Volumetrically Consistent Implicit Atlas Learning via Neural Diffeomorphic Flow for Placenta MRI

Athena Taymourtash; S. Mazdak Abulnaga; Esra Abaci Turk; P. Ellen Grant; Polina Golland

cs.CVMar 17, 2026

Volumetrically Consistent Implicit Atlas Learning via Neural Diffeomorphic Flow for Placenta MRI

Authors: Athena Taymourtash, S. Mazdak Abulnaga, Esra Abaci Turk, P. Ellen Grant, Polina Golland

Organizations: MIT Computer Science and Artificial Intelligence Laboratory · Massachusetts General Hospital, Harvard Medical School · Boston Children’s Hospital, Harvard Medical School

Abstract

Establishing dense volumetric correspondences across anatomical shapes is essential for group-level analysis but remains challenging for implicit neural representations. Most existing implicit registration methods rely on supervision near the zero-level set and thus capture only surface correspondences, leaving interior deformations under-constrained. We introduce a volumetrically consistent implicit model that couples reconstruction of signed distance functions (SDFs) with neural diffeomorphic flow to learn a shared canonical template of the placenta. Volumetric regularization, including Jacobian-determinant and biharmonic penalties, suppresses local folding and promotes globally coherent deformations. In the motivating application to placenta MRI, our formulation jointly reconstructs individual placentas, aligns them to a population-derived implicit template, and enables voxel-wise intensity mapping in a unified canonical space. Experiments on in-vivo placenta MRI scans demonstrate improved geometric fidelity and volumetric alignment over surface-based implicit baseline methods, yielding anatomically interpretable and topologically consistent flattening suitable for group analysis.

Figures & tables

Figure 1: Method overview. The warping function transforms point samples of shape $i$ to their canonical positions, which are then mapped to SDF values by the implicit template.

	Chamfer-L2 $(\downarrow)$	EMD $(\downarrow)$	NC $(\uparrow)$	Precision $(\uparrow)$			Recall $(\uparrow)$			$\mathrm{F}_{1}$ $(\uparrow)$
Model				@0.01	@0.03	@0.05	@0.01	@0.03	@0.05	@0.01	@0.03	@0.05
DeepSDF [ 29 ]	0.27	0.05	0.97	0.24	0.98	0.99	0.24	0.99	1.00	0.24	0.99	0.99
DIT [ 45 ]	0.17	0.05	0.97	0.37	0.98	0.99	0.37	0.99	1.00	0.38	0.99	0.99
DIF-Net [ 12 ]	0.12	0.04	0.98	0.43	0.99	1.00	0.43	0.99	1.00	0.43	0.99	1.00
NDF [ 35 ]	0.22	0.05	0.97	0.28	0.99	1.00	0.28	0.99	1.00	0.28	0.99	1.00
Ours	0.12	0.04	0.98	0.43	0.99	1.00	0.43	0.99	1.00	0.43	0.99	1.00

Table 1: Surface accuracy metrics on the placenta dataset. CD: Chamfer Distance (multiplied by

10^{3}

), EMD: Earth Mover’s Distance, and NC: Normal Consistency. Precision, Recall, and

\mathrm{F}_{1}

are evaluated at distance thresholds of 0.01, 0.03, and 0.05.

	FlipRate $(\downarrow)$	logDet- $\mathrm{L}_{1}$ $(\downarrow)$	CycleError $(\downarrow)$
DIF-Net [ 12 ]	15.34	0.81	0.24
DIT [ 45 ]	11.88	0.67	0.29
NDF [ 35 ]	8.78	0.90	0.26
Ours	4.04	0.69	0.20

Table 2: Diffeomorphism metrics computed on tetrahedral embeddings. FlipRate measures the percentage of tetrahedra with negative signed volume, logDet–

\mathrm{L}_{1}

captures the average deviation of local volume change from unity, and CycleError quantifies the inverse-consistency of the forward and backward flows. All values are averaged across subjects; lower is better.

Figure 2: Distribution of discrete Laplacian energy $\|Lu\|_{2}^{2}$ of vertex displacements across subjects. Lower values correspond to smoother deformation fields.

Figure 3: Dense pointwise correspondences via the learned implicit template. (a) Two subject instances mapped to the canonical template through the diffeomorphic flow. (b) ACVD‐remeshed surfaces (5 k vertices) with vertex colors propagated from the template. Consistent colors across subjects visually demonstrate stable, smooth correspondences.

	Vol $(\downarrow)$	Areal $(\downarrow)$	Edge $(\downarrow)$	SymDir $(\downarrow)$	Conformal $(\downarrow)$
DIF-Net [ 12 ]	4.36	2.8	2.43	12.91	11.47
DIT [ 45 ]	2.02	0.99	1.13	8.48	10.89
NDF [ 35 ]	4.17	2.26	2.32	13.75	10.96
Ours	1.94	1.17	1.19	8.02	9.74

Table 3: Maximum distortion per instance, averaged across subjects. Smaller values correspond to more isotropic, low‐distortion mappings. SymDir and Conformal report symmetric Dirichlet and condition‐number–based distortions.

Figure 4: Pose‐invariant flattening and intensity mapping across two maternal positions of the same subject. The placenta in each position is mapped diffeomorphically to the canonical template via $\Phi(\cdot;c_{i})$ and $\Phi(\cdot;c_{j})$ , producing consistent, topology‐preserving flattened intensity maps.

Figure 5: Volumetric flattening. Given the same tetrahedral placenta mesh (upper left panel), our method produces a coherent, uniformly compressed volumetric flattening. DIT and NDF maintain surface alignment but distort the interior, exhibiting radial compression and anisotropic stretching of tetrahedra toward a mid-surface layer.

Model	CD-L2 $\downarrow$	FlipRate $\downarrow$	logDet–L1 $\downarrow$	SymDir $\downarrow$	LapE $\downarrow$
$\mathcal{L}_{rec}$	0.13	13.75	0.69	10.99	26.34
w/ $\mathcal{L}_{d}$	0.22	10.92	0.61	9.08	22.88
w/ $\mathcal{L}_{\text{Jac}}$	0.12	14.76	0.80	12.07	33.05
w/ $\mathcal{L}_{\text{biH}}$ (ours)	0.12	4.04	0.69	8.02	8.72

Table 4: Ablation of loss terms on the Placenta dataset.

Figure 6: Flattened intensity maps obtained via volumetric pullback. Our method preserves interior geometry, yielding coherent anatomical texture in the flattened domain, cotyledons and vascular structure are immediately apparent in our flattened images, whereas NDF and DIT cause intensities to be interpolated across collapsed surface to mid-surface layers.

Figure 7: Distribution of gestational ages for our dataset of EPI BOLD placenta scans.

Figure 8: Preprocessing and model outputs for a representative instance with gestational age of 34w+4d (a) Initial surface extracted from the manual segmentation using Marching Cubes (b) Dense signed-distance samples generated using depth-based nearest-surface queries (red: outside; blue: inside)(c) Overlay of the SDF samples with the initial mesh; a random subset of 5k points is used for training (d) Reconstructed implicit surface produced by our template-conditioned SDF decoder; since the representation is continuous, the surface can be extracted at arbitrarily high resolution independently of the input mesh resolution (e) Overlay of the reconstructed surface with the input SDF samples, illustrating geometric consistency (f) Dense pointwise correspondences obtained from the learned diffeomorphic flow, mapping the subject into the template space.

Figure 9: Neural ODE–based deformation module. Top: a velocity field is predicted by a residual MLP from the current point position and latent code $c_{i}$ , and integrated with an ODE solver to produce the updated position. Middle: The full deformation $\Phi_{i}$ is obtained by concatenating four NODE blocks, where the output of block $k$ serves as the input to block $k+1$ . Bottom: Visualization of the progressive deformation steps, illustrating the smooth, monotonic trajectory that warps each placenta instance into the learned template space.

Figure 10: Distribution of diffeomorphism and distortion metrics across gestational age.

Medical Image Analysis

Medical image analysis uses computational methods to interpret clinical images, measure anatomy and disease, and support diagnosis and treatment.

See all 281 papers

INFANiTE: Implicit Neural representation for high-resolution Fetal brain spatio-temporal Atlas learNing from clinical Thick-slicE MRI
May 11, 2026Xiaotian Hu, Mingxuan Liu, Hongjia Yang +10Implicit Neural Representations Longitudinal Medical Image Analysis
Tsinghua University · University of Oxford · Sichuan University
Aligning Fetal Anatomy with Kinematic Tree Log-Euclidean PolyRigid Transforms
Mar 2, 2026Yingcheng Liu, Athena Taymourtash, Yang Liu +5Fetal MRI Deformable Image Registration
Computer Science and Artificial Intelligence Lab, MIT, Cambridge, USA · California Institute of Technology, Pasadena, USA · Boston Children’s Hospital and Harvard Medical School, Boston, USA +1
Two-Parameter Flow Map Learning for Continuous-Time Diffeomorphic Image Registration
Sep 9, 2026Mohammadjavad Matinkia, Nilanjan RayMedical Image Registration Flow Map Learning
University of Alberta, Canada

May 11, 2026J/K move · Enter open · S save

INFANiTE: Implicit Neural representation for high-resolution Fetal brain spatio-temporal Atlas learNing from clinical Thick-slicE MRI

Xiaotian Hu, Mingxuan Liu, Hongjia Yang, Tongxi Song+9

Tsinghua University · University of Oxford · Sichuan University

Implicit Neural Representations Longitudinal Medical Image Analysis Neuroimaging Brain MRI Fetal MRI

Open paper AskPDF arXiv

Spatio-temporal fetal brain atlases are important for characterizing normative neurodevelopment and identifying congenital anomalies. However, existing atlas construction pipelines necessitate days for slice-to-volume reconstruction (SVR) to generate high-resolution 3D brain volumes and several additional days for iterative volume registration, thereby rendering atlas construction from large-scale cohorts prohibitively impractical. We address these limitations with INFANiTE, an Implicit Neural Representation (INR) framework for high-resolution Fetal brain spatio-temporal Atlas learNing from clinical Thick-slicE MRI scans, bypassing both the costly SVR and the iterative non-rigid registration steps entirely, thereby substantially accelerating atlas construction. Extensive experiments demonstrate that INFANiTE outperforms existing baselines in subject consistency, reference fidelity, intrinsic quality and biological plausibility, even under challenging sparse-data settings. Additionally, INFANiTE reduces the end-to-end processing time (i.e., from raw scans to the final atlas) from days to hours compared to the traditional 3D volume-based pipeline (e.g., SyGN), facilitating large-scale population-level fetal brain analysis. Code: https://github.com/hu2274898/INFANiTE

Abstract

Medical Image Analysis

Explore similar work

INFANiTE: Implicit Neural representation for high-resolution Fetal brain spatio-temporal Atlas learNing from clinical Thick-slicE MRI

Aligning Fetal Anatomy with Kinematic Tree Log-Euclidean PolyRigid Transforms

Two-Parameter Flow Map Learning for Continuous-Time Diffeomorphic Image Registration