Feature-Enhanced Residual Module (FERM)

• The paper demonstrates that FERM improves image registration by effectively fusing multi-scale features with channel-wise attention and residual learning.
• FERM’s architecture, comprising Feature Fusion, Squeeze Excitation, and Deformation Field Estimator blocks, refines anatomical detail and mitigates error propagation.
• Empirical results show that incorporating FERM into TCIP leads to higher Dice coefficients and robust performance across diverse medical imaging datasets.

A Feature-Enhanced Residual Module (FERM) is a composite architectural unit that augments classic residual learning with mechanisms for controlled feature fusion, channel-wise attention, and guided enhancement, with the overarching objective of improving detailed representation in deep neural networks for tasks such as segmentation and image registration. FERMs are typified by their ability to effectively integrate hierarchical information and facilitate robust optimization, especially in data-constrained or structurally complex scenarios.

1. Structural Composition and Mathematical Formulation

FERM, as instantiated in the Threshold-Controlled Iterative Pyramid (TCIP) network (Wu et al., 9 Oct 2025), consists of three sequentially arranged submodules at each decoding layer:

1. Feature Fusion Block (FFB): Responsible for anatomical semantic extraction via fusion of fixed and moving image features.
2. Squeeze Excitation Block (SEB): Applies channel-wise attention to suppress irrelevant or spurious information, thereby enhancing deformation-relevant structures.
3. Deformation Field Estimator (DeF): Translates the refined feature representations into estimates of the deformation field for the current scale.

The process is formalized as follows:

• Let $F_l$ and $M_l$ denote the multi-scale features for the fixed and moving images at scale $l$. At the coarsest scale ($l=4$), they are concatenated directly: $|M_4, F_4|$.
• At finer scales ($l \in \{1,2,3\}$), the deformation field $\phi_{l+1}$ from the previous scale is upsampled and applied (via a spatial transformer) to warp $M_l$, producing $M^\mathcal{W}_l$; these are then concatenated with $F_l$.
• The FFB applies two 3D convolutional layers with LeakyReLU activations and a residual connection:

$$\text{FFB}(x) = \gamma(C_2(\gamma(C_1(x)))) + \gamma(C_1(x)),$$

where $C_1$ and $C_2$ are convolutions and $\gamma$ is LeakyReLU.

• SEB uses global average pooling to create a channel descriptor $Z_l$ for each channel $c$:

$Z_{l,c} = \frac{1}{HWD} \sum_{i,j,d} R_{l,c,i,j,d}$

This is followed by two fully-connected layers ($W_1$: reduction, $W_2$: restoration), separated by LeakyReLU and final sigmoid activation:

$S_l = \sigma(W_2\cdot \gamma(W_1 Z_l))$

The refined feature map is then:

$O_{l,c} = R_{l,c} \odot S_{l,c}$

where $\odot$ denotes channel-wise multiplication.

• The Deformation Field Estimator consists of two convolutions reducing $O_l$ to three channels (3D displacement vectors):

$\phi_l = C_4(C_3(O_l))$

This arrangement ensures efficient extraction, attention-based enhancement, and geometrically meaningful output at each pyramid level.

2. Integration within Iterative Pyramid Registration

FERM operates as the central decoder at every spatial resolution in the TCIP pipeline. The encoder provides multi-scale features for both inputs; FERM is then responsible for:

• Fusing and enhancing representations at each scale, progressively refining the anatomical detail.
• Propagating deformation estimates hierarchically from coarse to fine scales.
• Mitigating error accumulation by means of channel-wise attentive suppression of non-informative details.

The TCIP model further employs a dual-stage Threshold-Controlled Iterative (TCI) mechanism which dynamically determines the number of decoding iterations per input, guided by criteria on stability and convergence.

3. Impact on Registration Performance

Empirical studies, as presented in (Wu et al., 9 Oct 2025), demonstrate that integrating FERM into TCIP yields improvements in both Dice coefficient and registration accuracy compared to state-of-the-art pyramid-based models. Notable observations include:

• On Mindboggle–101, LPBA, and IXI datasets, TCIP achieves Dice scores of approximately 66.4%, 73.3%, and 80.5% respectively, surpassing baselines.
• Inference speed is maintained at a level comparable to existing techniques, with model parameter size (~80% that of IIRP) reduced.
• Ablation studies indicate that removing the SEB or FFB in FERM leads to a measurable reduction in accuracy, validating the necessity of both feature fusion and channel-wise attention operations.

4. Mechanisms for Feature Refinement and Suppression of Misalignment

FERM’s design specifically targets the common issue of propagating anatomical misalignments across decoder layers in pyramid networks. The SEB provides global context, learns to reweight channels based on their deformation relevance, and suppresses artifacts. This not only reduces inter-iteration error accumulation, but also enhances the focus on semantically meaningful anatomical regions.

The residual connection within the FFB preserves detailed representations, supporting gradient propagation and the aggregation of multi-scale contextual cues. The fusion of warped moving and fixed image features at each level further sharpens the alignment process.

5. Generalizability and Compatibility with Other Architectures

FERM is architecturally modular and demonstrates compatibility with a broad range of multi-scale registration networks. Incorporating FERM as the replacement decoder in models such as IIRP, PR++, and I2G produces consistent performance gains across both Dice and Mean Squared Error. This indicates that FERM’s core mechanisms—feature fusion, residual enrichment, and channel-wise attention—are not confined to a specific network architecture, but are robust enhancements applicable to various registration paradigms.

6. Computational Efficiency and Scalability

Despite the added complexity of attention and multi-branch fusion, FERM maintains computational tractability:

• The parameter count is kept lower than or comparable to prevailing decoders due to compact convolutional designs within FFB and DeF.
• Use of global pooling and fully connected layers for SEB introduces negligible overhead relative to the volumetric convolutions commonly used in registration.
• FERM’s design is thus amenable to deployment in resource-constrained clinical and research workflows.

7. Contextual Significance and Applications

FERM was introduced to address domain-specific challenges in deformable medical image registration, such as the cumulative propagation of anatomical misalignments and limited generalizability of existing decoders under substantial deformation variability. Its demonstrated performance on both brain MRI and abdomen CT datasets, and its successful transfer to other registration models, suggest applicability to a range of 3D medical imaging tasks where fine anatomical detail and robust iterative refinement are required. These strengths also make FERM a candidate for broader applications in biomedical image analysis requiring detail-preserving, attention-focused feature extraction within a residual learning framework.