Guided Cost Volume Excitation (GCE)

• Guided Cost Volume Excitation is a module for stereo matching that employs image-guided and region-guided channel excitation to enhance disparity estimation at object boundaries.
• It injects spatially varying channel attention via lightweight 1x1 convolutions, improving semantic consistency during 3D cost volume aggregation.
• Integration in models like CoEx and SGCE has yielded marked improvements in accuracy, efficiency, and boundary sharpness compared to conventional methods.

Guided Cost Volume Excitation (GCE) is a class of architectural modules designed to improve the local adaptivity and semantic consistency of stereo matching networks by using image-guided or region-guided channel excitation in cost volume aggregation. GCE operates by injecting spatially varying, feature-driven attention into the cost volume, typically at multiple stages of the 3D convolutional cost aggregation tower, thereby enhancing disparity estimation particularly at object boundaries. Two prominent implementations are standard channel-wise excitation driven by reference image features (Bangunharcana et al., 2021), and extensions leveraging soft or hard superpixel constraints for higher-order semantic context (Liu et al., 20 Nov 2024).

1. Principles and Network Integration

GCE is instantiated within cost volume-based stereo matching frameworks, where dense disparity estimation is formulated as a probabilistic regression problem over a 4D cost volume. Classical pipelines (e.g., GwcNet, GC-Net) perform feature extraction for left/right images, cost volume construction, multi-scale 3D cost aggregation, and regression via soft-argmin. GCE modules are inserted immediately before cost aggregation stages, operating on the cost volume $$C \in \mathbb{R}^{N \times D \times H \times W \times c}$$ and reference image features.

In CoEx (Bangunharcana et al., 2021), the pipeline uses MobileNetV2 for feature extraction, cost volume construction by feature correlation, hourglass-style 3D convolutional aggregation, and per-pixel regression. GCE is applied at all spatial scales by computing spatially varying channel weights $\alpha \in \mathbb{R}^{H_s \times W_s \times c}$ via $1 \times 1$ convolution and sigmoid applied to image features, then broadcasting $\alpha$ over the disparity dimension for element-wise channel scaling.

In SGCE [Editor’s term, (Liu et al., 20 Nov 2024)], superpixel-based context $\phi(I_l)_k$ at multiple scales from a segmentation branch is fused by a short-connection module $g$ and mapped to an attention map $W$ for channel-wise excitation of $C_{cost}$ prior to each 3D aggregation layer.

2. Mathematical Formalization

The GCE operation is governed by weight generation and broadcasted channel-wise gating:

• Image-guided channel attention (Bangunharcana et al., 2021):

$$\alpha = \sigma(F^{2D}(I^{(s)})), \quad C_o^{(s)}(d, x, y, k) = \alpha(x, y, k) \cdot C_i^{(s)}(d, x, y, k)$$

• Superpixel-guided cost volume excitation (Liu et al., 20 Nov 2024):

$$W = \sigma(g(\{\phi(I_l)_k\}_k)), \quad C'_{cost}(d, c, x, y) = W(c, x, y) \cdot C_{cost}(d, c, x, y)$$

Cost volume probabilities $C_{prob}(d, x, y)$ are aggregated within superpixels $s$ via probability pooling:

$$P_s(d) = \left(\prod_{p \in \tilde{m}_s} C_{prob}(d, p)\right)^{1/n}, \quad \ln P_s(d) = \frac{1}{n} \sum_{p \in \tilde{m}_s} \ln C_{prob}(d, p)$$

3. Loss Functions and Consistency Constraints

Modern GCE frameworks incorporate multiple loss terms to enforce intra-region or intra-superpixel consistency. In SGCE (Liu et al., 20 Nov 2024), three losses are jointly optimized:

• Disparity regression loss:

$$L_{reg} = \frac{1}{N} \sum_{p} \text{Smooth}_{L1}(\hat{d}_p, d_p^{gt})$$

• Superpixel cross-entropy loss: aligns predicted per-superpixel distributions $P_s(d)$ to unimodal Laplace-kernel ground truths $P_s^{gt}(d)$:

$$L_{sce} = -\frac{1}{N_s} \sum_s \sum_{d=0}^{D-1} P_s^{gt}(d) \log P_s(d)$$

• Superpixel reconstruction loss: incentivizes compact, disparity-coherent superpixels via regularization on association maps $Q$:

$$L_{recon} = \frac{1}{N} \sum_p \left\lVert d_p - d'_p \right\rVert_1 + w\cdot \left\lVert p - p' \right\rVert_2$$

Total loss combines all terms with $\lambda = 1$, $\mu = 0.1$.

4. Implementation Variants and Computational Efficiency

Below is a summary of representative implementations and their layer/hyper-parameter choices:

Model	GCE Placement	Guidance Source
CoEx (Bangunharcana et al., 2021)	Each aggregation scale	Image features
SGCE (Liu et al., 20 Nov 2024)	Pre-aggregation, multi-scale	Superpixel features

CoEx applies pointwise $1 \times 1$ convolutions and sigmoid gating at all hourglass scales, using lightweight 3D convolutional stacks and top-k selection for disparity regression. SGCE employs a learned superpixel segmentation branch (inspired by SFCN [26]), outputting soft pixel-to-superpixel association maps $Q$; this branch is used only during training. Both approaches demonstrate that GCE incurs minimal computational overhead relative to spatially-varying or neighborhood-based aggregation schemes such as GA-Net or graph convolution filters.

5. Quantitative Performance and Boundary Accuracy

Empirical results across SceneFlow, KITTI 2012/2015, and Middlebury illustrate the superiority of GCE in terms of accuracy and boundary sharpness:

• SceneFlow (final pass, (Liu et al., 20 Nov 2024)):
  • Baseline GwcNet: EPE = $0.76$ px, 1-px error = $8.03\,\%$
  • +SGCE+L_{sce}: EPE = $0.59$ px (–22%), 1-px error = $6.00\,\%$
• KITTI 2012 (Liu et al., 20 Nov 2024):
  • GwcNet+SGCE: 3-px error = $0.93\,\%$ (vs. $1.03\,\%$), EPE = $0.50$ px
  • Soft Edge Error (SEE) improved by $\sim 10-15\,\%$
• CoEx (Bangunharcana et al., 2021):
  • EPE = $0.69$ (SceneFlow), KITTI 3px = $1.93\,\%$, D1 = $2.13\,\%$, runtime $=27$ ms
  • CoEx matches or outperforms AANet (62 ms) and neighbor-based aggregation at half the runtime

Table: Comparison of SceneFlow EPE and inference time (from (Bangunharcana et al., 2021)):

Method	GCE Applied	Top-k	EPE	Time (ms)
Corr-only	No	48	1.053	223
Corr + GCE	Yes	48	0.824	26
Corr + GCE + k=2 (CoEx)	Yes	2	0.685	27

Ablation studies demonstrate that both SGCE (channel excitation) and superpixel cross-entropy loss are critical for maximizing accuracy. Detailed qualitative maps show visually sharper boundaries with suppressed multi-modal artifacts in object boundary regions.

6. Contextualization within Stereo Matching and Related Methods

GCE distinguishes itself from graph-aggregator and CSPN-style methods by relying on single-channel spatial excitation informed by image or region context, rather than explicit spatial neighborhood filtering. This design avoids quadratic parameter and FLOP blow-up associated with neighborhood-based approaches. GCE leverages the representational power of 3D convolution towers, requiring only lightweight pointwise feature gating for spatial adaptivity. The plausibility is that cost-volume channels already encode most geometric cues, so learned attention gates selectively reinforce salient signals.

Recent extensions using superpixels (Liu et al., 20 Nov 2024) further enhance semantic consistency by encouraging unimodal disparity distributions within adaptive regions aligned to object boundaries, yielding improved accuracy with negligible inference overhead. This suggests that higher-order region-guided cost volume gating is a promising direction, especially for scenarios requiring robust boundary localization in disparity estimation.

7. Future Directions and Interpretations

A plausible implication is that GCE provides a unifying abstraction for cost-volume guidance, adaptable to various input signals (image, superpixels, segmentation masks) and cost aggregation schemes. Future research may explore hierarchical or multi-modal region cues, end-to-end learned gating architectures, and extension to multi-view or non-stereo dense matching tasks. A further possibility is to combine GCE-style excitation with contrastive learning objectives or uncertainty-aware regression frameworks to enhance generalization and boundary sensitivity.

The emergence of superpixel-guided cost volume excitation (Liu et al., 20 Nov 2024) indicates that region-based context integration will remain a focus, especially for high-precision 3D reconstruction and robotics perception applications.