A Strong Linear Baseline for Whole-Heart Cardiac Shape Completion on CT, with an Open Eleven-Structure Statistical Shape Model
Authors: Matej Gazda, Jakub Gazda, Juraj Gazda, Peter Drotar
Organizations: Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 1/9, 042 00 Košice, Slovakia · 2nd Department of Internal Medicine, Faculty of Medicine, Pavol Jozef Šafárik University and L. Pasteur University Hospital, Trieda SNP 1, 040 11 Košice, Slovakia · Department of Computers and Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 1/9, 042 00 Košice, Slovakia
Public cardiac cohorts annotate different subsets of the heart, so shapes from separate sources cannot be pooled without shared correspondence. Among released cardiac shape resources, none we identified carries the atrial appendage, pulmonary veins, and caval stumps as separate blocks in one mesh. Completion benchmarks also compare deep models against a least-squares projection onto shape modes, not the conditional estimator the same fitted model implies. We release an eleven- structure cardiac computed-tomography (CT) statistical shape model, built from 383 automatically labelled cases in 11 571-vertex correspondence, and compare completion estimators under one frozen internal split and endpoint. On a 76-case internal list held out from fitting, a closed-form conditional-Gaussian estimator reconstructed the missing non-chamber structures at 3.717 mm mean per-vertex error, averaged equally over one, three, five, and nine observed structures. A five-refit mask-conditioned graph variational autoencoder reached 5.248 mm and nearest-neighbour retrieval 8.931 mm. The paired difference was 1.531 mm (95% confidence interval 1.384 to 1.711), and the ordering held in a raw-coordinate sensitivity arm. Expert manual labels exist for 58 external CT cases, but our registered reference is close enough to score only five structures. There the closed-form estimator again had lower average surface distance, 95th-percentile Hausdorff distance, and Chamfer error for both completed atria. On a second public benchmark of 20 cases the reference was close enough for three of four completed structures, and the same ordering held there. Four structures have no expert reference. The released model and its completion operator support cohort-unification research on aligned CT, not clinical use.
Figures & tables
Resource
Anatomy outside the four chamber walls
Public package
Hoogendoorn et al. [ 20 ]
Detailed multiregion whole-heart atlas, including great vessels
Atlas and SSM reported; no reusable model package located
Rodero et al. [ 2 ]
AO and PA walls; PV and caval openings tagged; LAA body omitted
SSM parameters and 1 000 synthetic finite-element meshes
Strocchi et al. [ 3 ]
AO and PA walls; LAA, PV, SVC and IVC at cut rings
24 patient-specific finite-element meshes
This work
AO, PA, LAA, PV, SVC and IVC as separate surface blocks in one shared topology
Template, per-case displacement fields and reconstruction code
TABLE I: Closest multistructure CT geometry resources. “Public package” means a direct public download of a reusable model or mesh cohort, assessed from the cited publications and their linked repositories at the time of writing; boundary tags or cut rings are not counted as separate anatomical surface bodies. None of the prior resources supports missing-label conditioning; this work conditions on any observed structure-block subset.
Fig. 1: End-to-end pipeline and frozen evaluation benchmark. After segmentation QC, joint-label registration, registration/FOV QC, and same-structure R-local repair, the 383 corresponding meshes are divided into a development set used for model selection and a 76-case evaluation set withheld from every fit reported here (the graph architecture predates this partition; Section V ). The orange block carries the conditional-mean equation; all comparators use the same split, panels, endpoint, and evaluation cases. CARE2026 and MM-WHS provide separate expert-surface validation without fitting or tuning.
Internal (TotalSegmentator)
CARE2026
MM-WHS CT
Role
SSM fit; internal eval.
indep. validation
indep. secondary
Source cases
631
60 (A/B/G)
20
Segmentation QC
−206 (vol., extent, centr.) → 425
–
–
Affine check
–
−2 (non-orthon.)
–
Registration QC
−26 ( > 25 mm) → 399
–
–
FOV truncation
−16
–
–
TABLE II: The three cohorts and the exclusions that produce them. The released internal metadata supplies age, sex, manufacturer, scanner model, tube voltage, pathology class, and study type; “n/a” attributes are absent from the released metadata and are not estimated, and “none” means no fitting or tuning. The 76-case evaluation list is frozen (split file released with the artifacts). Both CARE2026 exclusions fall in subset B; MM-WHS has no exclusions.
ID
Structure
Abbrev.
Vertices
1
Left ventricle
LV
1 502
2
Myocardium
MYO
2 502
3
Right ventricle
RV
2 002
4
Left atrium
LA
1 002
5
Right atrium
RA
1 002
6
Aorta
AO
1 202
TABLE III: Eleven cardiac structures and template vertex counts. MYO is the left-ventricular wall; the other ten are blood-pool or luminal surfaces. The model therefore carries no right-ventricular or atrial wall and does not represent total myocardial mass.
Fig. 2: The eleven-structure whole-heart template mesh (11 571 vertices) in anterior, posterior, left, and right views, each structure a colour-coded surface in fixed vertex correspondence. This single template is warped into every patient’s space to build the SSM.
Structure
Median
p25
Structure
Median
p25
LV
0.981
0.979
AO
0.824
0.787
MYO
0.962
0.944
PA
0.969
0.910
RV
0.974
0.965
LAA †
0.941
0.938
LA
0.978
0.977
PV †
0.918
0.891
RA
0.975
0.971
SVC †
0.725
0.619
IVC †
0.528
0.461
TABLE IV: Per-structure warp-overlap Dice (SyN-warped patient segmentations vs template), CARE2026 ( n=58 ): a registration-consistency measure, not accuracy against a manual reference. Structures marked † (LAA, PV, SVC, IVC) are silver-only. Chambers is the mean of the five per-chamber medians. p25 is the 25th percentile.
Fig. 3: The completion operator. A selection matrix Po extracts whichever structure blocks or partial vertex sets are observed. The covariance is fitted once; inference extracts the corresponding covariance blocks and evaluates the conditional mean. Observed coordinates are copied to the output; missing coordinates are predicted. The figure writes the operator in covariance form for readability; the implementation evaluates the low-rank coefficient-space posterior of Eq. (1), whose ridge acts on the posterior precision rather than on Coo .
Representation
Method
k=1
k=3
k=5
k=9
Four- k [95% CI]
Raw
Mean shape
11.218
11.278
11.189
10.909
11.149 [10.310, 12.040]
Nearest neighbour
10.096
9.031
8.508
8.644
9.070 [8.621, 9.563]
Cond-G
5.479
3.918
3.193
3.003
3.898 [3.629, 4.206]
β -VAE
6.596
5.238
4.693
4.748
5.319 [4.991, 5.701]
PPCA ( K=1 )
5.524
3.958
3.248
3.064
3.948 [3.683, 4.251]
Local Cond-G †
5.479
3.918
3.193
3.003
3.898 [3.629, 4.206]
TABLE V: Frozen 76-case internal evaluation completion MPVED (mm). Each k entry is the case mean over its fixed panels; the four- k column equally weights the four k values, with a case-bootstrap 95% CI. PPCA is the selected K=1,q=160 limit; local Cond-G reuses the exact global prediction by construction.
Contrast
Difference (mm)
95% CI (mm)
Multiplicity result
R-local β -VAE minus Cond-G, four- k primary
1.531
[1.384, 1.711]
Unadjusted p<0.001 (floor)
Raw β -VAE minus Cond-G, four- k
1.421
[1.264, 1.610]
pHolm<0.002
R-local β -VAE minus Cond-G, k=1
1.218
[1.023, 1.439]
pHolm<0.002
R-local β -VAE minus Cond-G, k=3
1.440
[1.298, 1.602]
pHolm<0.002
R-local β -VAE minus Cond-G, k=5
1.613
[1.466, 1.800]
pHolm<0.002
R-local β -VAE minus Cond-G, k=9
1.852
[1.689, 2.047]
pHolm<0.002
TABLE VI: Frozen paired family. Differences are challenger minus Cond-G, so positive values favour Cond-G. The R-local four- k primary is unadjusted; the next seven rows are the complete Holm family ( m=7 ). The final row is an identity check rather than empirical evidence.
Method
Type
Internal 76
MM-WHS ( n=20 )
Cond-G
Closed-form linear
3.717 [3.480, 3.984]
4.823 [4.446, 5.226]
Latent optimisation ‡
Published method
5.044 [4.746, 5.389]
6.248 [5.755, 6.777]
β -VAE
Feed-forward deep
5.248 [4.935, 5.613]
6.616 [6.109, 7.152]
SpiralNet++ §
Published operator
6.710 [6.283, 7.218]
8.916 [8.105, 9.741]
Nearest neighbour
Retrieval floor
8.931 [8.503, 9.405]
10.907 [10.145, 11.684]
Mean shape
Population floor
11.090 [10.245, 11.990]
13.174 [12.045, 14.419]
TABLE VII: Additional non-linear baselines, R-local representation, MPVED (mm) with case-bootstrap 95% intervals. The internal column is the frozen 76-case split at four observed-structure counts; the MM-WHS column is exhaustive panels at k=1,3,5 over the seven expert-overlap structures, so only the ordering within a column is comparable. Both arms lie outside the prespecified Holm family and are descriptive; the latent-optimisation setting is not retuned externally. Cond-G, the β -VAE and the floors repeat Table V for reference; the same arms on CARE2026 expert surfaces, a different endpoint, are in Table VIII .
Method
Type
LA
RA
Cond-G
Closed-form linear
3.275 / 7.846 / 4.138
3.479 / 9.007 / 4.586
Latent optimisation
Published method
3.902 / 8.941 / 4.822
4.243 / 10.265 / 5.413
β -VAE
Feed-forward deep
3.934 / 8.990 / 4.860
4.333 / 10.372 / 5.495
SpiralNet++
Published operator
4.299 / 9.701 / 5.266
4.605 / 10.868 / 5.779
TABLE VIII: Additional non-linear baselines on CARE2026 expert surfaces, R-local, biventricular panel, mean ASSD / HD95 / Chamfer RMS (mm) over 58 cases. The endpoint is distance to expert manual segmentations and is not comparable to Table VII . AO and PA are suppressed for every method by the prespecified reference-closeness rule. Cond-G and the β -VAE repeat Table IX for reference.
Fig. 4: Completion across six observed-structure panels, one internal TotalSegmentator case (TS, s0365) beside one external CARE2026 case (A_Case1020), each the median case of its cohort by the displayed Cond-G estimator’s mean missing-vertex error over the six panels. Observed structures are grey; the conditional-Gaussian model completes the rest, coloured by per-vertex error (mm). The estimator is the selected configuration of Table V , fitted on the 307 development cases in the R-local domain.
Population
Method
LA
RA
Pooled
Cond-G
3.275 / 7.846 / 4.138
3.479 / 9.007 / 4.586
Pooled
β -VAE
3.934 / 8.990 / 4.860
4.333 / 10.372 / 5.495
A
Cond-G
2.634 / 6.643 / 3.353
3.035 / 8.085 / 3.989
A
β -VAE
3.103 / 7.553 / 3.911
3.780 / 9.373 / 4.811
B
Cond-G
4.010 / 9.642 / 5.032
4.028 / 10.598 / 5.351
B
β -VAE
4.878 / 11.412 / 6.034
4.706 / 11.572 / 6.011
TABLE IX: R-local CARE biventricular native prediction-versus-expert surface metrics, pooled ( n=58 ) and by acquisition subset (A/B/G contain 20/18/20 cases). The panel observes LV/MYO/RV; values are mean ASSD / HD95 / Chamfer RMS in mm. AO and PA are omitted after failing the reference-closeness rule.
Missing structure
Population
Cond-G
β -VAE
LV
Pooled
2.362 / 6.407 / 3.119
3.899 / 9.623 / 4.942
A
1.818 / 4.744 / 2.358
3.367 / 8.177 / 4.254
B
3.697 / 10.361 / 4.969
4.841 / 12.575 / 6.258
G
1.704 / 4.510 / 2.215
3.582 / 8.411 / 4.446
MYO
Pooled
2.056 / 5.667 / 2.729
2.943 / 7.583 / 3.769
A
1.695 / 4.541 / 2.212
2.526 / 6.257 / 3.171
TABLE X: R-local CARE leave-one-expert-structure-out completion, pooled ( n=58 ) and by acquisition subset (A/B/G contain 20/18/20 cases). Values are mean ASSD / HD95 / Chamfer RMS in mm. AO and PA are omitted because their references are too far.
Structures
Internal benchmark
CARE2026 expert check
MM-WHS expert check
LV, MYO, RV
never a completion target
reference close enough (leave-one-out panel)
expert label, but observed as input
LA, RA
never a completion target
reference close enough (both panels)
reference close enough; Cond-G better
AO
Cond-G better at every k
reference too far
reference too far
PA
Cond-G better at every k
reference too far
reference close enough under R-local; Cond-G better
LAA, PV, SVC, IVC
Cond-G better at every k
no expert label
no expert label
TABLE XI: The evidence behind each structure; structures with identical status share a row. “Reference close enough” means the registered reference lies within the fixed distance limits of the expert surface, so a native comparison is meaningful; the internal benchmark scores only structures that are completion targets there. “Cond-G better” is the lower descriptive mean error against the β -VAE at every k . AO’s reference is too far because the expert annotations cover a shorter aortic extent than the whole-aorta reference, not because of misregistration (Section V-D ).
Internal ( n=76 )
CARE2026 ( n=58 )
Structure
MAE (mL)
medAPE
Δ [95% CI]
MAE (mL), medAPE
LA
7.99
8.3%
−6.84 [ −9.43 , −4.43 ]
18.47, 18.5%
RA
9.61
8.9%
−7.29 [ −10.36 , −4.35 ]
20.89, 25.7%
AO
13.81
5.6%
−7.99 [ −12.75 , −3.33 ]
23.08, 13.1%
PA
6.74
8.5%
−4.51 [ −6.35 , −2.68 ]
13.39, 17.5%
LAA
0.93
10.7%
−0.49 [ −0.71 , −0.27 ]
1.41, 14.8%
TABLE XII: Morphometric retention from the biventricular panel: per-structure volume agreement between the completion and the case’s own registered mesh. MAE is mean absolute error; medAPE is median absolute percentage error; Δ is the paired difference in absolute error against the development-only regression on the three observed chamber volumes, with its 95% case-bootstrap interval (negative favours completion). Vessel and appendage rows are segment volumes under the fixed template crop.
Cond-G
β -VAE
Observed panel
typical
atypical
typical
atypical
LV
1.000
0.946 [0.868, 0.998]
0.128
0.105 [0.071, 0.138]
LV, MYO, RV
1.000
0.944 [0.878, 0.991]
0.129
0.140 [0.104, 0.174]
Five chambers
1.000
0.974 [0.953, 0.993]
0.141
0.139 [0.103, 0.175]
Nine structures
1.000
0.999 [0.996, 1.000]
0.205
0.194 [0.110, 0.281]
TABLE XIII: Nominal 95% ellipsoid coverage by out-of-support stratum, R-local, 76 evaluation cases (64 typical, 12 atypical). Strata come from the frozen development 95th-percentile Mahalanobis threshold. Exploratory and post-hoc; brackets are descriptive case-bootstrap intervals.
We propose Bi-PT, a pipeline for reconstructing 3D four-chamber human heart meshes from clinical sparsely sampled cardiac magnetic resonance imaging (CMR) data. This work addresses the error-prone generation of 3D cardiac shape from a sparse point cloud (SPC) extracted from 2D long-axis and short-axis views used in routine clinical CMR protocols. Bi-PT enables accurate inference of the four-chamber heart mesh from the SPC by learning robust point features via bidirectional point cross-attention between an atlas and the SPC, together with per-point semantic labels that improve correspondence estimation. We formulate the deformation field as a Neural Ordinary Differential Equation (NODE) parameterized by a per-point affine transformation and translation to deform the atlas toward the target heart shape. By learning such a NODE, we can guarantee the deformation field to be a locally affine diffeomorphic deformation. We also integrate a semantic label loss into the Chamfer distance to encourage label-consistent correspondences and add a smoothness regularization to stabilize and improve the learning of the deformation field. Extensive experiments demonstrate that Bi-PT achieves accurate and robust performance compared to baselines.
Chenchuhui Hu, Shaoming Pan, Leon Axel +1
Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, USA · School of Medicine, New York University, New York, NY, USA
Computational models of the human heart are widely used to study electromechanical and fluid-dynamical cardiac function and to support applications such as in silico clinical trials. However, most studies remain limited to single or patient-specific anatomies, restricting the inclusion of population-level variability required for uncertainty quantification. A key challenge is translating medical-image segmentations, which may contain artifacts, mesh defects or disjoint domains, into topologically coherent geometries suitable for multiphysics simulations. In this work, we present a semi-automatic pipeline that converts CT-based segmentations into simulation-ready cardiac meshes within a few minutes while preserving anatomical and topological consistency. Building on modern deep learning segmentation methods, the framework incorporates a template-based registration stage to regularize artifacts and enforce mesh-quality constraints. A Chamfer-distance morphing strategy deforms a high-quality template toward each segmented heart, matching individual chambers while preserving topology. The resulting meshes are watertight, isotopological, and endowed with consistent point-to-point correspondence. The pipeline is validated on 58 healthy cardiac CT scans, including all cardiac chambers and proximal vessel segments. The resulting meshes can be represented in a unified shape space, enabling the construction of a statistical shape model of the heart and major vessels. Principal Component Analysis shows that a low-dimensional latent space efficiently captures population variability, while Gaussian Mixture Modeling enables synthetic anatomy generation. Overall, the proposed framework (released open-source) provides a pathway from raw segmentations to simulation-ready cardiac geometries, enabling anatomically consistent virtual cohorts for large-scale in silico studies.
Francesco Fabbri, Martino Andrea Scarpolini, Paolo Ciancarella +4
Gran Sasso Science Institute (GSSI), L’Aquila, Italy. · European Hospital, Rome, Italy. · University of Edinburgh, Edinburgh, Scotland. +2
Accurate cardiac anatomy modeling requires the model to be able to handle intricate interrelations among structures. In this paper, we propose VecHeart, a unified framework for holistic reconstruction and generation of four-chamber cardiac structures. To overcome the limitations of current feed-forward implicit methods, specifically their restriction to single-object modeling and their neglect of inter-part correlations, we introduce Hybrid Part Transformer, which leverages part-specific learnable queries and interleaved attention to capture complex inter-chamber dependencies. Furthermore, we propose Anatomical Completion Masking and Modality Alignment strategies, enabling the model to infer complete four-chamber structures from partial, sparse, or noisy observations, even when certain anatomical parts are entirely missing. VecHeart also seamlessly extends to 3D+t dynamic mesh sequence generation, demonstrating exceptional versatility. Experiments show that our method achieves state-of-the-art performance, maintaining high-fidelity reconstruction across diverse challenging scenarios. Code is available at https://github.com/Scalsol/VecHeart.