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Multi-times Monte Carlo Rendering for Inter-reflection Reconstruction
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Ref-MC^2 performs full inverse rendering with multi-times Monte Carlo ray tracing to model inter-reflections, using a diffuse-map self-supervision and specularity-adaptive sampling plus an SG-encoded SDF initialization refined with FlexiCubes.
Problem
Inverse rendering of reflective objects with inter-reflections among multiple smooth objects, where ignoring indirect illumination corrupts geometry and material disentanglement, and multi-bounce Monte Carlo tracing is computationally expensive.
Approach
Trace indirect illumination with multi-times Monte Carlo sampling, but approximate the diffuse part of indirect light with a Lambertian diffuse map learned via self-supervision so only a small specular lobe needs tracing; initialize geometry with an SDF model using Spherical Gaussian encoding and refine it with FlexiCubes.
Key results
- Ours achieves 28.1 PSNR versus 26.9 for Nvdiffrec, 25.7 for Nvdiffrecmc, and 22.3 for Nefii on the custom dataset.
- Ours (3 samples) reaches 28.4 PSNR, only marginally above 2-time sampling, at roughly 4x the cost per extra sampling time.
- Chamfer Distance on Materials scene drops to 0.0030 for Ours versus 0.0057 for NeRO and 0.016 for Nvdiffrec/Nvdiffrecmc.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add multi-times Monte Carlo sampling (ablation) | Ref-MC² · Reflective dataset | PSNR: 27.3 -> 28.1 | Helped |
| add geometry initialization (ablation) | Ref-MC² · Reflective dataset | PSNR: 24.6 -> 28.1 | Helped |
| add specularity-adaptive acceleration (ablation) | Ref-MC² · Reflective dataset | Training time: 11.5h -> 6.5h | Helped |
| add specularity-adaptive acceleration (ablation) | Ref-MC² · Reflective dataset | PSNR: 28.0 -> 28.1 | No clear effect |
| increase sampling from 2 times to 3 times (ablation) | Ref-MC² · Reflective dataset | PSNR: 28.1 -> 28.4 | Helped |
| increase sampling from 2 times to 3 times (ablation) | Ref-MC² · Reflective dataset | Training time: 6.5h -> 26.5h | Hurt |
| use 2 sampling times rather than 1 (ablation) | Ref-MC² · Reflective dataset | PSNR: 27.3 -> 28.1 | Helped |
| use 2 sampling times rather than 1 (ablation) | Ref-MC² · Reflective dataset | Training time: 2.25h -> 6.5h | Hurt |
| replace IPE with Spherical Gaussian encoding (ablation) | Ref-MC² geometry initialization · Reflective dataset | geometry and reflection reconstruction quality | Helped |
| use Lambertian diffuse approximation for indirect light (ablation) | Ref-MC² · Reflective dataset | computational efficiency | Helped |
Surprising findings
- Two-time sampling is nearly as good as three-time sampling, so deeper tracing gives minimal gains.
- Without geometry initialization, multi-time sampling can produce worse materials than single-time sampling because geometric errors are amplified.
Limitations
- Two-time sampling cannot handle extremely reflective objects such as mirrors, since specular energy barely degrades after reflections.
- Training time remains long compared with prior methods (6.5h versus 30-45min for Nvdiffrec/Nvdiffrecmc).
- Increasing sampling depth raises computation about 4x per time and makes the pipeline highly sensitive to geometry.
Experimental setup
Datasets: custom multi-object inter-reflection dataset (16 groups) NeRO real-scene dataset
Benchmarks: custom multi-object inter-reflection dataset NeRO real-scene dataset
Metrics: PSNR Chamfer Distance training time
Baselines: Nvdiffrec Nvdiffrecmc Nefii NeRO
Builds on: Nvdiffrec Nvdiffrecmc FlexiCubes Monte Carlo integration multiple importance sampling
Closest papers by meaning
- Inverse Rendering using Multi-Bounce Path Tracing and Reservoir Sampling (ICLR 2025 · similarity 0.91)
- MaterialRefGS: Reflective Gaussian Splatting with Multi-view Consistent Material Inference (NeurIPS 2025 · similarity 0.89)
- SpecTRe-GS: Modeling Highly Specular Surfaces with Reflected Nearby Objects by Tracing Rays in 3D Gaussian Splatting (CVPR 2025 · similarity 0.89)
- Eclipse: Disambiguating Illumination and Materials using Unintended Shadows (CVPR 2024 · similarity 0.89)
- Factored-NeuS: Reconstructing Surfaces, Illumination, and Materials of Possibly Glossy Objects (CVPR 2025 · similarity 0.89)
- Reflective Gaussian Splatting (ICLR 2025 · similarity 0.88)
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