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Stereo Risk: A Continuous Modeling Approach to Stereo Matching
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Proposes Stereo Risk, which predicts continuous disparity by minimizing an L1 risk over a Laplacian-interpolated categorical disparity distribution, with binary search for the forward pass and implicit-function-theorem gradients for end-to-end training.
Problem
Deep stereo matching typically discretizes disparity and predicts continuous values via expectation or offset regression, which blurs multi-modal distributions at object boundaries and generalizes poorly across domains.
Approach
Treat disparity prediction as minimizing expected L1 risk under a continuous density obtained by Laplacian-kernel interpolation of the discrete cost-volume distribution; solve the non-differentiable minimizer by binary search and backpropagate through it with the implicit function theorem.
Key results
- On SceneFlow test, the method reaches EPE 0.43 and >1px error 4.22, the best among compared methods including IGEV (0.47 EPE, 5.21 >1px).
- Trained only on SceneFlow, it reduces Middlebury >1px All error from 13.76 (DLNR) to 12.63 and ETH3D >1px All error from 4.05 (IGEV) to 2.71.
- Applying L1-risk only at test time improves ACVNet and PCWNet on Middlebury without retraining, e.g. ACVNet >1px Noc 22.68 to 22.32.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Stereo Risk instead of ACVNet | Stereo matching · SceneFlow test | >1px error: 5.00 to 4.22 | Helped |
| Use Stereo Risk instead of PCWNet | Stereo matching · KITTI 2012 | >2px error, Noc: 1.69 -> 1.58 | Helped |
| Use Stereo Risk instead of IGEV | Stereo matching · KITTI 2015 | D1_all, All: 1.59 -> 1.63 | Hurt |
| Use Stereo Risk instead of DLNR | Cross-domain stereo matching · Middlebury train, quarter resolution | >1px error, All: 13.76 to 12.63 | Helped |
| Use Stereo Risk instead of IGEV | Cross-domain stereo matching · ETH 3D train | >1px error, All: 4.05 to 2.71 | Helped |
| Use L1-Risk at test time instead of expectation (ablation) | Stereo Risk · Middlebury train, quarter resolution | >1px error, All: 13.27 -> 13.22 | Helped |
| Use L1-Risk at both training and test time instead of expectation (ablation) | Stereo Risk · Middlebury train, quarter resolution | >1px error, All: 13.27 -> 12.63 | Helped |
| Replace expectation with L1-Risk at test time (ablation) | ACVNet · Middlebury train, quarter resolution | >1px error, All: 26.49 -> 26.14 | Helped |
| Replace expectation with L1-Risk at test time (ablation) | PCWNet · Middlebury train, quarter resolution | >1px error, All: 21.36 -> 21.08 | Helped |
| Increase binary-search tolerance from 0.1 to 0.3 (ablation) | Stereo Risk · Middlebury train, quarter resolution | >1px error, All: 12.63 -> 12.67 | Hurt |
| Decrease binary-search tolerance from 0.1 to 0.01 (ablation) | Stereo Risk · Middlebury train, quarter resolution | >1px error, All: 12.63 -> 12.63 | No clear effect |
| Replace L1 loss with L2 loss (ablation) | Stereo Risk · Middlebury train, quarter resolution | >1px error, All: 12.63 -> 13.19 | Hurt |
Surprising findings
- Swapping only the test-time disparity readout to L1-risk improves existing networks (ACVNet, PCWNet) without retraining.
Limitations
- Closed-form L1 minimizer is unavailable, so binary search and a clipped implicit-gradient approximation are needed.
- Gains over expectation are modest on several benchmarks (e.g., KITTI 2012 >2px All 2.20 vs IGEV 2.17), and KITTI 2015 Noc results are compared only among published methods.
Experimental setup
Datasets: SceneFlow KITTI 2012 KITTI 2015
Benchmarks: SceneFlow KITTI 2012 KITTI 2015 Middlebury 2014 ETH3D
Metrics: EPE >0.5px error >1px error >2px error >3px error D1 outlier rate
Baselines: CFNet PCWNet ACVNet DLNR IGEV CREStereo LaC+GANet CroCo LEAStereo PSMNet GCNet
Builds on: CasMVSNet PSMNet ACVNet PCWNet RAFT-Stereo
Closest papers by meaning
- Learning the Distribution of Errors in Stereo Matching for Joint Disparity and Uncertainty Estimation (CVPR 2023 · similarity 0.91)
- Revisiting Non-Parametric Matching Cost Volumes for Robust and Generalizable Stereo Matching (NeurIPS 2022 · similarity 0.91)
- CFNet: Cascade and Fused Cost Volume for Robust Stereo Matching (CVPR 2021 · similarity 0.90)
- Adaptive Unimodal Cost Volume Filtering for Deep Stereo Matching (AAAI 2020 · similarity 0.90)
- Modeling Stereo-Confidence out of the End-to-End Stereo-Matching Network via Disparity Plane Sweep (AAAI 2024 · similarity 0.89)
- Stereo Anywhere: Robust Zero-Shot Deep Stereo Matching Even Where Either Stereo or Mono Fail (CVPR 2025 · similarity 0.88)
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