Shape from Thermal Radiation:
Passive Ranging Using Multi-spectral LWIR Measurements
Yasuto Nagase1 Takahiro Kushida1 Kenichiro Tanaka2 Takuya Funatomi1 Yasuhiro Mukaigawa1
1Nara Institute of Science and Technology (NAIST), Japan 2Ritsumeikan University, Japan

Is passive ranging possible using a single thermal camera?
• We propose a novel depth sensing technique refer to physicsbased cues, long wavelength infrared (LWIR).
• The proposed method is the first attempt to prove that LWIR is usefulfor depth sensing.

MethodExperiments• Thermal radiation theory

1. Black body target

All objects radiate LWIR light according to Planck's law, depending on theirtemperature and emissivity.
Planck's law

Temperature 𝑻Emissivity εAdvantages

2𝜋ℎ𝑐 2𝑀𝑒 𝜆; 𝑇 =𝜆5
ObjectOur method overcomes many weakness of conventional methods.
Stereo cameras

Structured light

LiDAR

Ours

Impossible

Possible

Possible

Possible

NoYes

Yes

Yes

Far range

Baseline

Impossible

Possible

Possible

OutdoorPossible

Difficult

Possible

Possible

Risk of interfering

LowHighHighLow

Stealth measurement

Yes

NoNo

Yes

Key idea

LWIR light• Light attenuation and imaging model

LWIR camera

Lambert-Beer law expresses transmission of the air.
By using a filter, attenuated LWIR light at a specific wavelength can be observed.

Black body
A device with emissivity ≈ 1 can control the temperature.

depth 𝒅Temperature 𝑻Emissivity ε

All unknowns are estimated roughly correct compared to Ground Truth.

2. Practical targetfilter
Extinction coefficient𝜎𝐴𝑖𝑟 (𝜆)𝜆depth 𝒅
LWIR camera

Target object

𝜆1

Lambert-Beer law(Air attenuation model)

𝐼 𝜆 = 𝑖 𝜆 𝑒 −𝜎𝐴𝑖𝑟 𝜆 𝑑Air
𝜆2

Temperature 𝑻Emissivity εℎ𝑐𝑒 𝜆𝑘𝑇 − 1

𝜆3

LWIR camera

AirImaging model𝐼 𝜆 = 𝜺𝑀𝑒 𝜆; 𝑻 𝑒−𝜎𝐴𝑖𝑟 (𝜆)𝒅Three unknowns

Band-passfilter• The main idea is modeling LWIR light attenuation through the air.
• Multi-spectral observation enables estimate not only depth but
also temperature and emissivity.

Assumptions• The attenuating spectrum of the air is known.
• Emissivity of the target is not wavelength-dependent in LWIR.
• The target object does not reflect LWIR light from any otherheat source.

EstimatedTexture independenceBlack body1LWIR image(w/o filter)

Dark scene

Measure a black body, which is moved awayfrom the camera, every 1 m.
Estimate the each unknowns when the blackbody is set to 50℃ and 90℃.

Scene

Introduction: Challenge

Project page• Estimate depth
To estimate unknowns, we use three equations with different wavelengths.
Using filters enables to multi-spectral observation.
The depth can be derived from the difference in extinction coefficient at different wavelengths.
𝐼 𝜆1 = 𝜺𝑀𝑒 𝜆1 ; 𝑻 𝑒 −𝜎𝐴𝑖𝑟 (𝜆1)𝒅൞ 𝐼 𝜆2 = 𝜺𝑀𝑒 𝜆2 ; 𝑻 𝑒 −𝜎𝐴𝑖𝑟 (𝜆2)𝒅𝐼 𝜆3 = 𝜺𝑀𝑒 𝜆3 ; 𝑻 𝑒 −𝜎𝐴𝑖𝑟 (𝜆3)𝒅Solve unknowns

1, Deriving 𝑇: Find 𝑇 that satisfies this equation.
1𝐼 𝜆1 𝑀𝑒 𝜆2 ; 𝑇ln
𝜎𝐴𝑖𝑟 𝜆2 − 𝜎𝐴𝑖𝑟 (𝜆1 )𝐼 𝜆2 𝑀𝑒 𝜆1 ; 𝑇2, Deriving 𝑑: substitute 𝑇.
1𝐼 𝜆1 𝑀𝑒 𝜆2 ; 𝑇ln
𝜎𝐴𝑖𝑟 𝜆2 − 𝜎𝐴𝑖𝑟 (𝜆1 )𝐼 𝜆2 𝑀𝑒 𝜆1 ; 𝑇=1𝜎𝐴𝑖𝑟 𝜆3 − 𝜎𝐴𝑖𝑟 (𝜆1 )ln

𝐼 𝜆1 𝑀𝑒 𝜆3 ; 𝑇𝐼 𝜆3 𝑀𝑒 𝜆1 ; 𝑇3, Deriving 𝜀 : substitute 𝑇 and 𝑑.
𝐼 𝜆1𝜀=𝑀𝑒 𝜆1 ; 𝑇 𝑒 −𝜎𝐴𝑖𝑟 (𝜆1)𝑑The results suggest that the proposed method can be adapted to real-world environments.

Conclusion•••

We propose a novel and unique depth sensing approach using an LWIR camera.
− Estimating not only depth but also temperature and emissivity.
We demonstrate the effectiveness in real-world experiments.
This is first attempt. We expect our findings will be improved to practical level.