Split Coordinate Attention (SCA)

• The paper introduces SCA, a novel plug-and-play attention module that leverages axis-wise pooling combined with a ResNeSt-style split-attention scaffold to improve building footprint extraction.
• SCA exploits per-split transformations and outer-product synthesis to produce rank-1, coordinate-aware attention maps that better delineate edges and small structures.
• Integrating SCA within SCANet yields superior IoU performance on benchmark datasets while maintaining a competitive parameter count compared to prior attention mechanisms.

Searching arXiv for the primary and related papers to ground the article in the current literature. arXiv search query: (Wang et al., 28 Jul 2025) Split Coordinate Attention (SCA) is a plug-and-play attention module introduced for building footprint extraction in remote sensing imagery. It is designed to capture spatially remote interactions while retaining precise positional information by combining axis-wise global pooling with a split-attention scaffold derived from ResNeSt-style grouping. In the formulation reported for SCANet, SCA operates on features $X \in \mathbb{R}^{C \times H \times W}$, partitions them into cardinal groups and splits, encodes each channel along the horizontal and vertical directions, generates per-split axis-attention vectors, synthesizes rank-1 two-dimensional attention maps through an outer product, and fuses the resulting modulated features through a residual pathway. Within the SCANet architecture, this mechanism is inserted into a 2D CNN encoder and paired with a UNet++ decoder, yielding the best IoU of $91.61\%$ on the WHU Building Dataset and $75.49\%$ on the Massachusetts Building Dataset (Wang et al., 28 Jul 2025).

1. Motivation and problem setting

SCA was proposed in the context of building footprint extraction, a task described as having great value in urban planning, land use, environmental protection and disaster assessment. The motivating difficulty is that both conventional and deep learning approaches continue to encounter significant challenges in remote sensing scenes containing multi-scale buildings, occlusions, adjacency effects, shadows, repetitive urban textures, and variability induced by sensor, meteorology, and topography (Wang et al., 28 Jul 2025).

The module is positioned against three limitations in prior attention designs. First, channel-only attention such as Squeeze-and-Excitation uses global average pooling,

$s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$

which removes precise location and makes it difficult to refine boundaries and small structures. Second, spatial attention such as CBAM aggregates over two-dimensional maps with convolutional kernels that remain local, making long-range dependencies across roof edges and repeated block-level patterns harder to model explicitly. Third, Coordinate Attention retains positional information by axis-wise encoding, but uses a single pooling range per axis and a single gating path; in complex scenes with varied building sizes and densities, that single axis-encoding can underspecify remote interactions and channel diversity (Wang et al., 28 Jul 2025).

Accordingly, SCA is intended to satisfy two simultaneous requirements: long-range interaction, so that semantically connected but distant regions can influence each other, and fine positional detail, so that building edges, holes, and small structures can be delineated accurately. This suggests that SCA is best understood not as a generic saliency layer, but as a structured coordinate-aware mechanism tailored to dense prediction under strong geometric variability.

2. Formal definition and computational pathway

The input feature tensor is $X \in \mathbb{R}^{C \times H \times W}$. Following a ResNeSt-style split-attention organization, SCA uses $K$ cardinal groups and $R$ splits per group, giving $G = K \cdot R$ feature groups. For $j \in \{1,\dots,G\}$, the per-group transformation is $U_j = \mathcal{F}_j(X)$. Within each cardinal group $91.61\%$0, the splits are first aggregated: $91.61\%$1

SCA then decomposes global spatial pooling into two axis-wise average-pooling operations. The horizontal pooling kernel spans the entire width with kernel size $91.61\%$2, and the vertical pooling kernel spans the entire height with kernel size $91.61\%$3. For the $91.61\%$4-th channel in group $91.61\%$5,

$91.61\%$6

These one-dimensional descriptors preserve exact position along one axis while aggregating global context along the other axis (Wang et al., 28 Jul 2025).

For each split $91.61\%$7, SCA concatenates the two axis encodings and applies a lightweight per-split transformation: $91.61\%$8 The result is split back into axis-specific components

$91.61\%$9

after which lightweight per-axis channel transforms with sigmoid gating produce

$75.49\%$0

The two one-dimensional gates are combined through an outer product to form a rank-1 two-dimensional attention map for each split: $75.49\%$1 The split-specific maps are then summed and used to modulate the aggregated group feature: $75.49\%$2 Finally, the $75.49\%$3 group outputs are concatenated,

$75.49\%$4

and fused residually: $75.49\%$5

The reported computational pathway is therefore: axis global average pooling; concatenation of axis encodings; per-split transform $75.49\%$6; split into axis-specific components; per-axis dense connections $75.49\%$7 and $75.49\%$8 with sigmoid gating; outer-product synthesis of two-dimensional gates; summation across splits; elementwise modulation of $75.49\%$9; channel concatenation across cardinal groups; and residual addition (Wang et al., 28 Jul 2025).

3. Relationship to SE, CBAM, Coordinate Attention, and split attention

SCA is explicitly framed as an extension beyond channel-only attention, spatial attention, and Coordinate Attention. Relative to SE, the distinction is that SE produces a global channel gate applied uniformly over space, whereas SCA preserves coordinate information through axis-wise pooling and reconstructs a two-dimensional attention map by outer product. Relative to CBAM, SCA does not rely on a local convolutional spatial branch; instead, it encodes long-range interactions separately along each axis and yields coordinate-aware rank-1 attention maps. Relative to Coordinate Attention, SCA retains the basic axis-wise global pooling idea but places it inside a split-attention scaffold with per-split gating diversity rather than a single gating path (Wang et al., 28 Jul 2025).

Coordinate Attention, introduced earlier for efficient mobile network design, factorizes channel attention into two one-dimensional encoding processes that aggregate features along the two spatial directions. In its reported form, for $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$0, the module computes

$s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$1

concatenates the resulting descriptors, applies a shared bottleneck transform, splits the result into two branches, and generates direction-aware gates that are multiplied with the input feature map (Hou et al., 2021). In that sense, SCA inherits the coordinate-aware principle of CA while modifying the computational context in which it operates.

The principal deltas reported for SCA are fourfold. The pooling strategy remains axis-wise global average pooling, but SCA performs it per cardinal group. The splitting strategy is more elaborate, because SCA leverages $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$2 grouping and introduces multiple per-split transformations and gates. The attention maps differ in that CA produces one pair of directional maps, while SCA produces per-split rank-1 maps $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$3 and sums them. The computational pathway also differs: SCA aggregates splits before gating, fuses them after gating, and integrates directly with split-attention residual blocks (Wang et al., 28 Jul 2025).

A common misconception is to treat SCA as merely a renaming of Coordinate Attention. The available formulations do not support that view. The two methods share axis-wise encoding, but SCA is defined by its operation inside a ResNeSt-style split-attention framework and by its multiple per-split gating paths, whereas CA uses a single shared bottleneck and two directional heads (Wang et al., 28 Jul 2025, Hou et al., 2021).

4. Complexity, parameters, and implementation characteristics

For channels $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$4, spatial dimensions $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$5 and $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$6, $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$7 cardinal groups, and $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$8 splits per group, the axis-pooling cost per cardinal group is $s_c = \frac{1}{H \cdot W}\sum_{h,w} X(c,h,w),$9, which gives $X \in \mathbb{R}^{C \times H \times W}$0 across all groups. Assuming lightweight $X \in \mathbb{R}^{C \times H \times W}$1 channel mixing, the per-split transformations contribute $X \in \mathbb{R}^{C \times H \times W}$2, and the attention application contributes $X \in \mathbb{R}^{C \times H \times W}$3. The dominant reported time complexity is therefore

$X \in \mathbb{R}^{C \times H \times W}$4

with moderate amortized overhead because $X \in \mathbb{R}^{C \times H \times W}$5 is small in practice. The space complexity is $X \in \mathbb{R}^{C \times H \times W}$6 for storing gates plus $X \in \mathbb{R}^{C \times H \times W}$7 for the feature map, with the latter dominating (Wang et al., 28 Jul 2025).

The parameter analysis reported for the building extraction setting emphasizes that SCA uses small per-split transforms $X \in \mathbb{R}^{C \times H \times W}$8 and per-axis dense connections $X \in \mathbb{R}^{C \times H \times W}$9 and $K$0, and does not introduce large channel MLPs. On the WHU ablation, a baseline ResNet + UNet++ model has $K$1M parameters and IoU $K$2; adding SA gives $K$3M parameters and IoU $K$4; adding CA gives $K$5M parameters and IoU $K$6; and adding SCA with UNet++ gives $K$7M parameters and IoU $K$8. Thus, SCA matches SA’s parameter count, is smaller than CA, and yields the best IoU in that comparison (Wang et al., 28 Jul 2025).

Implementation details reported for SCA consist of axis-wise global average pooling along width and height with kernels $K$9 and $R$0, lightweight per-split transforms $R$1 realized as $R$2 convolution or dense layers followed by an activation function applied after convolution, per-axis dense connections $R$3 and $R$4 with sigmoid gates, and a residual add $R$5 for shape matching. The reference implementation environment is PyTorch 1.13 with CUDA 11.8 on RTX 3090 (Wang et al., 28 Jul 2025).

5. Integration in SCANet for building footprint extraction

Within SCANet, SCA is inserted into a ResNeSt-like encoder with five stages. Each stage downsamples by $R$6, so an input of $R$7 yields feature maps of $R$8, $R$9, down to $G = K \cdot R$0. SCA replaces split attention inside residual bottleneck blocks of the encoder and operates over cardinal groups and splits at the point where split attention would otherwise be applied. The decoder is UNet++, which uses nested skip connections to parse high-level features and support multi-scale fusion and boundary refinement from encoder stages augmented by SCA outputs (Wang et al., 28 Jul 2025).

The training setup reported for SCANet uses the WHU Building Dataset and the Massachusetts Building Dataset, both uniformly cropped to $G = K \cdot R$1. WHU contains $G = K \cdot R$2 training tiles, $G = K \cdot R$3 validation tiles, and $G = K \cdot R$4 test tiles with high-quality labels. MASS contains images of $G = K \cdot R$5, cropped to $G = K \cdot R$6, with $G = K \cdot R$7 training images, $G = K \cdot R$8 validation images, and $G = K \cdot R$9 test images, and is described as having lower ground resolution and label accuracy relative to WHU. Optimization uses Binary Cross Entropy + Dice Loss, AdamW with initial learning rate $j \in \{1,\dots,G\}$0, IoU validation after each epoch, and a schedule that halves the learning rate if IoU does not improve for $j \in \{1,\dots,G\}$1 epochs. The batch size is $j \in \{1,\dots,G\}$2 for WHU and $j \in \{1,\dots,G\}$3 for MASS (Wang et al., 28 Jul 2025).

This architectural configuration situates SCA as the encoder-side mechanism for semantic feature extraction, while UNet++ supplies the decoder-side multi-scale aggregation. A plausible implication is that the reported gains attributed to SCA arise not only from improved long-range coordinate-aware modeling in the encoder, but also from the compatibility of those enriched features with nested skip fusion in the decoder.

6. Empirical performance, robustness, and scope

The reported quantitative results place SCANet ahead of recent state-of-the-art methods on both benchmark datasets. On WHU, SCANet achieves IoU $j \in \{1,\dots,G\}$4, Precision $j \in \{1,\dots,G\}$5, Recall $j \in \{1,\dots,G\}$6, and F1 $j \in \{1,\dots,G\}$7, outperforming ConvBNet at IoU $j \in \{1,\dots,G\}$8 and BCTNet at IoU $j \in \{1,\dots,G\}$9, for an IoU improvement of $U_j = \mathcal{F}_j(X)$0 over the prior state of the art. On MASS, SCANet achieves IoU $U_j = \mathcal{F}_j(X)$1, Precision $U_j = \mathcal{F}_j(X)$2, Recall $U_j = \mathcal{F}_j(X)$3, and F1 $U_j = \mathcal{F}_j(X)$4, corresponding to an IoU improvement of $U_j = \mathcal{F}_j(X)$5 over BCTNet at IoU $U_j = \mathcal{F}_j(X)$6 (Wang et al., 28 Jul 2025).

The ablation results on WHU attribute a substantial part of this improvement to SCA itself. The baseline ResNet + UNet++ obtains IoU $U_j = \mathcal{F}_j(X)$7 and F1 $U_j = \mathcal{F}_j(X)$8; adding SA yields IoU $U_j = \mathcal{F}_j(X)$9 and F1 $91.61\%$00; adding CA yields IoU $91.61\%$01 and F1 $91.61\%$02; SCA with UNet yields IoU $91.61\%$03 and F1 $91.61\%$04; and SCA with UNet++ yields IoU $91.61\%$05 and F1 $91.61\%$06. Across ResNet-14, ResNet-26, ResNet-50, and ResNet-101 backbones, SCANet is reported to yield consistent IoU gains over both ResNeSt and ResNet + CA while keeping parameters equal to the corresponding ResNeSt setup (Wang et al., 28 Jul 2025).

Qualitative analyses further support the proposed mechanism. Grad-CAM++ visualizations show stronger focus on buildings, especially small and dense structures, and improved handling of edges and holes such as inner courtyards. Diagonal pixel similarity matrices from Stage 4 show an expanded effective receptive field and stronger long-range spatial correlations than plain ResNet or ResNeSt (Wang et al., 28 Jul 2025).

The reported robustness claims are that SCANet works well across dense small buildings, sparse medium buildings, large continuous roofs, shadows, and visually similar materials. At the same time, the paper identifies several limitations. It does not report sensitivity analyses for $91.61\%$07 and $91.61\%$08; SCA remains CNN-centric despite the possibility that transformer backbones may further improve remote dependency modeling; and the method may still face difficulties under extreme occlusions or very low-resolution imagery where fine positional encoding alone is insufficient (Wang et al., 28 Jul 2025).

Beyond building extraction, the authors state that SCA’s axis-wise coordinate encoding and split-fusion make it applicable to medical segmentation such as vessels, road extraction in aerial images, instance segmentation with thin structures, and other edge-sensitive applications. This suggests that the defining contribution of SCA is not restricted to a particular dataset, but to a design pattern that combines coordinate-aware pooling with split-attention diversity in a form intended for 2D CNN-based dense prediction (Wang et al., 28 Jul 2025).