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Locally Orderless Images for Optimization in Differentiable Rendering
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Proposes locally orderless images (LOIs), matching per-pixel intensity histograms across inner, tonal, and extent scale spaces with a Wasserstein histogram loss, to extend gradient support for inverse differentiable rendering using standard RGB gradients.
Problem
Gradients of rendered images with respect to scene parameters that induce image-space motion are sparse, causing poor convergence and local minima in differentiable rendering inverse problems; existing multi-scale image pyramids are unreliable.
Approach
Replace image-pyramid matching with locally orderless images: each pixel maps to a histogram of intensities (tonal scale via Gaussian kernels), histograms are spatially integrated (extent scale), and combined with inner Gaussian blur, then matched with a closed-form 1D Wasserstein distance on CDFs. This preserves intensity modes across scales and requires no changes to the renderer.
Key results
- On 2D disk vectorization with 256 disks, the method reaches 21.57 PSNR / 0.90 SSIM versus 15.2 / 0.76 for LPIPS and 9.60 / 0.34 for Gaussian pyramid.
- On the Shadow Mini path-tracing scene, the method reaches 54.73 PSNR and 0.0033 MAE versus 27.74 PSNR and 6.0147 MAE for PRDPT.
- On rasterization Camera Pose and Material scenes, it reports PSNR 49.07 and 55.22 versus 33.01 and 32.43 for Xing et al. (RGBXY) in the table.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Match locally orderless image histograms instead of using LPIPS | Differentiable disk recovery with diffvg · 2D disk recovery, 256 disks | PSNR: 15.2 -> 21.57 | Helped |
| Use locally orderless image matching instead of PRDPT parameter-space blurring | Mitsuba 3 · Shadow Mini | PSNR: 27.74 -> 54.73 | Helped |
| Use locally orderless image matching instead of Gaussian pyramids | Nvdiffrast · Material | PSNR: 42.48 -> 49.07 | Helped |
| Use locally orderless image matching instead of RGBXY proxy gradients | Nvdiffrast · Translation | PSNR: 63.62 -> 51.77 | Hurt |
| Use locally orderless image matching instead of RGBXY proxy gradients | Nvdiffrast · Rotation | PSNR: 26.66 -> 30.73 | Helped |
| Use locally orderless image matching instead of RGBXY proxy gradients | Nvdiffrast · Shape | PSNR: 30.75 -> 28.22 | Hurt |
| Use locally orderless image matching instead of RGBXY proxy gradients | Nvdiffrast · Translation + Rotation | PSNR: 30.23 -> 36.23 | Helped |
| Use locally orderless image matching instead of RGBXY proxy gradients | Nvdiffrast · Camera Pose | PSNR: 23.50 -> 27.22 | Helped |
| Use locally orderless image matching instead of RGBXY proxy gradients | Nvdiffrast · Material | PSNR: 33.01 -> 49.07 | Helped |
| Use locally orderless image matching instead of RGBXY proxy gradients | Nvdiffrast · Environment Map | PSNR: 32.43 -> 55.22 | Helped |
| Remove α and β scale spaces, retaining only σ-space matching (ablation) | Locally orderless image optimization · Inverse rendering experiments | optimization recovery | Hurt |
| Use only β-space matching, without the α and σ scale spaces (ablation) | Locally orderless image optimization · Inverse rendering experiments | optimization recovery | Hurt |
Surprising findings
- Gaussian pyramids (sigma-only scale space) perform poorly, showing the tonal and extent scales are essential rather than just multi-resolution matching.
- For translation in rasterization, Xing et al. (RGBXY) achieves a higher PSNR (63.62) than the proposed method (51.77), though both have MAE 0.00.
Limitations
- Parameters that do not affect primary or secondary light effects (e.g., occluded geometry) still yield zero gradients, so the method cannot recover them alone.
- Only the beta-only tonal space was ablated; the method depends on combining the alpha and beta scale spaces, so it cannot be used in isolation.
- Real-data experiment is described as preliminary and involves a single scene.
Experimental setup
Datasets: synthetic 2D disk scenes Shadow, Shadow Mini, Caustics and Lights, Sort, Envlight scenes from PRDPT Xing et al. rasterization test scenes a real photograph of a glass orb
Benchmarks: 2D disk vectorization benchmark (n=4 to 256 disks) PRDPT five-scene path tracing benchmark Xing et al. rasterization scenes kaleidoscope real glass orb scene
Metrics: PSNR SSIM MAE MSE
Baselines: Gaussian pyramid (GP) MS-SSIM LPIPS PRDPT RGBXY (Xing et al.) Nvdiffrast with GP Nvdiffrast with MS-SSIM
Builds on: Gaussian pyramids locally orderless images (Koenderink and van Doorn) variational optimization (PRDPT) diffvg Mitsuba 3
Closest papers by meaning
- Inverse Rendering using Multi-Bounce Path Tracing and Reservoir Sampling (ICLR 2025 · similarity 0.85)
- Differentiable Point-based Inverse Rendering (CVPR 2024 · similarity 0.84)
- SVG-IR: Spatially-Varying Gaussian Splatting for Inverse Rendering (CVPR 2025 · similarity 0.84)
- LinPrim: Linear Primitives for Differentiable Volumetric Rendering (NeurIPS 2025 · similarity 0.84)
- CompactSplat: Spatially Adaptive Gaussian Distribution for Feedforward Scene Reconstruction (NeurIPS 2026 · similarity 0.84)
- Differentiable Inverse Rendering with Interpretable Basis BRDFs (CVPR 2025 · similarity 0.84)
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