Research map / 3D vision / Depth and stereo
A Theory of Joint Light and Heat Transport for Lambertian Scenes
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Proposes a physics theory linking visible light absorption to heat transport measured by a co-located thermal camera, enabling per-pixel albedo-shading separation for Lambertian scenes under unknown illumination.
Problem
Single-view intrinsic image decomposition (albedo vs. shading) for Lambertian scenes under unknown complex illumination is ill-posed; the light absorbed by the surface is typically unobserved.
Approach
Estimate the absorbed light per pixel from the transient temperature rise in a thermal video (solving the heat equation analytically without conduction), then use energy conservation (reflected + absorbed = irradiance) to make albedo and shading recoverable pixel-wise for arbitrary shape and illumination.
Key results
- On the color chart under 4 illuminations, the method's albedo si-MSE is 0.020 versus 0.034 for Retinex and 0.080 for Ordinal Shading.
- On the painted mask pseudo ground truth, albedo si-MSE is 0.084 for the method versus 0.253 (RGB-Retinex) and 0.399 (Ordinal Shading).
- Shading si-MSE on the same scene is 0.0005 for the method versus 0.0030 (Retinex) and 0.0080 (Ordinal Shading).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed absorbed-light-guided decomposition instead of Retinex | Intrinsic image decomposition · Color chart, 4 illuminations | mean albedo error: 0.034 -> 0.020 | Helped |
| Use the proposed absorbed-light-guided decomposition instead of Ordinal Shading | Intrinsic image decomposition · Color chart, 4 illuminations | mean albedo error: 0.080 -> 0.020 | Helped |
| Use the proposed method instead of RGB-Retinex | Painted mask scene · Painted mask scene | si-MSE, albedo: 0.253 -> 0.084 | Helped |
| Use the proposed method instead of Ordinal Shading | Painted mask scene · Painted mask scene | si-MSE, albedo: 0.399 -> 0.084 | Helped |
| Use the proposed method instead of RGB-Retinex | Painted mask scene · Painted mask scene | si-MSE, shading: 0.0030 -> 0.0005 | Helped |
| Use the proposed method instead of Ordinal Shading | Painted mask scene · Painted mask scene | si-MSE, shading: 0.0080 -> 0.0005 | Helped |
| Increase the thermal-video duration (ablation) | Absorbed-light curve fitting and albedo estimation · Color chart | albedo error | Mixed |
| Use grayscale approximation instead of the wavelength-dependent albedo formulation (ablation) | Albedo-shading separation · Soft toys scene | shading similarity | No clear effect |
Surprising findings
- Heat source estimates per pixel c2 (proportional to heat capacity) look like white noise, with a Gaussian-like histogram.
Limitations
- Requires thermal equilibrium before lights turn on and constant other heat sources.
- Assumes conduction is negligible; longer videos induce conduction and reduce accuracy.
- Background walls and high heat-capacity regions do not warm sufficiently, making estimation challenging; assumes Lambertian opaque scenes.
Experimental setup
Datasets: color chart captures under 4 illuminations custom real-world scenes captured with co-located visible and thermal cameras
Benchmarks: color chart albedo ground truth painted-texture pseudo ground truth (painted mask scene)
Metrics: scale-invariant MSE (si-MSE)
Baselines: Retinex Ordinal Shading
Builds on: Retinex Tanaka et al. thermal photometric stereo Ordinal Shading
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- Eclipse: Disambiguating Illumination and Materials using Unintended Shadows (CVPR 2024 · similarity 0.83)
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- DiffusionLight: Light Probes for Free by Painting a Chrome Ball (CVPR 2024 · similarity 0.83)
- ThermalGaussian: Thermal 3D Gaussian Splatting (ICLR 2025 · similarity 0.83)
- Practical Measurements of Translucent Materials with Inter-Pixel Translucency Prior (CVPR 2024 · similarity 0.83)
- DarkVGGT: Seeing Through Darkness Using Thermal Geometry without Daylight Tax (NeurIPS 2026 · similarity 0.83)
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