CardioMorphNet: 3D Cardiac Registration

• CardioMorphNet is a Bayesian recurrent deep learning framework that couples motion estimation with bi-ventricular segmentation using shape-guided registration.
• It replaces intensity-based image registration with probabilistic alignment of segmentation maps, ensuring anatomically accurate 3D cardiac motion estimation.
• The model integrates an RVAE backbone, DeformNet, and SegNet to estimate motion fields and uncertainty, achieving superior performance on UK Biobank SAX data.

CardioMorphNet (CMN) is a recurrent Bayesian deep learning framework for 3D cardiac shape-guided deformable registration from short-axis cine cardiac magnetic resonance (CMR) images. It was introduced to address a specific limitation of existing cardiac motion estimation methods: reliance on intensity-based image registration similarity losses that may overlook cardiac anatomical regions. CMN instead uses a Bayesian formulation in which motion estimation and bi-ventricular segmentation are coupled, and training is driven by recursive registration of segmentation maps rather than by intensity similarity terms. The model combines a recurrent variational autoencoder (RVAE), a motion posterior network, and a segmentation posterior network, and also produces uncertainty maps for the estimated motion fields (Movahed et al., 28 Aug 2025).

1. Problem setting and conceptual scope

Cardiac motion estimation from cine CMR is used for assessing cardiac function and detecting abnormalities. In this setting, the objective is not merely frame-to-frame image alignment, but anatomically meaningful estimation of the motion of structures such as the left ventricle (LV), left-ventricular myocardium (LVmyo), and right ventricle (RV). CMN is explicitly formulated for 3D deformable registration over the cardiac cycle using short-axis (SAX) CMR volumes, with spatio-temporal dependencies modeled across sequential frames (Movahed et al., 28 Aug 2025).

The model is designed around four latent and observed entities: image volumes $I_t$, segmentation masks $M_t$, motion fields $D_t$, and latent variables $Z_t$, together with a recurrent hidden state $h_t$. This organization reflects a joint probabilistic view of cardiac dynamics in which anatomy, motion, and latent temporal context are estimated together rather than in isolation.

A central methodological distinction is that CMN eliminates intensity-based image registration similarity loss. Instead, it aligns warped shapes with segmentation-derived shape posteriors. This suggests a deliberate shift from appearance-centric registration toward anatomy-centric registration. A plausible implication is that the method is less dependent on raw intensity consistency when anatomical correspondence is the dominant requirement.

2. End-to-end architecture

CMN consists of three main components arranged in an end-to-end recurrent variational framework: an RVAE backbone, DeformNet, and SegNet (Movahed et al., 28 Aug 2025).

Component	Role	Key specification
RVAE backbone	Spatio-temporal latent modeling	FeatNet encoder, InferZ posterior, ConvLSTM RecNet, and decoder
DeformNet	Motion posterior estimation	3D U-Net producing $\mu_{D_t}$ and $\sigma_{D_t}^2$
SegNet	Segmentation posterior estimation	3D U-Net producing class-probability maps for $K=4$ labels

The RVAE backbone begins with FeatNet, which takes $I_t \in \mathbb{R}^{1 \times H \times W \times D}$; for SAX data, $H=W=128$ and $M_t$0. FeatNet is a cascade of 3D convolutions with kernel size $M_t$1, stride $M_t$2 in height, width, and depth, and LeakyReLU activations. Its channel progression is $M_t$3, with intermediate spatial sizes reducing from $M_t$4 to $M_t$5. The flattened bottleneck is passed to InferZ, where two parallel fully connected layers compute posterior parameters $M_t$6 and $M_t$7 in $M_t$8, and $M_t$9 is sampled from a Gaussian posterior.

Temporal dependence is handled by RecNet, a ConvLSTM with hidden state $D_t$0 and $D_t$1 kernels. The recurrence is

$D_t$2

where the ConvLSTM fuses current image features, latent variables, and previous hidden state. The decoder contains FeatZ and DecNet. FeatZ upsamples $D_t$3 with a transposed 3D convolution to the encoder bottleneck dimension and merges it with encoder features via skip-connections. DecNet mirrors FeatNet through five 3D transposed convolutions with channel progression $D_t$4.

DeformNet is a 3D U-Net taking the concatenated input $D_t$5 and outputting the mean motion field $D_t$6 and per-voxel variance $D_t$7. Its covariance is modeled as

$D_t$8

with learned $D_t$9 to capture inter-channel correlations. SegNet is a second 3D U-Net with identical encoder-decoder structure, except for smaller final upsampling, and outputs class-probability maps $Z_t$0 for background, LV, LVmyo, and RV using a Softmax final layer. DeformNet and SegNet each have five down-sampling blocks with channels $Z_t$1 and five up-sampling blocks in reverse order, all using the same $Z_t$2 kernel sizes and stride conventions.

3. Bayesian formulation and optimization objective

CMN is trained by minimizing the negative evidence lower bound (ELBO) together with a smoothness regularizer (Movahed et al., 28 Aug 2025):

$Z_t$3

The smoothness term is

$Z_t$4

The ELBO is decomposed as

$Z_t$5

The shape term contains two parts. At end-diastolic (ED) and end-systolic (ES) frames, CMN uses a supervised shape loss, implemented as cross-entropy against ground-truth masks. For intermediate frames, it uses a semi-supervised shape loss defined as the KL divergence between the posterior segmentation distribution $Z_t$6 and the prior shape distribution $Z_t$7. This yields a mixed supervision regime in which sparse labeled anchor frames are combined with probabilistic regularization over the rest of the cardiac cycle.

The motion-field KL term $Z_t$8 is defined between a standard Gaussian prior $Z_t$9 and a Gaussian posterior $h_t$0. The latent-variable term $h_t$1 is the closed-form KL divergence between the recurrent prior $h_t$2 and the posterior $h_t$3. The reconstruction term $h_t$4 is a VAE-style $h_t$5 loss on reconstructed images $h_t$6.

The reported hyper-parameters are $h_t$7, $h_t$8, $h_t$9, and $\mu_{D_t}$0. The weighting shows that image reconstruction is retained, but the dominant conceptual innovation lies in the shape-guided registration term rather than in a conventional image-similarity objective.

4. Shape-guided registration and temporal propagation

The spatio-temporal structure of CMN is encoded through explicit factorization of the generative model and approximate posterior (Movahed et al., 28 Aug 2025):

$\mu_{D_t}$1

and

$\mu_{D_t}$2

The recurrence is

$\mu_{D_t}$3

This structure means that temporal context is propagated through $\mu_{D_t}$4, while motion estimation at time $\mu_{D_t}$5 depends on both the current latent representation and prior recurrent state. By conditioning $\mu_{D_t}$6 on $\mu_{D_t}$7, and $\mu_{D_t}$8 on $\mu_{D_t}$9, CMN carries motion-relevant context across the entire cardiac cycle rather than treating each pair of frames independently.

Its registration mechanism is explicitly shape-guided. The prior over the current mask is obtained by warping the previous mask with the estimated motion field:

$\sigma_{D_t}^2$0

SegNet provides the posterior class probabilities $\sigma_{D_t}^2$1. The KL divergence between these two multinomial distributions at each voxel forces DeformNet to produce motion fields that align the warped prior shape to the shape predicted from the current image.

Two clarifications follow from the reported ablation results. First, shape guidance is not interchangeable with temporal modeling: removing SegNet or RVAE degrades performance, and the larger single degradation occurs when SegNet is removed. Second, eliminating intensity-based similarity does not mean that image information is discarded. Images remain central through FeatNet, SegNet, the latent-variable posterior, and the recurrent state, but the registration criterion itself is centered on anatomical consistency.

5. Uncertainty quantification

A defining property of CMN is explicit uncertainty estimation for 3D motion fields (Movahed et al., 28 Aug 2025). Because DeformNet predicts a covariance for the motion posterior at each voxel,

$\sigma_{D_t}^2$2

the method can compute the Shannon entropy of the motion posterior:

$\sigma_{D_t}^2$3

In practice, the diagonal variance term $\sigma_{D_t}^2$4 and the learned low-rank term $\sigma_{D_t}^2$5 permit voxel-wise uncertainty maps indicating where the model is less certain about predicted displacements. This makes uncertainty a first-class output rather than a post hoc diagnostic. Within the reported evaluation protocol, uncertainty is specifically examined in the cardiac region.

The uncertainty mechanism also clarifies a broader point about Bayesian registration models. CMN does not limit uncertainty to scalar confidence scores; it parameterizes a covariance structure for displacement predictions. A plausible implication is that uncertainty is sensitive both to local ambiguity and to inter-channel correlations in 3D motion, although the paper reports this primarily through entropy-derived regional comparisons.

6. Dataset, training protocol, comparative performance, and limitations

CMN was validated on UK Biobank SAX data from 4,000 subjects (Movahed et al., 28 Aug 2025). Of these, 1,000 subjects were used to pre-train SegNet with an 80/10/10 split, and the remaining 3,000 subjects were used for training, validation, and testing of the full framework, again with an 80/10/10 split. Preprocessing consisted of downsampling 50-frame sequences to 6 frames spanning ED, ES, and cycle completion; cropping each slice around the heart with a 30-pixel margin; resizing to $\sigma_{D_t}^2$6; normalizing to $\sigma_{D_t}^2$7; and stacking slices into volumes of depth 16, with zero-padding if needed.

Training proceeded in two phases. In phase 1, SegNet was trained on segmentation alone using cross-entropy. In phase 2, SegNet encoder layers were frozen, and RVAE, DeformNet, and SegNet final layers were trained jointly using the ELBO-plus-smoothness objective. Optimization used Adam with learning rate $\sigma_{D_t}^2$8, batch size 8, and NVIDIA A5000 hardware. Evaluation used Dice Similarity Coefficient (DSC), Jaccard Index (JAC), Mean Surface Distance (MSD), 95%-tile Hausdorff Distance ($\sigma_{D_t}^2$9), number of voxels with negative Jacobian determinants (NJD), and uncertainty within the cardiac region.

CMN was compared against LCC-Demons, SyN (ANTs), VoxelMorph, DragNet, JMS, and SegMorph. The reported summary metrics emphasize both overlap quality and deformation regularity.

Metric	CMN	Selected comparators
LV DSC (%)	90.71±2.51	VoxelMorph 80.78±3.51; DragNet 81.94±2.88; SegMorph 85.39±1.98
LVmyo DSC (%)	79.40±4.02	VoxelMorph 67.99±4.25; DragNet 68.49±4.31; SegMorph 68.98±4.61
RV DSC (%)	86.90±3.30	VoxelMorph 73.57±5.10; DragNet 76.96±4.04; SegMorph 81.70±2.90
$K=4$0 (LV) (mm)	1.77±0.83	VoxelMorph 3.85±2.06; DragNet 3.52±1.62; SegMorph 2.97±1.39
NJD	580±36	VoxelMorph 902±418; DragNet 245±250; SegMorph 472±343

According to the reported results, CMN achieves the highest DSC and JAC, the lowest $K=4$1 and MSD, and low though not minimal NJD. This is an important qualification: the method is not presented as optimizing every deformation regularity metric in isolation, but as balancing anatomical accuracy, robustness, and uncertainty. The uncertainty assessment reports significantly lower motion uncertainty within the heart region than DragNet and SegMorph, with $K=4$2.

The ablation study further partitions the contribution of shape guidance and temporal modeling. The full model with RVAE and SegNet reports LV DSC of 90.7% and $K=4$3 of 1.77 mm. Removing SegNet yields LV DSC of 69.8% and $K=4$4 of 6.3 mm; removing RVAE yields LV DSC of 85.3% and $K=4$5 of 3.12 mm; removing both yields LV DSC of 76.5% and $K=4$6 of 4.71 mm. These results confirm that both components contribute, with SegNet having the larger single impact.

The reported limitations are high computational cost, which restricts the number of input frames during training, and propagation of residual segmentation errors into motion estimates. Future work is described as including mesh-based motion estimation using existing cardiac atlases. In that sense, CMN can be situated as a shape-constrained Bayesian recurrent model whose primary contribution is the replacement of intensity-driven registration losses with anatomically grounded probabilistic alignment.