Spatial-Frequency Focus Module (SFFM)

• SFFM is a refinement module that enhances fused decoder features for building extraction in degraded optical remote sensing imagery.
• It employs a large-receptive-field spatial attention pathway and a frequency-aware channel reweighting pathway guided by low-frequency anchors.
• Empirical results show improvements of up to +0.94 IoU and enhanced edge continuity, validating its effectiveness against haze and low-light noise.

Searching arXiv for the cited papers to ground the article in current literature. Spatial-Frequency Focus Module (SFFM) is a decoder-stage refinement block introduced in HaLoBuild-Net for building extraction from optical remote sensing imagery under hazy and low-light conditions. Its function is to take a fused decoder feature tensor $F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$ and produce a refined tensor $F_{out}$ of the same shape through the coupling of a large-receptive-field spatial-attention pathway and a frequency-aware channel reweighting pathway, followed by element-wise modulation of the original feature map (Sang et al., 16 Apr 2026). Within the cited formulation, SFFM is designed to mitigate meteorological interference on building features by coupling large receptive field attention with frequency-aware channel reweighting guided by stable low-frequency anchors, while the surrounding HaLoBuild-Net architecture further incorporates a Global Multi-scale Guidance Module (GMGM) and a Mutual-Guided Fusion Module (MGFM) (Sang et al., 16 Apr 2026).

1. Conceptual role and problem setting

SFFM is defined in the context of building extraction from optical remote sensing imagery affected by real-world hazy and low-light degradation. The underlying premise is explicit: under both haze and low-light, high-frequency detail becomes unreliable, whereas low-frequency structure remains stable (Sang et al., 16 Apr 2026). The module therefore combines spatial repair of broken or blurred edges with channel-wise suppression of noisy responses derived from frequency-domain statistics.

Architecturally, SFFM is inserted after multi-source feature fusion in the decoder. At each decoder stage, HaLoBuild-Net fuses features from multiple sources into a single feature tensor $F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$; SFFM then refines this tensor and outputs $F_{out}$ with identical shape (Sang et al., 16 Apr 2026). The described operational decomposition has three parts: a large-receptive-field spatial-attention pathway, a frequency-aware channel reweighting pathway using low-frequency anchors, and a final element-wise modulation that multiplies the two attention maps into the original feature (Sang et al., 16 Apr 2026).

This organization suggests that SFFM is not merely a late fusion block, but a feature-selection mechanism operating simultaneously in the spatial and spectral senses. A plausible implication is that its design targets failure modes typical of adverse remote-sensing imagery: edge fragmentation, haze-induced blur, low-light noise, and instability of fine-scale textural cues.

2. Decoder-stage formulation and tensor flow

The SFFM pipeline begins with a single input tensor: $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$

The module produces two intermediate attentional objects:

• a spatial-attention map

$$Attn_{spatial}\in\mathbb{R}^{B\times C\times H\times W},$$

• a frequency-derived channel weight

$W_{freq}\in\mathbb{R}^{B\times C\times 1\times 1}.$

These are combined with the original input through

$$F_{out}=F_{fused}\odot Attn_{spatial}\odot W_{freq},$$

where $F_{out}\in\mathbb{R}^{B\times C\times H\times W}$ and $\odot$ denotes element-wise multiplication (Sang et al., 16 Apr 2026).

The architectural overview characterizes SFFM as two parallel subnetworks whose outputs are multiplied together and then by the original feature (Sang et al., 16 Apr 2026). This is significant because the two branches do not perform redundant transformations: the spatial branch remains pixel-sensitive and contour-oriented, whereas the frequency branch collapses spatial support into a channel descriptor computed from cropped low-frequency Fourier coefficients.

In implementation terms, the module is used implicitly as part of the full segmentation network rather than being trained with a separate module-specific objective. The source description further states that each convolution or MLP layer is followed by BatchNorm (or LayerNorm) and that a residual connection is placed around the SFFM block for stable gradient flow; no extra spectral or orthogonality regularizer is applied beyond standard weight decay (Sang et al., 16 Apr 2026).

3. Large-receptive-field spatial attention pathway

The spatial pathway constructs a per-channel, per-pixel attention map intended to repair broken or blurred edges. Its equations are given as follows: $F_{out}$0

$F_{out}$1

$F_{out}$2

with

$F_{out}$3

(Sang et al., 16 Apr 2026).

Here, $F_{out}$4 is specified as a depthwise separable convolution of kernel size $F_{out}$5, and the second branch uses dilation $F_{out}$6 so that its effective receptive field covers a much larger neighborhood (Sang et al., 16 Apr 2026). The use of both $F_{out}$7 depthwise separable convolution and dilated $F_{out}$8 depthwise separable convolution indicates a two-scale local-to-expanded spatial encoding prior to attention estimation.

A two-channel spatial descriptor is then built by pooling along the channel dimension: $F_{out}$9

$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$0

$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$1

(Sang et al., 16 Apr 2026).

After splitting $F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$2 into two single-channel masks $F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$3 and $F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$4, the final spatial attention is

$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$5

(Sang et al., 16 Apr 2026).

The stated qualitative effect is that this branch “lights up along the real building contours—even in regions where haze has blurred edges—restoring structural continuity” (Sang et al., 16 Apr 2026). This suggests that the large-receptive-field design is used to stabilize contour inference when local gradients alone are insufficient.

4. Frequency-aware channel reweighting

The frequency pathway uses the low-frequency portion of the Fourier-transformed feature map as a stable anchor for channel reweighting. Its derivation is: $F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$6

$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$7

$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$8

where, if $F_{fused}\in\mathbb{R}^{B\times C\times H\times W}$9 and $F_{out}$0, only the central low frequencies are retained (Sang et al., 16 Apr 2026).

The branch then computes

$F_{out}$1

and

$F_{out}$2

(Sang et al., 16 Apr 2026).

The explicit motivation is that under haze and low-light, high-frequency detail becomes unreliable while low-frequency structure remains stable (Sang et al., 16 Apr 2026). In operational terms, the module therefore transforms $F_{out}$3 to the frequency domain, extracts a small low-frequency square around the center, collapses it to a channel descriptor, and feeds that descriptor through a tiny MLP and sigmoid to generate channel weights (Sang et al., 16 Apr 2026).

The reported qualitative behavior is correspondingly channel-selective: the frequency branch down-weights channels that are noisy due to heavy haze scattering or sensor noise in low light and up-weights channels that still retain strong low-frequency building signatures (Sang et al., 16 Apr 2026). The same source further states that, under heavy haze, the mid-frequency channels are completely suppressed, leaving only the most stable low-frequency structure (Sang et al., 16 Apr 2026). This indicates a form of channel gating tied to spectral robustness rather than purely semantic saliency.

5. Fusion rule, optimization, and empirical effects

The final SFFM output is formed by multiplicative modulation: $F_{out}$4 This preserves the original feature tensor as the carrier signal while applying spatially varying refinement and channel-wise spectral calibration (Sang et al., 16 Apr 2026).

SFFM is trained as part of the full HaLoBuild-Net segmentation objective: $F_{out}$5 where

$F_{out}$6

and

$F_{out}$7

The description further specifies that $F_{out}$8 is typically set to $F_{out}$9 and $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$0 is a small constant for stability (Sang et al., 16 Apr 2026).

The ablation isolating SFFM compares a baseline decoder without SFFM, MGFM, or GMGM against an otherwise identical system with SFFM inserted at each stage. The exact results from Table 5 are as follows (Sang et al., 16 Apr 2026):

Setting	HaLo-L (IoU / F1)	HaLo-H (IoU / F1)
Baseline	66.40 / 79.81	67.92 / 80.90
+ SFFM	67.28 / 80.44	68.86 / 81.56

These correspond to absolute gains of $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$1 IoU and $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$2 F1 on HaLo-L, and $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$3 IoU and $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$4 F1 on HaLo-H (Sang et al., 16 Apr 2026). When all three modules are used together, the network reaches HaLo-L IoU $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$5 and HaLo-H IoU $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$6, corresponding to gains of $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$7 and $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$8 over baseline, respectively (Sang et al., 16 Apr 2026).

The qualitative effects attached to these numbers are equally specific. The combined dual-domain modulation is reported to suppress spurious false positives such as bright vegetation under haze and to fill in gaps in texturally weak areas such as dark rooftops at night (Sang et al., 16 Apr 2026). This suggests that the measured gains are associated both with boundary recovery and with noise-aware feature pruning.

6. Distinction from related spatial-frequency fusion modules

A recurrent source of confusion is nomenclature. SFFM in HaLoBuild-Net should be distinguished from the Spatial-Frequency Fusion Interaction Module (SFFIM) used in BASFNet for camouflaged object detection (Yu et al., 20 Apr 2026). Although both modules operate across spatial and frequency cues, their roles, inputs, and internal logic are different.

In BASFNet, SFFIM is positioned after two upstream modules: the Frequency-Enhanced Edge Exploration Module (FEEM), which produces frequency-domain edge cues, and the Spatial Core Segmentation Module (SCSM), which produces spatial-domain object cues. At each scale, SFFIM receives $$F_{fused}\in\mathbb{R}^{B\times C\times H\times W}.$$9, $$Attn_{spatial}\in\mathbb{R}^{B\times C\times H\times W},$$0, and the previous fused feature $$Attn_{spatial}\in\mathbb{R}^{B\times C\times H\times W},$$1, then performs enhanced feature fusion, dual-branch local/global fusion, and refinement to produce $$Attn_{spatial}\in\mathbb{R}^{B\times C\times H\times W},$$2 (Yu et al., 20 Apr 2026). By contrast, SFFM in HaLoBuild-Net starts from a single already fused decoder tensor $$Attn_{spatial}\in\mathbb{R}^{B\times C\times H\times W},$$3 and applies parallel spatial and frequency attentional modulation to that tensor (Sang et al., 16 Apr 2026).

The distinction is not merely terminological. SFFIM in BASFNet explicitly merges outputs from separate frequency and spatial branches using local and global fusion blocks, whereas SFFM computes a large-receptive-field spatial-attention map and a low-frequency-guided channel weighting vector, then multiplies both into the original feature (Yu et al., 20 Apr 2026). A plausible implication is that SFFIM is a cross-stream interaction module, while SFFM is a single-stream refinement module with dual-domain attentional calibration.

This comparison also clarifies a broader methodological point. Spatial-frequency design in recent dense prediction systems is not a single template: one formulation can emphasize branch interaction across modalities or domains, while another can emphasize robustness-oriented reweighting within a fused representation. SFFM belongs to the latter category as specified in HaLoBuild-Net (Sang et al., 16 Apr 2026).