconstruction stage	RCA				LCA				Post-coarse time $\downarrow$
	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$
Coarse prediction	$19.47$ [-0.2ex] $(\pm 1.12)$	$20.40$ [-0.2ex] $(\pm 1.56)$	$9.70$ [-0.2ex] $(\pm 0.41)$	$1.324$ [-0.2ex] $(\pm 0.064)$	$14.92$ [-0.2ex] $(\pm 0.77)$	$13.94$ [-0.2ex] $(\pm 0.90)$	$12.37$ [-0.2ex] $(\pm 0.51)$	$1.605$ [-0.2ex] $(\pm 0.097)$	–
Direct per-scene optimisation	$41.02$ [-0.2ex] $(\pm 1.62)$	$50.02$ [-0.2ex] $(\pm 2.24)$	$6.65$ [-0.2ex] $(\pm 0.39)$	$1.243$ [-0.2ex] $(\pm 0.057)$	$28.75$ [-0.2ex] $(\pm 1.12)$	$33.16$ [-0.2ex] $(\pm 1.51)$	$9.29$ [-0.2ex] $(\pm 0.50)$	$1.421$ [-0.2ex] $(\pm 0.073)$	11 s
Learned geometry refiner	$\underline{65.89}$ [-0.2ex] $(\pm 1.44)$	$\mathbf{80.84}$ [-0.2ex] $(\pm 1.90)$	$\mathbf{3.16}$ [-0.2ex] $(\pm 0.27)$	$\underline{1.068}$ [-0.2ex] $(\pm 0.029)$	$\underline{48.43}$ [-0.2ex] $(\pm 1.29)$	$\mathbf{61.38}$ [-0.2ex] $(\pm 1.93)$	$\mathbf{5.98}$ [-0.2ex] $(\pm 0.47)$	$\mathbf{1.053}$ [-0.2ex] $(\pm 0.026)$	14 ms
Learned geometry and radius refiners	$\mathbf{66.92}$ [-0.2ex] $(\pm 1.50)$	$\underline{80.62}$ [-0.2ex] $(\pm 1.92)$	$\underline{3.16}$ [-0.2ex] $(\pm 0.27)$	$\mathbf{1.054}$ [-0.2ex] $(\pm 0.026)$	$\mathbf{49.45}$ [-0.2ex] $(\pm 1.32)$	$\underline{61.30}$ [-0.2ex] $(\pm 1.93)$	$\underline{5.98}$ [-0.2ex] $(\pm 0.47)$	$\underline{1.053}$ [-0.2ex] $(\pm 0.026)$	61 ms

Table 4: Refinement ablation in PPCAR-Net from a common two-view coarse initialisation. CD denotes Chamfer distance, and CC count denotes connected-component count. Values are mean

\pm

standard error; post-coarse time excludes the shared coarse prediction. The best result is shown in bold and the second-best result is underlined .

Figure 4: Qualitative two-view reconstruction. Columns show the input masks, 3D label, and the method outputs; rows show three RCA cases and three LCA cases, each rendered from two viewpoints. Arrows mark branches poorly visible in the input projections.

Figure 5: Qualitative reconstruction with PPCAR-Net on diseased CT anatomy and real X-ray angiography. (A) A diseased ASOCA ( Gharleghi et al., 2023 ) case with a visually identified region of local artery narrowing. The 3D label, simulated masks, and radius-coloured coarse and refined predictions are shown. (B) A real two-view X-ray angiography case from the AutoCAR dataset ( Zhu et al., 2025 ) . The middle column overlays the prediction on each angiographic view, and the final column shows the radius-coloured 3D prediction.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

View	RCA anchor	LCA anchor
1	LAO $40^{\circ}$ , CRA $10^{\circ}$	RAO $25^{\circ}$ , CAU $35^{\circ}$
2	RAO $75^{\circ}$ , CRA $10^{\circ}$	LAO $5^{\circ}$ , CAU $30^{\circ}$
3	AP, CRA $25^{\circ}$	AP, CAU $10^{\circ}$
4	RAO $20^{\circ}$ , CRA $20^{\circ}$	RAO $40^{\circ}$ , CRA $25^{\circ}$
5	LAO $20^{\circ}$	LAO $20^{\circ}$ , CRA $30^{\circ}$
6	RAO $75^{\circ}$ , CAU $20^{\circ}$	LAO $40^{\circ}$ , CRA $20^{\circ}$

Appendix

Table 5: Clinical acquisition-direction anchors used to generate the seven candidate projections for each artery. Each entry reports the primary RAO/LAO rotation followed by the secondary CRA/CAU angulation.

$K_{\mathrm{cp}}$	Centreline fitting error (mm) $\downarrow$				Vessel clDice (%) $\uparrow$
	RCA	LM–LAD	LCX	Overall	RCA	LM–LAD	LCX	Overall
8	$1.18$ [-0.2ex] $(\pm 0.72)$	$0.65$ [-0.2ex] $(\pm 0.40)$	$0.81$ [-0.2ex] $(\pm 0.38)$	$0.95$ [-0.2ex] $(\pm 0.60)$	$86.21$ [-0.2ex] $(\pm 17.91)$	$96.98$ [-0.2ex] $(\pm 7.11)$	$92.78$ [-0.2ex] $(\pm 9.66)$	$90.55$ [-0.2ex] $(\pm 14.21)$
12	$0.56$ [-0.2ex] $(\pm 0.41)$	$0.31$ [-0.2ex] $(\pm 0.21)$	$0.46$ [-0.2ex] $(\pm 0.26)$	$0.47$ [-0.2ex] $(\pm 0.33)$	$97.35$ [-0.2ex] $(\pm 6.61)$	$99.47$ [-0.2ex] $(\pm 2.24)$	$98.01$ [-0.2ex] $(\pm 4.45)$	$98.04$ [-0.2ex] $(\pm 5.08)$
20	$0.19$ [-0.2ex] $(\pm 0.13)$	$0.11$ [-0.2ex] $(\pm 0.08)$	$0.17$ [-0.2ex] $(\pm 0.11)$	$0.16$ [-0.2ex] $(\pm 0.11)$	$99.88$ [-0.2ex] $(\pm 0.84)$	$100.00$ [-0.2ex] $(\pm 0.06)$	$99.94$ [-0.2ex] $(\pm 0.49)$	$99.92$ [-0.2ex] $(\pm 0.62)$
Dense coordinates	$0.00$	$0.00$	$0.00$	$0.00$	$100.00$	$100.00$	$100.00$	$100.00$

Appendix

Table 6: Offline B-spline representation fidelity. Entries are mean

\pm

sample standard deviation. Centreline fitting error is reported in millimetres and vessel clDice as a percentage. The RCA and LCA statistics each use 750 cases. The overall statistic pools 1,500 source-case means, with each LCA case contributing the arithmetic mean of its LM–LAD and LCX branch metrics.

Stage	Centreline representation	RCA				LCA
		Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$
Coarse	Dense centreline	$10.22$ [-0.2ex] $(\pm 0.74)$	$10.23$ [-0.2ex] $(\pm 0.98)$	$13.81$ [-0.2ex] $(\pm 0.46)$	$\mathbf{1.284}$ [-0.2ex] $(\pm 0.056)$	$8.97$ [-0.2ex] $(\pm 0.53)$	$8.29$ [-0.2ex] $(\pm 0.76)$	$16.09$ [-0.2ex] $(\pm 0.59)$	$2.276$ [-0.2ex] $(\pm 0.125)$
	B-spline	$\mathbf{19.47}$ [-0.2ex] $(\pm 1.12)$	$\mathbf{20.40}$ [-0.2ex] $(\pm 1.56)$	$\mathbf{9.70}$ [-0.2ex] $(\pm 0.41)$	$1.324$ [-0.2ex] $(\pm 0.064)$	$\mathbf{14.92}$ [-0.2ex] $(\pm 0.77)$	$\mathbf{13.94}$ [-0.2ex] $(\pm 0.90)$	$\mathbf{12.37}$ [-0.2ex] $(\pm 0.51)$	$\mathbf{1.605}$ [-0.2ex] $(\pm 0.097)$
Refined	Dense centreline	$22.18$ [-0.2ex] $(\pm 1.07)$	$26.87$ [-0.2ex] $(\pm 1.57)$	$10.36$ [-0.2ex] $(\pm 0.47)$	$1.189$ [-0.2ex] $(\pm 0.050)$	$15.21$ [-0.2ex] $(\pm 0.68)$	$15.77$ [-0.2ex] $(\pm 0.91)$	$13.87$ [-0.2ex] $(\pm 0.58)$	$1.526$ [-0.2ex] $(\pm 0.087)$
	B-spline	$\mathbf{66.92}$ [-0.2ex] $(\pm 1.50)$	$\mathbf{80.62}$ [-0.2ex] $(\pm 1.92)$	$\mathbf{3.16}$ [-0.2ex] $(\pm 0.27)$	$\mathbf{1.054}$ [-0.2ex] $(\pm 0.026)$	$\mathbf{49.45}$ [-0.2ex] $(\pm 1.32)$	$\mathbf{61.30}$ [-0.2ex] $(\pm 1.93)$	$\mathbf{5.98}$ [-0.2ex] $(\pm 0.47)$	$\mathbf{1.053}$ [-0.2ex] $(\pm 0.026)$

Appendix

Table 7: Effect of centreline representation on coarse and refined reconstruction using two input views. The dense-centreline variant directly predicts and refines the

N=200

ordered centreline points, whereas the B-spline variant predicts and refines

K_{\mathrm{cp}}=20

control points before decoding them to the same number of dense points. All other model and evaluation settings are unchanged. CD denotes Chamfer distance, and CC count denotes connected-component count. Values are mean

\pm

standard error; bold indicates the better representation within each matched prediction stage.

Backbone	Output	RCA				LCA
		Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$
ResNet-101	Coarse	$18.94$ [-0.2ex] $(\pm 1.15)$	$19.94$ [-0.2ex] $(\pm 1.43)$	$9.37$ [-0.2ex] $(\pm 0.37)$	$1.428$ [-0.2ex] $(\pm 0.097)$	$13.88$ [-0.2ex] $(\pm 1.78)$	$13.69$ [-0.2ex] $(\pm 0.89)$	$12.99$ [-0.2ex] $(\pm 0.32)$	$1.878$ [-0.2ex] $(\pm 0.097)$
ResNet-101	Refined	$60.62$ [-0.2ex] $(\pm 1.29)$	$72.80$ [-0.2ex] $(\pm 1.61)$	$4.06$ [-0.2ex] $(\pm 0.47)$	$1.087$ [-0.2ex] $(\pm 0.029)$	$45.19$ [-0.2ex] $(\pm 1.71)$	$56.33$ [-0.2ex] $(\pm 1.50)$	$6.71$ [-0.2ex] $(\pm 0.44)$	$1.102$ [-0.2ex] $(\pm 0.064)$
VGGT	Coarse	$19.47$ [-0.2ex] $(\pm 1.12)$	$20.40$ [-0.2ex] $(\pm 1.56)$	$9.70$ [-0.2ex] $(\pm 0.41)$	$1.324$ [-0.2ex] $(\pm 0.064)$	$14.92$ [-0.2ex] $(\pm 0.77)$	$13.94$ [-0.2ex] $(\pm 0.90)$	$12.37$ [-0.2ex] $(\pm 0.51)$	$1.605$ [-0.2ex] $(\pm 0.097)$
VGGT	Refined	$66.92$ [-0.2ex] $(\pm 1.50)$	$80.62$ [-0.2ex] $(\pm 1.92)$	$3.16$ [-0.2ex] $(\pm 0.27)$	$1.054$ [-0.2ex] $(\pm 0.026)$	$49.45$ [-0.2ex] $(\pm 1.32)$	$61.30$ [-0.2ex] $(\pm 1.93)$	$5.98$ [-0.2ex] $(\pm 0.47)$	$1.053$ [-0.2ex] $(\pm 0.026)$

Appendix

Table 8: Two-view backbone comparison for RCA and LCA coarse and refined reconstruction. CD denotes Chamfer distance, and CC count denotes connected-component count. Values are mean

\pm

standard error.

Prediction stage	Branch-subset augmentation	RCA				LCA
		Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	CD (mm) $\downarrow$	CC count $\downarrow$
Coarse prediction	$\bm{\times}$	$11.38$ [-0.2ex] $(\pm 0.95)$	$10.89$ [-0.2ex] $(\pm 1.09)$	$13.42$ [-0.2ex] $(\pm 0.52)$	$1.338$ [-0.2ex] $(\pm 0.070)$	$9.82$ [-0.2ex] $(\pm 0.54)$	$8.81$ [-0.2ex] $(\pm 0.59)$	$14.70$ [-0.2ex] $(\pm 0.49)$	$1.882$ [-0.2ex] $(\pm 0.082)$
Coarse prediction	$\bm{\checkmark}$	$19.47$ [-0.2ex] $(\pm 1.12)$	$20.40$ [-0.2ex] $(\pm 1.56)$	$9.70$ [-0.2ex] $(\pm 0.41)$	$1.324$ [-0.2ex] $(\pm 0.064)$	$14.92$ [-0.2ex] $(\pm 0.77)$	$13.94$ [-0.2ex] $(\pm 0.90)$	$12.37$ [-0.2ex] $(\pm 0.51)$	$1.605$ [-0.2ex] $(\pm 0.097)$
Geometry refiner	$\bm{\times}$	$46.57$ [-0.2ex] $(\pm 1.45)$	$58.45$ [-0.2ex] $(\pm 2.04)$	$6.13$ [-0.2ex] $(\pm 0.43)$	$1.068$ [-0.2ex] $(\pm 0.029)$	$37.52$ [-0.2ex] $(\pm 1.04)$	$44.57$ [-0.2ex] $(\pm 1.51)$	$8.01$ [-0.2ex] $(\pm 0.45)$	$1.211$ [-0.2ex] $(\pm 0.054)$
Geometry refiner	$\bm{\checkmark}$	$65.89$ [-0.2ex] $(\pm 1.44)$	$80.84$ [-0.2ex] $(\pm 1.90)$	$3.16$ [-0.2ex] $(\pm 0.27)$	$1.068$ [-0.2ex] $(\pm 0.029)$	$48.43$ [-0.2ex] $(\pm 1.29)$	$61.38$ [-0.2ex] $(\pm 1.93)$	$5.98$ [-0.2ex] $(\pm 0.47)$	$1.053$ [-0.2ex] $(\pm 0.026)$

Appendix

Table 9: Effect of branch-subset augmentation on two-view coarse prediction and geometry refinement. CD denotes Chamfer distance, and CC count denotes connected-component count. Values are mean

\pm

standard error.

Method	Model inference time $\downarrow$	Post-processing time $\downarrow$	Total time $\downarrow$
SDF-CAR ( Reda et al., 2026 )	45 min	N/R	N/R
3DGR-CAR ( Fu et al., 2024 )	61 s	2.71 s	63.7 s
DeepCA ( Wang et al., 2025b )	700 ms	1.99 s	2.69 s
AutoCAR ( Zhu et al., 2025 )	330 ms	3.43 s	3.76 s
PPCAR-Net (coarse)	60 ms	–	0.06 s
PPCAR-Net (refined)	121 ms	–	0.12 s

Appendix

Table 10: Two-view reconstruction-time comparison on one NVIDIA GeForce RTX 4090 GPU. Model inference produces each method’s native output, post-processing converts that output into a vascular graph/skeleton representation when required, and total time is their sum. The best result is shown in bold and the second-best result is underlined ; post-processing times are ranked only among methods that require this stage. – denotes that post-processing is not required; N/R denotes that it was not recorded.

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Computer Aided Medical Procedures, Technical University of Munich, Munich, Germany · relAI – Konrad Zuse School of Excellence in Reliable AI, Munich, Germany · German Heart Center Munich, Munich, Germany +3

Sep 14, 2026, cs.CGJ/K move · Enter open · S save

Multi-Stage NeRF for Efficient 3D Coronary Artery Reconstruction from Two Narrow-Angle Angiographic Projections

Deyu Meng, Mojtaba Lashgari, Yiying Wang, Abhirup Banerjee

Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford, United Kingdom

Coronary Angiography Neural Radiance Fields Vessels Projection Integrated C++ Development

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X-ray coronary angiography is the clinical gold standard for coronary artery disease during real-time cardiac interventions, but provides only 2D projections of inherently 3D vessels. Existing learning-based 2D-to-3D reconstruction methods typically require wide angular coverage or multiple views, assumptions that are rarely satisfied in routine practice where only two projections with narrow angular separation are available. To address these challenges, we propose NeCA++, a multi-stage self-supervised neural radiance field (NeRF) framework tailored to clinically realistic acquisition constraints. The framework decomposes reconstruction into two stages that progressively refine spatial support and representation capacity. In the first stage, a coarse 3D representation of the vasculature is reconstructed, restricting the subsequent optimisation to regions with a higher likelihood of vessel presence, termed an active region. Afterward reconstruction is restricted to this region while higher-resolution representations are progressively activated to recover fine vascular details. This multi-stage strategy focuses learning on anatomically plausible regions, mitigates gradient dilution under extreme sparsity, and stabilises global topology before recovering fine vascular branches. Furthermore, two vessel-specific regularisations are introduced: a ray-aligned constraint to reduce projection-induced ambiguity, and a bimodal density penalty to enable early vessel-background separation. Extensive experiments across three datasets (ImageCAS, ASOCA, and Synthetic RCA) and four angular configurations demonstrate consistent superiority over state-of-the-art baselines, particularly under clinically realistic narrow-angle settings, while achieving reconstruction within 58 seconds per case.

Abstract

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