A new preprint reports that Cond-G, a regularised Gaussian estimator, filled in missing parts of aligned heart CT meshes with lower average error than a graph-based beta-VAE in the study's frozen internal test. Across four conditions, with 1, 3, 5 or 9 observed structures, the average distance over missing non-chamber vertices was 3.717 mm for Cond-G and 5.248 mm for the beta-VAE. The paired difference was 1.531 mm, with a 95% confidence interval of 1.384 to 1.711 mm and an unadjusted p-value below 0.001.
A model built to work with partial anatomy
The task was to complete a single 11-structure heart representation from whichever named anatomical structures a CT cohort provided. The system uses a fixed template mesh with 11,571 vertices, aligns it by centre of mass and then applies ANTs SyN registration to warp the template into each patient's space. Cond-G estimates missing coordinates as a regularised Gaussian posterior over shape components, so the observed input can be any coordinate subset.
The internal TotalSegmentator source pool contained 631 cases. Of those, 383 were retained, with 307 used for development and 76 held back for a frozen evaluation. Compatible estimators were selected on the same five development folds and tested on the same four observed-structure counts. The external material included 58 retained CARE2026 volumes and 20 MM-WHS cases.
The result was not limited to one model comparison
Supportive comparisons pointed in the same direction. In raw coordinates, the four-condition beta-VAE-minus-Cond-G gap was 1.421 mm, with a 95% confidence interval of 1.264 to 1.610 mm and a Holm-adjusted p-value below 0.002. A selected single-component PPCA baseline was only 0.047 mm worse than Cond-G. A latent-optimisation arm improved on the beta-VAE but remained 1.327 mm worse internally and 1.426 mm worse on MM-WHS.
The pattern held in outside tests
On the 58-case CARE2026 panel, Cond-G had lower values on three surface-distance measures for both atria. For the left atrium, average symmetric surface distance, or ASSD, was 3.275 mm versus 3.934 mm for the beta-VAE; for the right atrium, it was 3.479 versus 4.333 mm. The same ordering appeared for HD95 and Chamfer RMS, including left-atrial HD95 of 7.846 versus 8.990 mm and right-atrial HD95 of 9.007 versus 10.372 mm.
On the 20-case MM-WHS external validation, Cond-G again had lower ASSD for the three eligible structures: 2.854 versus 3.989 mm for the left atrium, 2.733 versus 3.435 mm for the right atrium, and 4.895 versus 5.441 mm for the pulmonary artery. The ordering was the same for HD95 and Chamfer RMS.
What the outside comparisons could not answer
The outside evidence did not cover all 11 structures. CARE2026 supplied expert labels for seven structures, but only five were close enough to score; MM-WHS admitted three targets, one only under the R-local representation. The left atrial appendage, pulmonary veins, superior vena cava and inferior vena cava had no external expert surface, and the aorta failed the closeness rule in both cohorts.
Nor did the shape results translate uniformly to volume estimates. Internally, five of seven structures beat all three volume alternatives; pulmonary-vein volume was not separated from regression, with a difference of -0.01 mL and an interval from -0.31 to +0.28 mL. In an external caval-volume comparison, Cond-G was 2.49 mL worse than a constant, with an interval from +1.65 to +3.35 mL.
Geometry and uncertainty remain open
Geometry audits found self-intersections, contacts between different structures and non-monotone truncation behaviour. The study therefore did not establish collision-free, watertight or simulation-ready meshes, nor did it establish clinical use.
The uncertainty audit pointed in opposite directions. Across the 76-case evaluation, Cond-G's nominal 50% and 95% ellipsoids covered 92.7% to 98.8% and 99.1% to 99.9% of missing non-chamber vertices, respectively. The beta-VAE's 160-draw second-moment estimate covered only 2.6% to 5.2% and 12.4% to 20.3%; the analysis classified Cond-G as overconservative and the beta-VAE as overconfident.
An early methods result
The tests were a benchmark for registered, CT-derived mesh representations, not a clinical validation. The document is an arXiv v1 preprint dated 20 August 2026 and says it was submitted to the IEEE for possible publication. The reported public repository includes the 11-structure template mesh, CT-to-correspondence pipeline and model code, while a versioned archive contains analysis scripts, frozen split and bootstrap files, manifests and machine-readable result tables.
Paper data and sources
Original title: 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
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text