Mamba-based Cardiac Motion Tracking (MCM)

• The paper introduces an end-to-end unsupervised framework that models myocardial motion as a temporally coherent deformation estimation problem over cine CMR sequences.
• It leverages bi-directional Mamba blocks in the encoder and a dual-path fusion decoder to integrate adjacent-frame context while maintaining linear-time sequence modeling.
• Empirical results on ACDC and M{content}Ms datasets demonstrate improved Dice scores and reduced negative Jacobian percentages, indicating smoother and more physically plausible deformations.

Searching arXiv for the main paper and closely related methods to support citations. Mamba-based Cardiac Motion Tracking Network (MCM) is an end-to-end, unsupervised cine CMR motion estimator that replaces isolated image-pair training with sequence-aware tracking while retaining linear-time sequence modeling. It is introduced in “MCM: Mamba-based Cardiac Motion Tracking using Sequential Images in MRI” (Yin et al., 23 Jul 2025), where myocardial motion tracking is framed as a temporally coherent deformation estimation problem over cine cardiac magnetic resonance (CMR) sequences rather than over independently sampled reference–target image pairs. The model couples a hierarchical encoder built from bi-directional Mamba blocks with a motion decoder that fuses multi-scale deformation features and explicitly integrates adjacent frames, with the stated aim of yielding smoother and temporally coherent deformation fields without significant computational overhead (Yin et al., 23 Jul 2025).

1. Clinical and methodological context

Left ventricular myocardial motion tracking quantifies cardiac function across space and time, supporting early diagnosis and stratification of myocardial diseases and LV dysfunction. Cine CMR is described as the gold standard for cardiac functional analysis because it provides high-resolution 2D short-axis sequences with detailed structural and dynamic information (Yin et al., 23 Jul 2025).

The motivating problem in MCM is the limitation of a large fraction of recent learning-based methods that estimate motion from a single reference frame, typically end-diastole (ED), to a randomly chosen target frame such as end-systole (ES), independently of the remainder of the cardiac cycle. According to the paper, this overlooks continuous myocardial dynamics and temporal dependencies, often producing motion fields that are locally accurate but globally inconsistent and non-smooth across time, with artifacts such as foldings, volume inconsistency, or jagged fields (Yin et al., 23 Jul 2025).

MCM is positioned against three broad methodological families. Pairwise registration methods such as VoxelMorph operate without sequence context; transformer-based temporal models capture longer-range dependencies but incur quadratic time and memory complexity; and RNN-based models can encode sequences but may be unstable or limited in effective memory. The central design premise is therefore to incorporate the target image sequence—specifically neighboring frames around the target frame—while avoiding transformer-like $O(N^2)$ cost (Yin et al., 23 Jul 2025). This is achieved through a Mamba-style structured state-space formulation, whose underlying sequence model was introduced in “Mamba: Linear-Time Sequence Modeling with Selective State Spaces” (Gu et al., 2023).

The paper’s problem formulation also makes explicit the geometric desiderata for cardiac motion fields: they should be smooth, diffeomorphic or near-diffeomorphic, preserve myocardial wall volume, and avoid foldings and discontinuities. In this setting, temporal context is not treated as an auxiliary cue but as a structural prior on plausible deformation dynamics (Yin et al., 23 Jul 2025).

2. Architectural organization

MCM takes as input a reference frame $I_0$ at ED and, for a target frame index $t$, constructs a target sequence

$S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$

of length $N_f = 2K+1$. Each frame in this sequence is paired with the reference frame to form

$$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$

where each pair has shape $[2, H, W]$ (Yin et al., 23 Jul 2025). For boundary conditions, nearest-frame padding is used; the paper gives the example that for $t=1, K=2$, one obtains $S_t = \{I_0, I_0, I_1, I_2, I_3\}$.

The encoder consists of four hierarchical bi-directional Mamba blocks (BMBs). Between blocks, patch embedding or patch merging downsamples spatially. At encoder level $i$, the update is given as

$I_0$0

$I_0$1

producing $I_0$2 (Yin et al., 23 Jul 2025). Layer normalization is applied prior to both the BiSM module and the MLP, and no explicit positional encoding is required because temporal order is imposed by the forward and backward scanning sequence construction.

The BiSM module is the core sequence model. For each spatial position, it constructs a temporal sequence across frames and applies two parallel selective state-space scans, one in forward temporal order and one in reverse order, then sums the outputs to obtain a unified spatiotemporal representation (Yin et al., 23 Jul 2025). This bi-directional scanning mechanism is intended to integrate information from both past and future frames at the feature level.

The decoder uses a progressive upsampling pathway to fuse multi-scale features $I_0$3 into a motion feature map

$I_0$4

A dual-path fusion head (DFH) then applies forward and backward 3D convolutions along the sequence dimension and averages the results before estimating the final 2D motion field:

$I_0$5

$I_0$6

with $I_0$7 (Yin et al., 23 Jul 2025). The paper explicitly attributes temporal consistency enhancement to this adjacent-frame integration in the decoder.

This encoder–decoder decomposition separates two forms of temporal reasoning. In the encoder, bi-directional scanning aggregates sequential evidence at fixed spatial positions. In the decoder, DFH integrates motion information from frames adjacent to the target frame. A plausible implication is that temporal coherence is enforced both in latent feature formation and in deformation decoding, rather than only through a terminal regularizer.

3. State-space formulation, deformation model, and optimization

The sequence model in MCM is based on the discrete-time linear state-space system

$I_0$8

where $I_0$9 is the input at time $t$0, $t$1 the hidden state, and $t$2 the output (Yin et al., 23 Jul 2025). In the BiSM module, for each encoder level $t$3 and spatial position $t$4, the per-position per-frame feature vector is treated as $t$5.

The forward scan is

$t$6

$t$7

and the backward scan, over reverse temporal order, is

$t$8

$t$9

The bi-directional fusion step is

$S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$0

The fused outputs are then reassembled into a tensor of shape $S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$1 (Yin et al., 23 Jul 2025).

The deformation representation is a dense 2D displacement field $S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$2 over the image domain $S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$3, with two channels corresponding to $S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$4- and $S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$5-displacements. For a pixel $S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$6, the transformed coordinate is

$S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$7

and the warped image is computed by bilinear interpolation:

$S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$8

This is the warping operator used during both training and evaluation (Yin et al., 23 Jul 2025).

Training is unsupervised and combines image similarity with spatial smoothness:

$S_t = \{I_{t-K}, \ldots, I_t, \ldots, I_{t+K}\}$9

where

$N_f = 2K+1$0

$N_f = 2K+1$1

The regularization weight is $N_f = 2K+1$2 in the reported experiments (Yin et al., 23 Jul 2025).

For deformation regularity assessment, the paper uses the Jacobian determinant

$N_f = 2K+1$3

Two Jacobian-derived metrics are reported: $N_f = 2K+1$4, the percentage of points where $N_f = 2K+1$5, and $N_f = 2K+1$6, the mean absolute deviation from unit Jacobian magnitude (Yin et al., 23 Jul 2025). In the paper’s interpretation, lower values correspond to more physically plausible and more volume-preserving deformations.

The computational rationale of MCM follows directly from the state-space design. Mamba’s selective scan is described as linear-time in sequence length $N_f = 2K+1$7, with complexity $N_f = 2K+1$8, whereas transformer attention is quadratic, $N_f = 2K+1$9 (Gu et al., 2023, Yin et al., 23 Jul 2025). In MCM, temporal scanning occurs across $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$0 frames at each spatial position, giving $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$1 per position and $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$2 per feature level (Yin et al., 23 Jul 2025).

4. Data, preprocessing, and evaluation protocol

The model is evaluated on two public cine CMR datasets with short-axis stacks covering the LV from base to apex (Yin et al., 23 Jul 2025).

Dataset	Train/Val/Test split
ACDC (Automated Cardiac Diagnosis Challenge)	80 / 20 / 50 subjects
M&Ms (Multi-Centre, Multi-Vendor, Multi-Disease Cardiac Segmentation Challenge)	150 / 34 / 136 subjects

All images are resampled to $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$3 mm in-plane resolution, center-cropped to $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$4 pixels, and normalized to $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$5 (Yin et al., 23 Jul 2025). Training is performed in PyTorch on an NVIDIA A100-SXM4 40GB GPU, using Adam with learning rate $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$6, for 200 epochs and batch size 32. Motion fields are estimated for all frames in the cardiac cycle, that is, ED$$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$7 for all $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$8, and the main comparison uses $$F_0 = \{(I_0, I_{t-K}), \ldots, (I_0, I_t), \ldots, (I_0, I_{t+K})\},$$9, corresponding to $[2, H, W]$0 frames (Yin et al., 23 Jul 2025).

The evaluation protocol focuses on ED$[2, H, W]$1ES motion on three representative slices: basal (25%), mid-ventricular (50%), and apical (75% LV length), consistent with prior cardiac motion studies (Yin et al., 23 Jul 2025). ED segmentation is warped to ES using the predicted $[2, H, W]$2 and compared to the ground-truth ES segmentation. Quantitative evaluation targets ED$[2, H, W]$3ES because ground-truth segmentation labels are available for ED and ES frames, whereas other frames lack labels (Yin et al., 23 Jul 2025).

The reported primary metrics are the Dice coefficient,

$[2, H, W]$4

the percentage of negative Jacobians $[2, H, W]$5, and the mean absolute $[2, H, W]$6 deviation from 1, $[2, H, W]$7 (Yin et al., 23 Jul 2025). Dice is higher-is-better; the Jacobian metrics are lower-is-better.

The paper also reports inference-time memory and latency:

Method	VRAM / inference time
VM	1.5 GB / 7.9 ms
TM	3.6 GB / 14.9 ms
MambaMorph	2.7 GB / 22.9 ms
MCM $[2, H, W]$8	3.2 GB / 16.3 ms
MCM $[2, H, W]$9	7.8 GB / 16.5 ms
MCM $t=1, K=2$0	12.4 GB / 17.1 ms

These figures are used in the paper to support the claim that inference time remains comparable to baselines as $t=1, K=2$1 increases, while VRAM scales with the number of buffered frames (Yin et al., 23 Jul 2025).

5. Reported performance and empirical behavior

On both ACDC and M&Ms, MCM is reported to quantitatively and qualitatively outperform conventional and state-of-the-art learning-based cardiac motion tracking methods (Yin et al., 23 Jul 2025). The paper compares against dDemons, VoxelMorph, TransMorph, and MambaMorph.

For ACDC, MCM reports the following Dice / $t=1, K=2$2 / $t=1, K=2$3 values across basal, mid, and apical slices, respectively: 83.4(7.1) / 0.14(0.31) / 0.17(0.06), 84.6(4.9) / 0.02(0.04) / 0.18(0.06), and 82.8(5.5) / 0.01(0.02) / 0.17(0.06) (Yin et al., 23 Jul 2025). For M&Ms, the corresponding values are 79.9(8.4) / 0.03(0.09) / 0.19(0.07), 83.6(6.2) / 0.12(0.29) / 0.18(0.06), and 77.6(11.5) / 0.15(0.40) / 0.19(0.08) (Yin et al., 23 Jul 2025).

The reported pattern is not limited to segmentation overlap. The paper emphasizes that MCM strongly reduces $t=1, K=2$4 and $t=1, K=2$5 relative to baselines, which it interprets as evidence for smoother, more physically plausible, and more volume-preserving deformations (Yin et al., 23 Jul 2025). Qualitatively, MCM is described as achieving the smoothest motion fields among the tested methods, with better alignment of warped ED contours to ES ground truth and fewer artifacts and foldings.

The ablation studies isolate the contributions of the bi-directional Mamba blocks and the scanning strategy. On ACDC ED$t=1, K=2$6ES motion, removing BMBs yields Dice values of 81.8(7.8), 82.4(4.7), and 81.4(6.1) on basal, mid, and apical slices, respectively; using BMBs with forward-only scan yields 83.1(6.6), 84.0(4.7), and 82.2(5.4); using BMBs with backward-only scan yields 82.8(6.8), 83.4(4.8), and 82.0(5.3); and using BMBs with BiSM yields 83.4(7.1), 84.6(4.9), and 82.8(5.5) (Yin et al., 23 Jul 2025). The paper’s conclusion is that BMBs are crucial and that bi-directional scanning yields the best performance. It further states that the gains are not merely due to more input frames, but stem from the proposed sequence-aware encoder.

The dual-path fusion head is likewise analyzed. Temporal consistency plots are reported to indicate that DFH improves stability and smoothness of motion across the cardiac cycle. Increasing sequence length from $t=1, K=2$7 to $t=1, K=2$8 further enhances temporal smoothness, with modest Dice gains of approximately $t=1, K=2$9 but visibly smoother fields (Yin et al., 23 Jul 2025). The smoothness weight $S_t = \{I_0, I_0, I_1, I_2, I_3\}$0 is also examined: stronger spatial smoothness regularization improves diffeomorphic properties but may sacrifice alignment accuracy, and $S_t = \{I_0, I_0, I_1, I_2, I_3\}$1 is reported as the optimal balance in the experiments.

6. Positioning, limitations, and practical considerations

MCM is positioned as a sequence-aware alternative to isolated-frame registration while avoiding transformer-style quadratic scaling (Yin et al., 23 Jul 2025). Relative to pairwise approaches such as VoxelMorph, it introduces adjacent-frame context, bi-directional temporal aggregation, and decoder-level temporal fusion. Relative to transformer-based temporal models such as TransMorph (Chen et al., 2021), it adopts a structured state-space mechanism with linear-time selective scan rather than attention-based global pairwise interactions. Relative to RNN-style sequence models, it processes per-position temporal sequences with structured state-space layers and fuses the resulting features across scales (Yin et al., 23 Jul 2025).

The model’s principal limitation, as stated in the paper, is memory growth with sequence length: VRAM rises from 3.2 GB at $S_t = \{I_0, I_0, I_1, I_2, I_3\}$2 to 12.4 GB at $S_t = \{I_0, I_0, I_1, I_2, I_3\}$3 because multiple frames must be buffered (Yin et al., 23 Jul 2025). The reported experiments are restricted to 2D short-axis sequences because the public datasets provide 2D stacks; extending the design to 3D would require 3D convolutions and more GPU memory. The paper also notes potential sensitivity to image quality and inter-scanner domain shifts, particularly in the multi-centre M&Ms dataset, and states that extreme motion or poor contrast may challenge the model.

At the same time, the paper reports cross-dataset gains on both ACDC and M&Ms without dataset-specific hand-tuning beyond split and preprocessing, which it presents as evidence of good generalization (Yin et al., 23 Jul 2025). A plausible implication is that the encoder’s explicit temporal structure and the decoder’s adjacent-frame fusion act as architectural priors that transfer across vendor and disease variation better than purely pairwise schemes.

The implementation is released at the repository specified in the paper, and the configuration notes emphasize the role of neighbor radius $S_t = \{I_0, I_0, I_1, I_2, I_3\}$4, with $S_t = \{I_0, I_0, I_1, I_2, I_3\}$5 as the main setting, and $S_t = \{I_0, I_0, I_1, I_2, I_3\}$6 as a default that balances smoothness and accuracy (Yin et al., 23 Jul 2025). The same notes state that adaptation to other sequences or modalities can preserve the common-reference pairing strategy while adjusting $S_t = \{I_0, I_0, I_1, I_2, I_3\}$7 to match frame rate; for 3D data, 2D operations in the encoder and decoder would be replaced by 3D variants, with corresponding increases in memory demand.

Within cardiac motion tracking, MCM therefore represents a shift from isolated-frame deformation estimation toward bidirectional state-space modeling over cine sequences. Its defining claim is not merely improved overlap accuracy, but the joint attainment of smoother and temporally consistent deformation fields, improved Jacobian behavior, and linear-time sequence modeling in cine CMR (Yin et al., 23 Jul 2025).