Neural Implicit 3D Cardiac Shape Reconstruction from Sparse CT Angiography Slices Mimicking 2D Transthoracic Echocardiography Views

Berto J. Bouma; Carolina Br\'as; Gino E. Jansen; Ivana I\v{s}gum; Mark J. Schuuring; R. Nils Planken

arxiv: 2602.05884 · v1 · submitted 2026-02-05 · 💻 cs.CV · cs.AI· cs.CE

Neural Implicit 3D Cardiac Shape Reconstruction from Sparse CT Angiography Slices Mimicking 2D Transthoracic Echocardiography Views

Gino E. Jansen , Carolina Br\'as , R. Nils Planken , Mark J. Schuuring , Berto J. Bouma , Ivana I\v{s}gum This is my paper

Pith reviewed 2026-05-16 06:48 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.CE

keywords neural implicit functions3D cardiac reconstructionsparse 2D viewstransthoracic echocardiographyCT angiographyvolume quantificationshape priors

0 comments

The pith

A neural implicit function reconstructs full 3D cardiac shapes from only four sparse planes that mimic standard transthoracic echocardiography views.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that training a neural network on complete 3D CT angiogram segmentations allows it to learn shape priors for the heart chambers and myocardium. At test time, this network reconstructs accurate 3D volumes when given only segmentations from four apical planes chosen to match common 2D echo views, by optimizing both the shape latent code and the plane positions. This yields an average Dice score of 0.86 across structures and reduces left-ventricle volume error to about 4.9 mL compared with 8.1 mL using the clinical Simpson biplane method. If the approach generalizes to actual ultrasound images, it would let clinicians obtain reliable 3D measurements during routine 2D scans without extra hardware.

Core claim

The authors show that a multi-layer perceptron can be trained to represent 3D cardiac anatomy as a continuous implicit function from full CTA data. When presented at inference with only four 2D segmentations simulating standard apical TTE views, jointly optimizing the latent shape code and the rigid alignment transforms of the planes produces multi-class 3D reconstructions whose volumes match the original CTA more closely than the established 2D clinical calculation.

What carries the argument

The neural implicit function (an MLP) that encodes the shape prior and is fitted at test time by optimizing the latent code together with the rigid transforms of the input planes.

If this is right

Volume errors for the left ventricle drop from 8.14 mL to 4.88 mL relative to the Simpson biplane rule.
Left atrium volume error falls from 37.76 mL to 6.40 mL under the same comparison.
Multi-structure Dice overlap reaches 0.86 on held-out CTA cases using only the four simulated planes.
3D chamber quantification becomes feasible within existing 2D echocardiography workflows.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Real transthoracic echo images could be fed directly into the same pipeline once plane detection is solved.
The method might combine with motion tracking to produce 4D reconstructions across the cardiac cycle.
Similar sparse-view implicit reconstruction could apply to other organs where full 3D CT is available for training but only 2D ultrasound is used clinically.

Load-bearing premise

Shape priors learned from dense CTA segmentations will still produce accurate results when the input consists of only four sparse, TTE-mimicking planes whose positions must also be estimated.

What would settle it

Reconstruct 3D shapes from actual clinical TTE images and compare the resulting chamber volumes against a reference 3D modality such as cardiac MRI acquired on the same patients.

Figures

Figures reproduced from arXiv: 2602.05884 by Berto J. Bouma, Carolina Br\'as, Gino E. Jansen, Ivana I\v{s}gum, Mark J. Schuuring, R. Nils Planken.

**Figure 2.** Figure 2: Example test result. (a) Initial orientation of TTE-mimicking slices showing that the outer [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Heatmap visualizations of surface distance errors of reconstructed whole-heart and left-ventricle [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

read the original abstract

Accurate 3D representations of cardiac structures allow quantitative analysis of anatomy and function. In this work, we propose a method for reconstructing complete 3D cardiac shapes from segmentations of sparse planes in CT angiography (CTA) for application in 2D transthoracic echocardiography (TTE). Our method uses a neural implicit function to reconstruct the 3D shape of the cardiac chambers and left-ventricle myocardium from sparse CTA planes. To investigate the feasibility of achieving 3D reconstruction from 2D TTE, we select planes that mimic the standard apical 2D TTE views. During training, a multi-layer perceptron learns shape priors from 3D segmentations of the target structures in CTA. At test time, the network reconstructs 3D cardiac shapes from segmentations of TTE-mimicking CTA planes by jointly optimizing the latent code and the rigid transforms that map the observed planes into 3D space. For each heart, we simulate four realistic apical views, and we compare reconstructed multi-class volumes with the reference CTA volumes. On a held-out set of CTA segmentations, our approach achieves an average Dice coefficient of 0.86 $\pm$ 0.04 across all structures. Our method also achieves markedly lower volume errors than the clinical standard, Simpson's biplane rule: 4.88 $\pm$ 4.26 mL vs. 8.14 $\pm$ 6.04 mL, respectively, for the left ventricle; and 6.40 $\pm$ 7.37 mL vs. 37.76 $\pm$ 22.96 mL, respectively, for the left atrium. This suggests that our approach offers a viable route to more accurate 3D chamber quantification in 2D transthoracic echocardiography.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows neural implicits can reconstruct multi-class cardiac shapes from four simulated apical planes on CTA data with Dice 0.86 and lower volume errors than Simpson's rule, but it never tests the method on real TTE images.

read the letter

The core idea is straightforward: train an MLP implicit function on full 3D CTA segmentations to capture shape priors, then at test time optimize a latent code plus rigid transforms to fit segmentations from four apical planes chosen to mimic standard TTE views. On held-out CTA volumes this produces an average Dice of 0.86 across chambers and myocardium, plus LV volume error of 4.88 mL versus 8.14 mL for Simpson's biplane rule. The joint optimization of latent vector and plane poses is a reasonable way to handle the unknown alignment at inference time, and the multi-class output is a step beyond single-structure work in the area. That part is cleanly executed and the numbers on clean data look usable for a simulation study. The obvious limitation is that all quantitative results come from CTA-derived planes with perfect segmentations and no acoustic artifacts. Real transthoracic echo planes bring dropout, reverberation, lower resolution, and view-angle jitter that the current pipeline does not simulate, so the claim of a viable route to 3D quantification from routine 2D TTE rests on an untested assumption about generalization. The abstract also omits architecture details, training procedure, and full ablation results, which makes it harder to judge how sensitive the numbers are to those choices. This work is mainly for groups already using implicit representations in medical imaging who want to see the cardiac application tried. It is worth sending to peer review because the technical approach is coherent and the CTA results are concrete, even though the next step clearly needs real echo data before the clinical claim can be taken seriously.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a neural implicit function (MLP) to reconstruct 3D multi-class cardiac shapes (chambers and LV myocardium) from sparse 2D segmentations of four apical planes extracted from CTA volumes to mimic standard TTE views. Shape priors are learned during training from full 3D CTA segmentations; at test time a latent code and rigid plane transforms are jointly optimized to fit the observed planes. On held-out CTA data the method reports average Dice 0.86 ± 0.04 across structures and lower LV/LA volume errors than Simpson’s biplane rule (4.88 ± 4.26 mL vs. 8.14 ± 6.04 mL for LV).

Significance. If the reconstruction accuracy generalizes beyond clean CTA planes, the work would offer a practical route to 3D chamber quantification from routine 2D TTE exams, addressing a long-standing clinical limitation of 2D approximations such as Simpson’s rule.

major comments (2)

[Abstract / Results] Abstract and Results: all quantitative metrics (Dice 0.86 ± 0.04, volume errors) are obtained exclusively on CTA-derived planes that lack acoustic dropout, reverberation, lower resolution, and view-angle variability of real TTE. Because the test-time optimization depends on the observed planes being consistent with the CTA-learned prior, this leaves the central claim of viability for 2D TTE untested and is load-bearing for the stated clinical motivation.
[Methods] Methods: the manuscript provides no description of the MLP architecture (depth, width, activation), the precise loss terms used in test-time optimization, the initialization of the latent code and transforms, or any ablation on these choices. Without these details the reported performance cannot be reproduced or diagnosed, undermining claims of superiority over Simpson’s rule.

minor comments (2)

[Abstract] The ± ranges are reported but it is unclear whether they represent standard deviation across patients, across structures, or bootstrap intervals; this should be stated explicitly.
[Results] No comparison is shown against other 3D reconstruction baselines (e.g., direct 3D U-Net or shape-model fitting) that could also be applied to the same sparse planes; adding at least one such baseline would strengthen the evaluation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We have revised the manuscript to clarify the scope of the evaluation and to provide the missing methodological details.

read point-by-point responses

Referee: [Abstract / Results] Abstract and Results: all quantitative metrics (Dice 0.86 ± 0.04, volume errors) are obtained exclusively on CTA-derived planes that lack acoustic dropout, reverberation, lower resolution, and view-angle variability of real TTE. Because the test-time optimization depends on the observed planes being consistent with the CTA-learned prior, this leaves the central claim of viability for 2D TTE untested and is load-bearing for the stated clinical motivation.

Authors: We agree that the reported metrics are obtained on CTA planes chosen to mimic standard apical TTE views rather than on real TTE acquisitions that include acoustic dropout and other artifacts. The study is presented as a controlled feasibility investigation demonstrating that a neural implicit representation can recover 3D shapes from sparse, geometrically consistent planes. We have revised the abstract, results, and discussion to explicitly state that the current experiments use CTA-derived planes and that validation on real TTE data remains necessary future work. The observed improvement over Simpson’s biplane rule under these idealized conditions nevertheless provides quantitative support for pursuing the approach further. revision: yes
Referee: [Methods] Methods: the manuscript provides no description of the MLP architecture (depth, width, activation), the precise loss terms used in test-time optimization, the initialization of the latent code and transforms, or any ablation on these choices. Without these details the reported performance cannot be reproduced or diagnosed, undermining claims of superiority over Simpson’s rule.

Authors: We thank the referee for highlighting this omission. The revised Methods section now specifies the MLP architecture (five fully connected layers with 256 hidden units and ReLU activations), the test-time loss (binary cross-entropy on the observed plane segmentations plus L2 regularization on the latent code), and the initialization procedure (latent code initialized to the training-set mean; plane transforms initialized from standard apical-view geometry). An ablation study examining the effect of network depth, loss weighting, and initialization strategy has been added to the supplementary material. revision: yes

Circularity Check

0 steps flagged

No circularity in the derivation chain

full rationale

The paper trains a neural implicit MLP on full 3D CTA segmentations to learn shape priors, then at test time jointly optimizes a latent code and rigid transforms to reconstruct from sparse planes extracted from held-out CTA volumes that mimic TTE views. The reported Dice coefficients and volume errors are computed by direct comparison of the optimized reconstruction against the original full CTA ground-truth segmentations; this comparison is not equivalent to the inputs by construction, as the optimization could in principle produce incorrect geometry. No self-citations are load-bearing, no uniqueness theorems are imported from the authors' prior work, and no ansatzes or known empirical patterns are renamed as new derivations. The central claims rest on empirical reconstruction accuracy measured against an external CTA benchmark rather than definitional equivalence or fitted-input renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; the method assumes cardiac anatomy exhibits learnable shape priors representable by MLPs and that sparse plane observations plus rigid transforms suffice for unique reconstruction. No explicit free parameters, axioms, or invented entities are detailed beyond standard neural network assumptions.

pith-pipeline@v0.9.0 · 5680 in / 1279 out tokens · 38642 ms · 2026-05-16T06:48:02.526141+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

neural implicit function... MLP... latent code z... jointly optimizing the latent code and the rigid transforms
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Jcost not mentioned; volume errors compared to Simpson's rule

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

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Left atrial volume determination by biplane two-dimensional echocardiography: validation by cine computed tomography,

Kircher, B., Abbott, J. A., Pau, S., Gould, R. G., Himelman, R. B., Higgins, C. B., Lipton, M. J., and Schiller, N. B., “Left atrial volume determination by biplane two-dimensional echocardiography: validation by cine computed tomography,”American heart journal121(3), 864–871 (1991)

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[2] [2]

M., Badano, L

Lang, R. M., Badano, L. P., Mor-Avi, V., Afilalo, J., Armstrong, A., Ernande, L., Flachskampf, F. A., Foster, E., Goldstein, S. A., Kuznetsova, T., et al., “Recommendations for cardiac chamber quan- tification by echocardiography in adults: an update from the american society of echocardiography and the european association of cardiovascular imaging,”Euro...

work page 2015

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Beyond simpson’s rule: accounting for orientation and ellipticity assumptions,

Kim, W.-J. C., Beqiri, A., Lewandowski, A. J., Puyol-Anton, E., Markham, D. C., King, A. P., Leeson, P., and Lamata, P., “Beyond simpson’s rule: accounting for orientation and ellipticity assumptions,”Ultrasound in Medicine & Biology48(12), 2476–2485 (2022)

work page 2022

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Automatic multi-view pose estimation in focused cardiac ultrasound,

Freitas, J., Gomes-Fonseca, J., Tonelli, A. C., Correia-Pinto, J., Fonseca, J. C., and Queir´ os, S., “Automatic multi-view pose estimation in focused cardiac ultrasound,”Medical Image Analysis94, 103146 (2024). 7

work page 2024

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2D echocardiography video to 3D heart shape reconstruction for clinical application,

Laumer, F., Rubi, L., Matter, M. A., Buoso, S., Fringeli, G., Mach, F., Ruschitzka, F., Buhmann, J. M., and Matter, C. M., “2D echocardiography video to 3D heart shape reconstruction for clinical application,”Medical Image Analysis101, 103434 (2025)

work page 2025

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3D heart reconstruction from sparse pose- agnostic 2D echocardiographic slices,

Chen, Z., Chen, J., Zhuo, W., Xue, W., and Ni, D., “3D heart reconstruction from sparse pose- agnostic 2D echocardiographic slices,”arXiv preprint arXiv:2507.02411(2025)

work page arXiv 2025

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Group-wise similarity registration of point sets using student’s t-mixture model for statistical shape models,

Ravikumar, N., Gooya, A., C ¸ imen, S., Frangi, A. F., and Taylor, Z. A., “Group-wise similarity registration of point sets using student’s t-mixture model for statistical shape models,”Medical image analysis44, 156–176 (2018)

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Overcoming catastrophic forgetting in neural networks,

Kirkpatrick, J., Pascanu, R., Rabinowitz, N., Veness, J., Desjardins, G., Rusu, A. A., Milan, K., Quan, J., Ramalho, T., Grabska-Barwinska, A., et al., “Overcoming catastrophic forgetting in neural networks,”Proceedings of the national academy of sciences114(13), 3521–3526 (2017)

work page 2017

[9] [9]

Learning continuous shape priors from sparse data with neural implicit functions,

Amiranashvili, T., L¨ udke, D., Li, H. B., Zachow, S., and Menze, B. H., “Learning continuous shape priors from sparse data with neural implicit functions,”Medical Image Analysis94, 103099 (2024)

work page 2024

[10] [10]

Diagnostic yield of ecg-gated cardiac ct in the acute phase of ischemic stroke vs transthoracic echocardiography,

Rinkel, L. A., Guglielmi, V., Beemsterboer, C. F., Groeneveld, N.-S., Lob´ e, N. H., Boekholdt, S. M., Bouma, B. J., Muller, F. F., Beenen, L. F., Marquering, H. A., et al., “Diagnostic yield of ecg-gated cardiac ct in the acute phase of ischemic stroke vs transthoracic echocardiography,”Neurology99(14), e1456–e1464 (2022)

work page 2022

[11] [11]

Deep learning-based whole-heart seg- mentation in 4D contrast-enhanced cardiac CT,

Bruns, S., Wolterink, J. M., van den Boogert, T. P., Runge, J. H., Bouma, B. J., Henriques, J. P., Baan, J., Viergever, M. A., Planken, R. N., and Iˇ sgum, I., “Deep learning-based whole-heart seg- mentation in 4D contrast-enhanced cardiac CT,”Computers in Biology and Medicine142(3 2022)

work page 2022

[12] [12]

Deep learning for segmentation using an open large-scale dataset in 2D echocardiography,

Leclerc, S., Smistad, E., Pedrosa, J., Østvik, A., Cervenansky, F., Espinosa, F., Espeland, T., Berg, E. A. R., Jodoin, P.-M., Grenier, T., et al., “Deep learning for segmentation using an open large-scale dataset in 2D echocardiography,”IEEE transactions on medical imaging38(9), 2198–2210 (2019)

work page 2019

[13] [13]

Video-based ai for beat-to-beat assessment of cardiac function,

Ouyang, D., He, B., Ghorbani, A., Yuan, N., Ebinger, J., Langlotz, C. P., Heidenreich, P. A., Harrington, R. A., Liang, D. H., Ashley, E. A., et al., “Video-based ai for beat-to-beat assessment of cardiac function,”Nature580(7802), 252–256 (2020)

work page 2020

[14] [14]

G., Addetia, K., Afilalo, J., D’Alto, M., Freed, B

Mukherjee, M., Rudski, L. G., Addetia, K., Afilalo, J., D’Alto, M., Freed, B. H., Friend, L. B., Gargani, L., Grapsa, J., Hassoun, P. M., et al., “Guidelines for the echocardiographic assessment of the right heart in adults and special considerations in pulmonary hypertension: recommendations from the american society of echocardiography,”Journal of the A...

work page 2025