RDTE-UNet: Hybrid Medical Segmentation

• RDTE-UNet is a neural architecture for precise medical image segmentation that integrates local convolutions with global transformer modules for enhanced edge detection and fine anatomical detail preservation.
• It introduces three key modules: ASBE for adaptive edge sharpening, HVDA for directional feature attention, and EulerFF for effective feature fusion.
• Evaluated on Synapse CT and BUSI ultrasound datasets, RDTE-UNet achieves higher Dice scores and lower boundary errors, demonstrating significant performance improvements.

RDTE-UNet is a neural architecture designed for precise medical image segmentation, targeting enhanced boundary accuracy and preservation of fine anatomical details. It achieves this by integrating local convolutional modeling with global Transformer-based context awareness. The architecture introduces three principal innovations: the Adaptive Shape-aware Boundary Enhancement (ASBE) module for edge sharpening, the Horizontal-Vertical Detail Attention (HVDA) block for fine-grained directional feature modeling, and the Euler Feature Fusion (EulerFF) module for direction- and channel-sensitive skip connection fusion. Evaluated on Synapse multi-organ CT and BUSI breast ultrasound datasets, RDTE-UNet demonstrates advanced segmentation performance in both quantitative and qualitative terms (Qu et al., 3 Nov 2025).

1. Architectural Overview

RDTE-UNet adopts a U-shaped encoder–decoder topology, comprising five encoder and five decoder stages connected via classical skip-links. The encoder alternates between standard ResBlock stages (1–3) and "Details Transformer" stages (4–5). The architecture is organized as follows:

• Front-end ASBE Module: Replaces the initial convolution with an edge-aware block. ASBE utilizes Adaptive Rectangular Convolution for shape-dependent kernel learning and a boundary-difference operator for edge sharpening.
• Hybrid Encoder Backbone: Stages 1–3 are implemented as ResBlocks for strong local representation. Stages 4–5 transition to a Details Transformer block comprising HVDA—emphasizing horizontal and vertical features using directional “StairConv” mechanisms—followed by a channel MLP and Pre-LN residual structures for global modeling.
• Decoder Path and Fusion: At each upsampling stage, corresponding encoder features are fused with the decoder stream via the EulerFF module, allowing dynamic weighting of horizontal, vertical, and channel responses through a complex-valued Eulerian formulation.
• Output Head: A final $1\times1$ convolution maps integrated features to class logits for segmentation.

2. Module Formulations

The RDTE-UNet's three chief modules are mathematically defined as follows:

2.1 Adaptive Shape-Aware Boundary Enhancement (ASBE)

Given $x\in\mathbb{R}^{H\times W\times C}$,

$f_0 = \mathrm{Conv}_{1\times1}(x)$

Feature branches: $$f_{\mathrm{pool}} = \mathrm{AvgPool}_{s}(f_0), \qquad f_{\mathrm{ar}} = \mathrm{ARConv}(f_0)$$ Boundary-difference enhancement: $$\Delta f = f_{\mathrm{pool}} - f_{\mathrm{ar}}, \qquad f_e = \sigma(\alpha\, \Delta f) \odot f_{\mathrm{ar}}$$ Channels fused: $$f_{\mathrm{out}} = \mathrm{Conv}_{1\times1}\left(\left[f_e,\, f_0\right]\right)$$

2.2 Horizontal-Vertical Detail Attention (HVDA)

For $x_\mathrm{in}\in\mathbb{R}^{h\times w\times d}$: $$x_{hd} = \mathrm{StairConv}_h(x_\mathrm{in}), \qquad x_{vd} = \mathrm{StairConv}_v(x_\mathrm{in})$$ Concatenation and fusion: $$x_{\mathrm{cat}} = \mathrm{ReLU}\left(\mathrm{BN}(\mathrm{Conv}_{1\times1}([x_{hd}, x_{vd}]))\right) + x_{hd} + x_{vd}$$

$$x_{\mathrm{fuse}} = \mathrm{ReLU}\left(\mathrm{BN}(\mathrm{Conv}_{3\times3}(x_C)) + x_C\right) + x_{hd} + x_{vd}$$

Self-attention module: $$Q = W_Q x_{\mathrm{fuse}},\ K = W_K x_{\mathrm{fuse}},\ V = W_V x_{\mathrm{fuse}}$$

$$B = \mathrm{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right),\quad \mathrm{HVDA}(x_{\mathrm{in}}) = BV$$

StairConv operations use asymmetric, multi-scale padded convolutions for directional feature extraction.

2.3 Euler Feature Fusion (EulerFF)

Given features $x_s$ (skip) and $x_d$ (decoder), project both into a complex Eulerian domain: $$\mathcal{F}^{(h)} = A_h \cos(\theta_h) + jA_h \sin(\theta_h)$$

$$\mathcal{F}^{(v)} = A_v \cos(\theta_v) + jA_v \sin(\theta_v)$$

Apply group convolutions separately to real and imaginary parts for horizontal and vertical branches, aggregate channel-wise, and fuse: $$\mathcal{F}_{\mathrm{out}} = \mathrm{Conv}_{1\times1}\left([x_s, x_d, \widetilde{\mathcal{T}}_h, \widetilde{\mathcal{T}}_v, \widetilde{\mathcal{T}}_c]\right)$$

3. Network Assembly and Layerwise Pipeline

The layerwise pipeline is as follows:

f0 = ASBE(I) # → R^{H×W×C'} e1 = ResBlock(f0) # H/2, W/2, 2C' e2 = ResBlock(e1) # H/4, W/4, 4C' e3 = ResBlock(e2) # H/8, W/8, 8C' e4 = DetailsTransformer(e3) # H/16, W/16, 16C' e5 = DetailsTransformer(e4) # H/32, W/32, 32C' d5 = Deconv(e5) # H/16, W/16, 16C' d5 = EulerFF(skip=e4, dec=d5) d4 = Deconv(d5) # H/8, W/8, 8C' d4 = EulerFF(skip=e3, dec=d4) d3 = Deconv(d4) # H/4, W/4, 4C' d3 = EulerFF(skip=e2, dec=d3) d2 = Deconv(d3) # H/2, W/2, 2C' d2 = EulerFF(skip=e1, dec=d2) d1 = Deconv(d2) # H, W, C' d1 = EulerFF(skip=f0, dec=d1) out = Conv_{1×1}(d1) # H×W×N_classes return out

This schema reflects the mixed convolutional-transformer design, edge-aware enhancement, and direction-sensitive post-processing prior to segmentation output.

4. Training Protocols and Hyperparameters

• Loss Function: Combination of Dice loss and cross-entropy

$$\mathcal{L} = \lambda_{\mathrm{Dice}} (1 - \mathrm{Dice}(P,T)) + \lambda_{\mathrm{CE}}\,\mathrm{CE}(P,T)$$

with $$\lambda_{\mathrm{Dice}} = \lambda_{\mathrm{CE}} = 0.5$$.

• Optimizer: Adam, parameters $(\beta_1=0.9,\, \beta_2=0.999)$, initial learning rate $1\times10^{-4}$, weight decay $1\times10^{-5}$.
• Learning Rate Scheduling: Cosine annealing with warm restarts (SGDR), training for 200 epochs.
• Batch Sizes: 8 (Synapse), 16 (BUSI).
• Data Augmentation: Random rotations (±15°), flips, intensity scaling.

5. Quantitative and Qualitative Results

On Synapse CT (multi-organ) and BUSI breast ultrasound benchmarks, RDTE-UNet achieves the following:

Synapse Dataset (60/40 split)

Method	DSC (%) ↑	HD95 (mm) ↓
Trans-UNet	79.15	28.47
Swin-UNet	81.03	19.54
MT-UNet	80.72	22.48
RWKV-UNet	85.62	14.83
RDTE-UNet	86.63 ★	11.69 ★

BUSI Dataset (70/30 split)

Method	DSC (%) ↑	HD95 (mm) ↓
Trans-UNet	60.42	32.78
Swin-UNet	62.91	30.67
MT-UNet	62.13	39.08
RWKV-UNet	64.85	29.57
RDTE-UNet	66.31 ★	27.73 ★

The superior boundary quality and structural consistency are substantiated by sharper edges and fewer false positives, particularly around complex morphologies such as the pancreas and fine-grained vasculature.

6. Context and Comparative Significance

RDTE-UNet advances the segmentation performance over previously reported methods by coupling explicit boundary enhancement (ASBE), refined directionality (HVDA), and mathematically principled fusion (EulerFF). The improvements are most pronounced in boundary-sensitive metrics (HD95) and Dice similarity coefficient (DSC). Its hybrid convolution-transformer backbone distinguishes it from pure CNN or typical hybrid architectures by its two-stream encoder and detail- and shape-aware auxiliary branches. This suggests the benefit of modeling interactions between local and long-range detail, especially when segmenting anatomically complex or ambiguous regions.

A plausible implication is that future segmentation methods in computational medicine may increasingly incorporate direction- and boundary-aware modules alongside global context mechanisms to simultaneously address fine structure delineation and region-level accuracy.