HFF-Net: Frequency Fusion for Brain Tumor Segmentation

• The paper introduces HFF-Net as a 3D dual-branch encoder–decoder that explicitly decomposes MRI into low-frequency and multi-directional high-frequency components.
• It employs Frequency Domain Decomposition, Adaptive Laplacian Convolution, and Frequency Domain Cross-Attention to achieve sharper boundary delineation and improved texture sensitivity.
• Empirical results show significant improvements in Dice scores and boundary accuracy over conventional segmentation methods, particularly for challenging tumor subregions.

Searching arXiv for papers using the term "HFF-Net" and closely related variants. Search query: HFF-Net frequency brain tumor segmentation arXiv HFF-Net most commonly denotes the Harmonized Frequency Fusion Network, a frequency-aware 3D brain tumor segmentation architecture that decomposes multi-modal MRI into complementary low-frequency and multi-directional high-frequency representations, processes them in separate branches, and fuses them for subregion delineation (Shao et al., 11 Jun 2025). In later BraTS-PED 2025 work, the same model family is used as the frequency-aware component of an ensemble with nnU-Net and Swin UNETR, where its intended contribution is sharper boundary modeling and improved sensitivity to texture-rich tumor regions in pediatric MRI (Yi et al., 18 Sep 2025). The name is not unique across recent literature, however, and has also been used in unrelated contexts, making terminological disambiguation necessary.

1. Terminology and scope

In current arXiv literature, HFF-Net primarily refers to a medical image segmentation model built around explicit frequency decomposition of MRI volumes (Shao et al., 11 Jun 2025). That usage is the dominant one in brain tumor segmentation and is the basis of the BraTS-PED 2025 ensemble instantiation (Yi et al., 18 Sep 2025).

The term is nevertheless ambiguous. Separate papers use closely related names for different systems and learning paradigms. Only the first two entries below refer to the same segmentation lineage.

Name in paper	Domain	Source
HFF-Net	Harmonized Frequency Fusion Network for 3D brain tumor segmentation	(Shao et al., 11 Jun 2025)
HFF-Net	Frequency-aware branch in a BraTS-PED 2025 ensemble	(Yi et al., 18 Sep 2025)
HFF-Net / HF-FMs	Hierarchical networked system for federated foundation models over wireless networks	(Abdisarabshali et al., 3 Sep 2025)
HFF	Hyperspherical Forward-Forward local learning algorithm	(Sarode et al., 30 Apr 2026)
HFFN	High-Frequency Focused Network for single-image super-resolution	(Weng et al., 2023)

In the segmentation literature, HFF-Net is motivated by the observation that low-frequency MRI content encodes smooth global morphology, whereas high-frequency content captures sharp boundaries, anisotropic textures, and subtle variations that are particularly important for enhancing tumor segmentation (Shao et al., 11 Jun 2025). The BraTS-PED 2025 paper adopts that frequency-aware premise and applies it to pediatric high-grade glioma segmentation, where heterogeneous anatomy, small lesions, and acquisition variability are emphasized as central difficulties (Yi et al., 18 Sep 2025).

2. Problem setting and clinical target structure

The original HFF-Net paper formulates the method for 3D brain tumor segmentation on multi-modal MRI, with a particular emphasis on contrast-enhancing tumor regions visible in post-contrast T1-weighted MRI (Shao et al., 11 Jun 2025). The datasets listed for evaluation are BraTS2019, BraTS2020, MSD-BTS, and BraTS2023-MEN, using four modalities per case: T1, T1Gd or T1C, T2, and FLAIR or T2-FLAIR, depending on the benchmark.

Its core segmentation targets are the three major BraTS subregions: ET, WT, and TC. In the BraTS-PED 2025 ensemble setting, the label space is expanded to six regions: ET (enhancing tumor), NET (non-enhancing tumor), CC (cystic component), ED (peritumoral edema), TC (tumor core), and WT (whole tumor), with the standard BraTS compositional semantics that $$\mathrm{TC} = \mathrm{ET} \cup \mathrm{NET} \cup \mathrm{CC}$$ and $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$ (Yi et al., 18 Sep 2025).

The frequency-domain rationale is consistent across both papers. Low-frequency components are described as supporting smooth tissue contours and robust global delineation, while high-frequency components emphasize directional edges, fine textures, and boundary detail. In the pediatric setting, this division is explicitly linked to the hypothesis that low-frequency structure helps ED and overall tumor extent, whereas high-frequency structure helps ET and CC characterization (Yi et al., 18 Sep 2025). This suggests that HFF-Net is not merely a preprocessing variant of a conventional encoder-decoder, but a model designed to encode a specific anatomical prior about how tumor evidence is distributed across spectral bands.

3. Architecture and frequency-aware representation

HFF-Net is a dual-branch 3D encoder-decoder that separately processes low-frequency and high-frequency information and fuses them at deeper stages of the network (Shao et al., 11 Jun 2025). In the full formulation, three named modules define the architecture: Frequency Domain Decomposition (FDD), Adaptive Laplacian Convolution (ALC), and Frequency Domain Cross-Attention (FDCA).

Frequency Domain Decomposition

FDD decomposes each modality into one low-frequency component and multiple directional high-frequency components. The low-frequency path uses the Dual-Tree Complex Wavelet Transform (DTCWT), while the high-frequency path uses the Nonsubsampled Contourlet Transform (NSCT). In the compact formulation reported for BraTS-PED 2025, for each modality $m$ and slice $s$,

$$LF_m[s] = \phi_{\mathrm{DTCWT}} * I_m[s], \qquad HF_{m,k}[s] = \psi_{\mathrm{NSCT},k} * I_m[s], \; k \in \{1,2,3,4\}.$$

Stacking slices reconstructs 3D low-frequency and high-frequency volumes at the original spatial resolution (Yi et al., 18 Sep 2025).

In the original HFF-Net paper, the FDD outputs are given as

• $x^L \in \mathbb{R}^{M \times D \times H \times W}$ for low-frequency tensors, and
• $x^H \in \mathbb{R}^{4M \times D \times H \times W}$ for high-frequency tensors,

with four directional high-frequency subbands per modality (Shao et al., 11 Jun 2025). In the BraTS-PED 2025 implementation this becomes 20 input channels per case: 4 low-frequency channels and 16 high-frequency channels (Yi et al., 18 Sep 2025).

Adaptive Laplacian Convolution

ALC is the mechanism that adapts high-frequency filtering while preserving explicit edge sensitivity. Its kernels are initialized with the discrete 3D Laplacian operator,

$$(\Delta X)(i,j,k) = X(i+1,j,k)+X(i-1,j,k)+X(i,j+1,k)+X(i,j-1,k)+X(i,j,k+1)+X(i,j,k-1) - 6X(i,j,k),$$

and are then regularized with an Elastic Weight Consolidation scheme that preserves weights deemed important by Fisher information after a 40-epoch warmup (Shao et al., 11 Jun 2025). Operationally, the paper summarizes the module as

$$y = \mathrm{Conv}(x; K_{\mathrm{ALC}}), \qquad K_{\mathrm{ALC}} = \mathrm{LaplaceInit} + \Delta K.$$

This design is intended to preserve high-pass behavior while still adapting to multimodal, multi-directional data. The paper further reports that the discrete Laplacian outperforms Sobel, Scharr, and Kirsch initializations in its operator-sensitivity study (Shao et al., 11 Jun 2025).

Frequency Domain Cross-Attention

FDCA performs cross-frequency fusion in the frequency domain using semantic, positional, and slice-specific attentions. For feature maps $F \in \mathbb{R}^{c \times n \times h \times w}$, FFT is applied to obtain real and imaginary components, and three attention stages are computed in sequence. The module is described as integrating semantic, positional, and slice-specific information to improve anisotropic volumetric fusion and cross-frequency consistency (Shao et al., 11 Jun 2025).

The slice-attention mechanism is particularly specific to the 3D setting: it operates along the depth axis $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$0, and the paper states that it is intended to simulate inter-slice variability and maintain volumetric coherence. This distinguishes HFF-Net from purely spectral or purely spatial attention schemes.

Encoder-decoder organization

The original paper describes dedicated LF and HF encoders, deep fusion, and a symmetric decoder with skip connections and side-output supervision (Shao et al., 11 Jun 2025). The BraTS-PED 2025 summary, which relies on the previously introduced HFF-Net, describes the model more generically as a standard 3D encoder-decoder with skip connections in both LF and HF branches and fusion near the bottleneck or decoder, while noting that exact layer counts, kernel sizes, channel widths, and module details are not disclosed there (Yi et al., 18 Sep 2025).

4. Training objectives, normalization, and optimization

HFF-Net is trained on 3D patches of size $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$1 and applies instance-level or volume-level z-score normalization,

$\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$2

This normalization is explicitly reported in the BraTS-PED 2025 implementation and is also consistent with the preprocessing described in the original paper (Yi et al., 18 Sep 2025).

In the full HFF-Net formulation, the optimization target is

$\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$3

where supervised segmentation uses Dice loss, unsupervised LF-HF consistency is enforced through a 3D Dynamic Focal Loss (DFL) in the frequency domain, and $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$4 constrains ALC kernels relative to the Laplacian prior (Shao et al., 11 Jun 2025). The supervised Dice formulation is

$\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$5

The original training protocol uses SGD, momentum 0.9, weight decay $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$6, initial learning rate 0.3, multiplicative decay by 0.53 every 50 epochs, total 350 epochs, batch size 1, and a 40-epoch warmup for EWC and the ramping of $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$7 to $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$8 (Shao et al., 11 Jun 2025). Augmentations are random flipping along each axis, rotations within $\mathrm{WT} = \mathrm{TC} \cup \mathrm{ED}$9, and random crops centered around the brain.

The BraTS-PED 2025 paper reports a closely related but not identical schedule for its HFF-Net component: 450 epochs, batch size 1, patch size $m$0, SGD with momentum 0.9, weight decay $m$1, and initial learning rate 0.3 with progressive decay; mixed precision, HFF-Net-specific augmentations beyond z-score normalization, and the exact loss are not stated there (Yi et al., 18 Sep 2025). That paper also explicitly notes that, unlike Swin UNETR, HFF-Net is trained from scratch in the pediatric setting.

5. Empirical results and role within ensembles

On the multi-dataset evaluation reported for the original model, HFF-Net achieves the following representative Dice and HD95 results (Shao et al., 11 Jun 2025):

• BraTS2023-MEN: Dice ET 96.16%, WT 95.56%, TC 96.34%; HD95 ET 5.576 mm, WT 6.272 mm, TC 6.432 mm.
• MSD-BTS: Dice ET 87.28%, WT 94.03%, TC 89.09%.
• BraTS2020: Dice ET 87.36%, WT 92.37%, TC 88.22%.
• BraTS2019: Dice ET 85.35%, WT 91.58%, TC 87.59%.

The abstract reports an average relative improvement of 4.48\% in mean Dice across ET, WT, and TC, with a range of 2.39\% to 7.72\%, and an average relative improvement of 7.33\% in ET Dice, with a range of 5.96\% to 8.64\% (Shao et al., 11 Jun 2025). The paper also states that HFF-Net shows significantly higher Dice and lower HD95, with $m$2 in multiple comparisons against baselines including UNETR, VT-UNet, PANet, SegMamba, UNETR++, and nnU-Net, especially for ET.

Ablation results support the architectural decomposition. On BraTS23-MEN, FDD alone yields ET 92.89, WT 91.38, TC 92.48; FDD + ALC improves ET by +1.96 to 95.89; FDD + FDCA raises TC to 95.56; and the full model reaches ET 96.16, WT 95.56, TC 96.34, with ~37.76M parameters and ~573.06 GFLOPs (Shao et al., 11 Jun 2025).

In the BraTS-PED 2025 ensemble study, standalone HFF-Net validation performance is reported as Dice 0.683 for CC, 0.934 for ED, 0.703 for ET, 0.900 for NET, 0.928 for TC, and 0.928 for WT, with corresponding NSD-0.5 values of 0.673, 0.934, 0.638, 0.653, 0.674, and 0.675 (Yi et al., 18 Sep 2025). The paper states that HFF-Net’s strongest standalone improvement appears on ET, which it associates with the model’s emphasis on boundaries and directional texture.

The final pediatric ensemble uses equal-weight probability averaging,

$m$3

followed by argmax, with no post-processing (Yi et al., 18 Sep 2025). The reported challenge summary scores are 72.3% for ET, 95.6% for NET, 68.9% for CC, 89.5% for ED, 92.3% for TC, and 92.3% for WT. On the validation table, the ensemble reaches ET 0.689, CC 0.723, ED 0.956, NET 0.895, TC 0.923, and WT 0.923.

6. Computational profile, reproducibility, and implementation

The original HFF-Net study reports implementation in PyTorch 2.1.2 with CUDA 11.8, training on an NVIDIA RTX 4090 (24 GB) (Shao et al., 11 Jun 2025). The reported full-model computational profile includes around 36.01M parameters and ~541.18 GFLOPs in the BraTS2020 table, increasing to ~37.76M parameters and ~573.06 GFLOPs in ablations. Reported inference performance is ~6.71 images/s with ~159.3 ms/image GPU latency.

The BraTS-PED 2025 ensemble implementation reports NVIDIA GeForce RTX 4080 (16 GB) hardware and an HFF-Net training time of ≈48 hours (Yi et al., 18 Sep 2025). For comparison within the same paper, a single-fold nnU-Net requires ≈37 hours, and Swin UNETR requires ≈4 days. Parameter counts, memory footprint, and inference-time latency are not reported there.

The reproducibility path is unusually explicit at the preprocessing level. The pediatric paper specifies:

1. skull stripping via a public nnU-Net-based pipeline,
2. per-modality frequency decomposition through DTCWT for LF and NSCT for four directional HF subbands,
3. reassembly into 3D 20-channel inputs,
4. z-score normalization of each channel volume,
5. training on $m$4 patches,
6. equal-weight probability averaging with nnU-Net and Swin UNETR (Yi et al., 18 Sep 2025).

Both the original HFF-Net study and the pediatric ensemble reference the same code repository: https://github.com/VinyehShaw/HFF (Shao et al., 11 Jun 2025). The pediatric paper additionally notes that no post-processing such as connected-component filtering, hole filling, or region-size filtering is applied (Yi et al., 18 Sep 2025).

7. Limitations, open questions, and related misconceptions

A persistent limitation is that ET remains the most challenging class even with frequency-aware modeling in the pediatric setting, which the paper attributes to small, irregular, and heterogeneous enhancement patterns (Yi et al., 18 Sep 2025). The original study also notes failure cases in which missing or corrupted FLAIR impairs the separation of ED from NCR/NET, indicating that decomposition alone does not neutralize modality unreliability (Shao et al., 11 Jun 2025).

Another limitation is that the frequency transforms used in the BraTS-PED configuration are fixed rather than learned. The paper explicitly remarks that robustness to acquisition variability may therefore be limited, because the network cannot adapt cutoffs or orientations to scanner-dependent artifacts (Yi et al., 18 Sep 2025). The full HFF-Net paper likewise acknowledges the computational burden of the model relative to lightweight baselines, despite reporting favorable clinical applicability (Shao et al., 11 Jun 2025).

The future directions named across the two papers are technically coherent. They include adaptive frequency masks, learned cutoffs and orientations, learnable wavelet- or contourlet-like convolutions, multi-scale frequency fusion, wavelet packet or hybrid spatial-frequency transformers, and lightweight post-processing for ET and CC suppression of spurious high-frequency false positives (Yi et al., 18 Sep 2025). The original paper also motivates further work on preserving more spatial information beyond the current FDCA and decoder design, while maintaining the clinical advantages of end-to-end inference without post-processing (Shao et al., 11 Jun 2025).

A common misconception is to treat HFF-Net as a generic “frequency-domain CNN.” The published description is narrower and more structured than that. It is specifically a 3D dual-branch encoder-decoder whose spectral inductive bias is implemented through DTCWT-based LF decomposition, NSCT-based directional HF decomposition, Laplacian-initialized adaptive high-pass filtering, and frequency-domain cross-attention (Shao et al., 11 Jun 2025). A second misconception is terminological: not every paper using a similar acronym refers to this segmentation model. The wireless networking literature’s HFF-Net is a hierarchical orchestration fabric for federated foundation models, not a medical segmentation architecture (Abdisarabshali et al., 3 Sep 2025), and HFF is also used for a hyperspherical reformulation of the Forward-Forward learning algorithm (Sarode et al., 30 Apr 2026).