AtrousMamba: Enhanced Visual State Space Model

• AtrousMamba is a visual state space model for remote sensing change detection that improves locality preservation with multi-rate atrous-window selective scans.
• It integrates an AWVSS module combining atrous-window scanning, depth-wise convolution, and channel recalibration to enhance both fine-grained detail and global context.
• The architecture achieves linear computational complexity and outperforms CNNs and Transformers in dense prediction tasks through effective sequence serialization.

AtrousMamba denotes a visual state space model architecture specifically developed for remote sensing change detection, addressing a key limitation of prior visual Mamba/state space models: the loss of locality in image-to-sequence serialization. While Mamba-based state space models efficiently capture long-range dependencies in image data with linear complexity, their standard scan strategies often fail to preserve neighborhood structure crucial for dense prediction tasks such as change detection. AtrousMamba modifies the scan mechanism to maintain spatial locality while simultaneously expanding the receptive field, thereby enhancing both fine-grained detail extraction and global context modeling (Wang et al., 22 Jul 2025).

1. Atrous-Window Selective Scan Mechanism

The central innovation is the atrous-window selective scan, implemented within the Atrous Window Visual State Space (AWVSS) module. Rather than flattening images globally or performing purely directional scans as in prior VMamba formulations, AtrousMamba partitions the encoded 2D feature map $X\in\mathbb{R}^{H\times W\times C}$ into multiple groups of windows defined by distinct atrous (dilation) rates $r\in\{2,5,7,9\}$. For each $r$, the feature map is divided into windows (e.g., $2\times2$, $5\times5$, $7\times7$, $9\times9$) and each group is independently serialized and processed by a separate selective state space (S6/Mamba) module.

The sequence of operations within AWSS2D is:

1. Atrous Window Scan ($\operatorname{AWScan}_r$): Partition $X$ into window groups at rate $r$.
2. Selective Scan: Each group undergoes 1D sequence serialization and is processed by an S6 block.
3. Atrous Window Scan Merge (AWSMerge): Independently processed outputs are merged with channel recalibration.

This strategy reduces the sequence distance between locally connected 2D tokens, substantially improving preservation of local semantic regions. The scan design provides a progression from small windows (emphasizing local structure) to large windows (capturing global context), processing all in parallel.

Mathematically, the effective receptive field for a window of side $r\in\{2,5,7,9\}$0 and rate $r\in\{2,5,7,9\}$1 is approximated as $r\in\{2,5,7,9\}$2, expanding the context coverage while maintaining locality within each atrous window. The merged result fuses these windowed representations via a channel attention-style recalibration, using two fully connected layers and channel-wise sigmoid activation.

2. AWVSS Module and Underlying Mathematical Formulation

The AWVSS module builds upon the continuous and discretized state space model formulations. The base continuous-time SSM is:

$r\in\{2,5,7,9\}$3

where $r\in\{2,5,7,9\}$4 is the input, $r\in\{2,5,7,9\}$5 the hidden state, and $r\in\{2,5,7,9\}$6 are parameter matrices.

Discretization via zero-order hold yields: $r\in\{2,5,7,9\}$7 with discretized state evolution

$r\in\{2,5,7,9\}$8

Mamba-type selective SSMs enhance this by making $r\in\{2,5,7,9\}$9, $r$0, $r$1 input-dependent.

AWVSS is designed as a residual block with two computational branches:

• Feature branch: Depth-wise convolution followed by AWSS2D.
• Gating branch: Linear mapping and activation to produce a multiplicative gate.

Formally,

$r$2

The AWSS2D operation is specified as

$r$3

where $r$4. AWSMerge fuses the multi-rate outputs using global average pooling, channel-wise MLP, and sigmoidal recalibration: $r$5

3. End-to-End Architectures: AWMambaBCD and AWMambaSCD

Two specialized remote sensing change detection frameworks are constructed atop AWVSS:

AWMambaBCD (Binary Change Detection)

• Encoder: Weight-sharing Siamese backbone based on VMamba, generating four-scale multiresolution features from bi-temporal imagery.
• Decoder: Models spatio-temporal relationships by three explicit feature rearrangements—concatenation, width-wise arrangement, and alternating interleaving—each processed through a separate AWVSS block. Outputs are merged, channel-adjusted, and upsampled in a hierarchical decoder.

The BCD task uses pixel-wise binary cross-entropy loss: $r$6 with $r$7 the predicted change probability.

AWMambaSCD (Semantic Change Detection)

• Encoder: Two-branch Siamese VMamba, as above.
• Decoder: Triple-branch multi-task structure (change detection head + two semantic segmentation heads, one per temporal input). At each level, semantic/context features are upsampled, fused, and refined by AWVSS and a residual block.

Losses:

• Semantic segmentation: multi-class cross-entropy.
• Consistency: cosine similarity-based semantic change loss.
• Overall loss: $r$8

4. Computational Complexity and Practical Efficiency

AtrousMamba maintains linear complexity with respect to sequence length due to both the underlying selective state space paradigm and the fixed number ($r$9) of parallel atrous-window scan branches: $2\times2$0 for $2\times2$1 tokens. This compares favorably against:

• Transformers: $2\times2$2
• CNNs: $2\times2$3 (fixed small $2\times2$4)

Empirically, AtrousMamba demonstrates parameter and FLOP counts competitive with or lower than canonical Transformer and CNN models, while delivering higher accuracy.

Model	Params (M)	FLOPs (G)
AWMambaBCD-T	30.55	18.81
AWMambaBCD-S	50.15	28.85
AWMambaSCD-T	35.03	26.86
AWMambaSCD-S	54.63	36.89

5. Benchmark Results and Ablations

AtrousMamba frameworks were evaluated on six remote sensing datasets: CLCD, SYSU-CD, WHU-CD (BCD tasks), and SECOND, Landsat-SCD, JL1-SCD (SCD tasks). For BCD, the key metrics are OA, IoU, and F1; for SCD, F1, mIoU, and SeK.

AWMamba variants consistently outperform both CNN- (e.g., ResNet50) and Transformer-based backbones (e.g., Swin-Small), as well as prior Mamba-based methods on all datasets.

Representative Results

Method	OA	IoU	F1	Dataset
AWMambaBCD-S	97.33	68.35	81.20	CLCD
AWMambaBCD-S	92.51	70.94	83.00	SYSU-CD
AWMambaBCD-S	99.49	88.32	93.80	WHU-CD
AWMambaSCD-S (F1)	64.24	89.03	90.90	SECOND/Landsat/JL1-SCD

An explicit ablation contrasted AtrousMamba's scan with VMamba’s cross-scan module, finding that the atrous-window scanning mechanism led to notable improvements in OA, IoU, and F1 across all testbeds.

6. Locality, Global Context, and Architectural Significance

AtrousMamba's fundamental contribution is reconciling dense local detail extraction with global context aggregation within a state space model framework, breaking with the architecture-dependent trade-off exemplified by CNNs (locality, but limited field) and Transformers (global context, costly computation). By introducing multi-scale, locality-preserving scan orders, AtrousMamba substantially improves delineation of fine structures such as boundaries and small changing objects, critical in remote sensing change detection. It preserves both semantic region continuity and cross-region context, avoids the drift and discontinuity endemic to prior Mamba/VMamba scan strategies, and achieves competitive efficiency on large-scale remote sensing imagery (Wang et al., 22 Jul 2025).

This architecture demonstrates that the sequence scan order in visual state space models is a determinant of both locality preservation and global information flow, and that judicious scan design—here via multi-rate atrous windows—enables state space models to address dense prediction challenges as effectively as, and more efficiently than, alternative paradigms.