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Passive LWIR Hyperspectral Ranging via Transmittance Extraction and Distance Alignment

Zhihe Chen, Chen Fan, Shuo Liu, Xiaolin Huang, Yunze He, Xiaofeng He, Lilian Zhang

arXiv:2609.28967v1cs.CV

TL;DR

Passive LWIR ranging can use atmospheric absorption as a distance cue, but residual-based baseline methods can absorb weak or broadened absorption features. TEDA extracts transmittance with an absorption-aware baseline and aligns it to sensor-domain models at candidate distances. It reports lower simulated RMSEs and faster processing than per-range joint inversion, with range estimates closer to LiDAR in the foreground-tree patch.

  • Problem

    Residual-based baseline methods can absorb weak or instrument-broadened atmospheric absorption features, reducing the distance information recovered in transmittance.

    Source: §I · p. 1

  • Method

    TEDA extracts transmittance using an absorption-direction-invariant baseline and aligns it with sensor-domain models recomputed for candidate distances.

    Source: §I · p. 2

  • Results

    8.19 s versus 24,076.50 s for per-range joint inversion over the complete ROI; TEDA also attained lower RMSEs in simulations and was closer to LiDAR in the foreground-tree patch.

    Source: A. Simulation Results · p. 9, D. Real Data Results · p. 11

  • Takeaways & Limitations

    The formulation separates baseline estimation from distance search while preserving atmospheric structure used for alignment.

    Source: §VI · p. 12

    Real-data experiments exclude pixels dominated by reflected downwelling radiance, which can bias transmittance extraction and range estimation on strongly reflective surfaces.

    Source: §VI · p. 13

Abstract

from arXiv · show

Passive long-wave infrared (LWIR) hyperspectral ranging enables distance estimation in low-light and nighttime scenes by exploiting atmospheric absorption features in thermal radiance received through the atmosphere.Joint estimation of temperature, emissivity, and distance is computationally expensive. Reference-range joint inversion also uses a distance-invariant effective attenuation coefficient, which can bias range estimates.We introduce transmittance extraction and distance alignment (TEDA), which decouples range estimation from temperature--emissivity inversion. In the first stage, a baseline estimator with a data-fidelity term invariant to the known absorption direction yields two closed-form smoothing branches for the slowly varying thermal continuum. An observation-derived gate combines the branches, and subtracting the blended baseline in the log domain recovers atmospheric transmittance. The second stage estimates range by matching the recovered transmittance to sensor-domain transmittance models recomputed for each candidate distance. Monte Carlo simulations show that TEDA effectively reduces the ranging bias caused by the distance-invariant attenuation coefficient approximation. In a measured scene, TEDA's mean range estimates are closer to the LiDAR medians than those of reference-range joint inversion in both evaluated patches. TEDA processes a complete $256\times256$ region of interest in 8.19~s versus 159.47~s for reference-range joint inversion, an approximately 20-fold speedup.

I. INTRODUCTION

Passive LWIR hyperspectral ranging uses atmospheric absorption in thermal radiance as a distance cue, but joint temperature–emissivity–distance inversion is costly and can be biased by finite sensor spectral response. TEDA separates transmittance extraction from distance alignment, using known absorption structure and sensor-domain models to address these issues.

I. INTRODUCTION

  • Thermal radiance carries a passive range cue through atmospheric absorption, which varies with path length and is sampled across multiple features by hyperspectral measurements.Passive sensing avoids the probe emissions of active systems, while passive monocular and stereo methods can degrade under low illumination, weak texture, occlusion, or long-range disparities.Source: §I · p. 1
  • Prior joint inversion estimates range, temperature, and emissivity but is computationally expensive and can bias range through a distance-invariant effective attenuation coefficient.Finite spectral response makes an integrated channel's effective attenuation coefficient vary with distance because Beer–Lambert propagation precedes channel integration.Source: §I · p. 1
  • Residual-based baseline reweighting can absorb weak or instrument-broadened absorption features, reducing the distance information recovered in transmittance.Baseline extraction must preserve the absorption structure that encodes distance.Source: §I · p. 1
  • TEDA extracts transmittance by estimating and subtracting a log-domain baseline with absorption-direction-invariant fidelity, then aligns the result to sensor-domain models at candidate distances.Two closed-form smoothing branches are combined by an observation-derived gate, avoiding iterative baseline reweighting.Source: §I · pp. 1–2
  • Its sensor-response-consistent transmittance model applies Beer–Lambert propagation before spectral-response integration at each candidate distance.This avoids the ranging bias associated with the distance-invariant attenuation-coefficient approximation.Source: §I · p. 2
  • TEDA applies the same extraction operator to observations and modeled log-transmittance, with radiance-contrast channel weights; evaluation uses controlled simulations and measured LWIR data.Additional measured scenes assess pixelwise range structure in the DARPA Invisible Headlights dataset.Source: §I · pp. 2–3

II. RELATED WORK

Related work addresses absorption-based ranging, atmospheric compensation, and baseline correction as largely separate problems. The paper identifies a gap in combining known absorption structure with a transmittance extractor that preserves distance dependence under finite spectral resolution.

A. Absorption Ranging

  • Absorption ranging progressed from band-ratio and calibrated-contrast systems to multispectral LWIR and hyperspectral methods for natural scenes.Hyperspectral approaches combine distributed atmospheric features, while related work also formulated natural-scene recovery as regularized joint estimation of range, temperature, and emissivity.Source: A. Absorption Ranging · p. 3

B. Atmospheric Compensation

  • Atmospheric-compensation methods estimate transmittance and path radiance to recover surface-leaving quantities, rather than treating range as the retrieval objective.Approaches include scene-based estimates and physics-based radiative-transfer models, spectral subspaces, or look-up tables.Source: B. Atmospheric Compensation · p. 3

C. Baseline Estimation

  • Baseline correction methods model a smooth continuum directly or use residual-based reweighting, but weak or broadened absorption features can be mistaken for baseline variation.For absorption ranging, baseline estimates must preserve absorption magnitude's distance-dependent variation, unlike baseline correction used mainly for qualitative peak characterization.Source: C. Baseline Estimation · p. 3
  • Prior studies separate atmospheric compensation, baseline correction, and absorption ranging; they lack a unified extractor that uses known absorption structure while preserving finite-resolution distance dependence.This paper addresses that combination.Source: C. Baseline Estimation · p. 3

III. SENSOR-RESPONSE-DEPENDENT MODEL FOR THERMAL HYPERSPECTRAL RANGING

Finite sensor spectral response makes effective attenuation distance-dependent, so reusing a coefficient estimated at one reference range can bias range estimates. The section models transmittance by applying Beer–Lambert propagation before spectral-response integration at each candidate distance.

Sensor-response-dependent transmittance

  • Beer–Lambert propagation and spectral-response integration do not commute, making the effective attenuation coefficient represented by sensor measurements distance-dependent.The proposed correction recalculates continuous-spectrum transmittance and its spectral-response integral at each searched distance.Source: §III · pp. 3–4

Radiative-transfer assumptions

  • The model assumes near-ground clear air with negligible scattering and a uniform atmospheric layer; it neglects reflected radiance for high-emissivity natural-scene surfaces, while strongly reflective surfaces violate this assumption.The received radiance comprises attenuated target radiance and atmospheric path radiance.Source: §III · p. 4

Sensor-response-dependent transmittance

  • Sensor measurements integrate received radiance over each ISRF, while target emissivity and the Planck function are treated as locally smooth relative to narrower atmospheric absorption structure.Spectral-response integration broadens and smooths unresolved H2O absorption structure.Source: §III · pp. 4–5

Distance-invariant attenuation approximation

  • The reference-range model overestimates transmittance and biases distance upward for 0 < d < d0, with bias peaking at an intermediate distance; beyond d0, both inequalities reverse.The bias vanishes at zero distance and at the reference distance d0.Source: §III · p. 5

Per-range joint inversion

  • Per-range joint inversion replaces the distance-invariant coefficient with transmittance calculated at each searched distance, but repeatedly solves for temperature and emissivity, incurring substantial computational cost.The distance with minimum fitting error is selected.Source: §III · p. 5

IV. TRANSMITTANCE EXTRACTION AND DISTANCE ALIGNMENT

TEDA separates passive LWIR range estimation into transmittance extraction and distance alignment. It extracts transmittance without explicitly solving for target temperature or emissivity, then aligns it to models calculated at different distances.

IV. TRANSMITTANCE EXTRACTION AND DISTANCE ALIGNMENT

  • TEDA divides range estimation into transmittance extraction followed by distance alignment to reduce the computational cost of per-range joint inversion.The overall framework is shown in Fig. 1, and its computational procedure is summarized in Algorithm 1.Source: §IV · p. 5
  • Stage I uses an atmospheric-absorption prior to extract transmittance from received thermal radiance without explicitly solving for target temperature or spectral emissivity.Source: §IV · p. 5
  • Stage II estimates range by aligning the extracted transmittance to model transmittances calculated at different distances.Source: §IV · p. 5

A. Stage I: Transmittance Extraction

Stage I estimates the slowly varying thermal-continuum baseline while preserving the absorption structure that carries range information. It blends two closed-form smoothing branches using an observation-derived gate, then uses the residual to recover transmittance.

A. Stage I: Transmittance Extraction

  • The smooth-continuum assumption separates slowly varying thermal terms from finer atmospheric absorption structure in the log-domain spectrum.The baseline error determines the transmittance error, so extraction must preserve absorption features that encode distance.Source: A. Stage I: Transmittance Extraction · p. 6
  • Euclidean data fidelity can pull the smooth baseline toward absorption features, weakening residual contrast and biasing extracted transmittance toward unity.The absorption-direction-invariant data-fidelity term prevents this leakage by making the corresponding baseline component governed by smoothness rather than the observation.Source: A. Stage I: Transmittance Extraction · p. 6
  • The quadratic baseline objective yields closed-form branch operators that can be precomputed for the atmospheric state, sensor response, channel grid, and smoothing strength.The operators must be recomputed if the absorption direction changes.Source: A. Stage I: Transmittance Extraction · p. 6
  • An observation-derived gate combines two fixed smoothing strengths because weak smoothing can absorb absorption structure, while strong smoothing can underfit structured continua.The gate down-weights the strong branch when the two branch baselines disagree.Source: A. Stage I: Transmittance Extraction · p. 6
  • The residual error depends on how strongly the true thermal-continuum baseline aligns spectrally with the absorption prior.Across ECOSTRESS emissivity spectra, baseline-correlation medians range from 0.11 to 0.26, compared with 0.98 for sensor-domain log-transmittance.Source: A. Stage I: Transmittance Extraction · p. 7
  • After projection, absolute median range bias does not exceed 1.4 m in any material category, versus material-dependent errors of tens of meters for unprojected η = 10^4.The projected estimator requires no explicit emissivity model; remaining material dependence is set by baseline–absorption overlap.Source: A. Stage I: Transmittance Extraction · p. 7

B. Stage II: Distance Alignment

Stage II aligns the extracted transmittance with sensor-domain models evaluated at candidate distances. Applying the same extraction operator to the observation and models accounts for baseline-removal distortion during matching.

B. Stage II: Distance Alignment

  • The sensor-domain transmittance model is evaluated at each candidate distance, and the same blended extraction operator is applied to the models before alignment.The gate is estimated once per observation and held fixed across candidate distances.Source: B. Stage II: Distance Alignment · p. 7
  • A contrast-weighted mean-squared error matches extracted and modeled transmittance, with weights that down-weight wavelengths having low radiance contrast.The weights approximate wavelength-dependent range sensitivity using the target-to-air radiance contrast.Source: B. Stage II: Distance Alignment · p. 7
  • The range estimate is the candidate-grid distance that minimizes the matching objective.A 1 m grid spacing preserves the accuracy of finer grids while reducing search cost.Source: B. Stage II: Distance Alignment · pp. 7–8
  • The two branch operators are precomputed once per scene; each pixel then requires two branch baselines, one gate evaluation, and one weighted grid search.The algorithm takes sensor radiance and atmospheric parameters, including air temperature, water-vapor VMR, and pressure, as inputs.Source: B. Stage II: Distance Alignment · p. 8

V. EXPERIMENTAL RESULTS

The experiments assess TEDA’s ranging bias, accuracy, and computational cost using simulations and measured LWIR hyperspectral data.

V. EXPERIMENTAL RESULTS

  • Simulation and measured-data experiments characterize ranging bias associated with the distance-invariant attenuation approximation and assess TEDA’s accuracy and computational cost.Comparing reference-range and per-range joint inversion isolates the effect of the forward-model approximation.Source: §V · p. 8
  • Comparisons with residual-driven baseline extractors and component ablations assess the absorption prior and operator-consistent matching.Source: §V · p. 8
  • Measured-data experiments compare range estimates with LiDAR references and report each method’s runtime.Source: §V · p. 8

A. Simulation Results

In noisy Rock simulations, TEDA preserves range-bearing absorption structure and achieves the lowest RMSE among practical methods across tested temperature differences. Recomputing transmittance for each distance reduces joint-inversion bias but incurs substantially greater computational cost.

A. Simulation Results

  • In controlled simulations, a target with an ECOSTRESS-library emissivity spectrum is placed 100 m from the sensor; 100 independent Monte Carlo trials test ∆T = −8, −5, and −2 K, each colder than air.Channel radiances use a 40 nm-FWHM Gaussian ISRF and additive white Gaussian noise with standard deviation 1 microflick (0.01 W m−2 sr−1 µm−1). TEDA smoothing strengths are selected sequentially on a 1,528-spectrum library and frozen before benchmark reruns: ηlow = 2, then ηhigh = 16.Source: A. Simulation Results · p. 8
  • The oracle uses the true simulated baseline to measure the Stage I error floor, while TEDA uses no ground-truth quantity and applies its blended operator to candidate models.Methods select distance by minimizing contrast-weighted matching error on a common 0.05 m grid.Source: A. Simulation Results · p. 8
  • TEDA retains absorption-feature locations and contrast, approaching oracle-baseline transmittance despite substantial differences in estimated transmittance and distance across methods.Several methods reproduce the radiance measurement despite those differences.Source: A. Simulation Results · p. 9, Figure 6 · p. 9
  • arPLS suppresses atmospheric structure, while NasPLS fails to extract a usable absorption profile and reaches the upper search boundary in nearly all trials.The paper attributes NasPLS instability to applying non-sensitive-area reweighting to dense molecular-line structure.Source: A. Simulation Results · pp. 9–10
  • TEDA achieves the lowest RMSE among practical methods at every tested temperature difference and remains close to the oracle-baseline bound.Table I compares distance RMSE and batch runtime for six methods on noisy Rock measurements at 100 m.Source: A. Simulation Results · p. 9, Table I · p. 9
  • Recomputing sensor-domain transmittance at every candidate distance reduces RMSE to per-range values, identifying attenuation approximation as the dominant error but raising batch time by about 50×.Per-range joint inversion re-fits temperature and emissivity for each candidate distance.Source: A. Simulation Results · p. 9
  • As the absolute target–air temperature difference decreases, all estimators’ errors increase; TEDA’s increase is smaller than arPLS and NasPLS, and its error remains below per-range joint inversion at ∆T = −2 K.The trials use ∆T = −8, −5, and −2 K, with the target colder than the air.Source: A. Simulation Results · pp. 8, 10

B. Component Ablation

The component ablation shows that absorption-direction projection, operator-consistent matching, and contrast weighting each contribute to ranging performance, while the best smoothing choice varies by evaluation scope.

B. Component Ablation

  • Removing the absorption-direction projection increases RMSE at every temperature difference, while removing the operator-consistent model bank produces a large negative bias.Table II reports distance RMSE over 100 noise realizations per temperature difference for the Rock simulation at 100 m.Source: B. Component Ablation · p. 10, Table II · p. 10
  • Replacing contrast weights with uniform weights degrades the ablation result.The ablation compares component replacements on the same Rock-target simulation as Table I.Source: B. Component Ablation · p. 10, Table II · p. 10
  • On this Rock simulation, single η = 16 is marginally better than dual smoothing, but the dual configuration is retained for its best cross-material score.Strong smoothing alone is competitive on this material.Source: B. Component Ablation · p. 10

C. Cross-Material Comparison

Across the spectral material library, dual smoothing has the lowest overall RMSE among the three tested configurations, although strong smoothing alone performs slightly better on vegetation.

C. Cross-Material Comparison

  • Dual η = 2/16 attains the lowest overall RMSE at 9.5 m, versus 9.7 m for single η = 2 and 12.6 m for single η = 16.Table III compares the three smoothing configurations on the spectral material library.Source: C. Cross-Material Comparison · p. 10
  • On vegetation, single η = 16 is slightly better than dual smoothing because strong smoothing alone suffices for its smooth, highly emissive spectra.Source: C. Cross-Material Comparison · p. 10
  • The cross-material comparison evaluates single η = 2, single η = 16, and dual η = 2/16 using overall RMSE.Source: C. Cross-Material Comparison · p. 10

D. Real Data Results

In the selected measured scene, TEDA preserves the principal range layers and runs substantially faster than per-range joint inversion. Additional acquisitions show qualitative agreement with LiDAR, though approximate sensor registration and invalid LiDAR regions limit local comparisons.

Measurement and preprocessing

  • The measured setup uses a 256-channel vehicle-mounted LWIR push-broom camera and generates reference transmittances at candidate distances after wavelength recalibration.The atmospheric model holds air temperature, pressure, and H2O VMR constant over the scene.Source: D. Real Data Results · p. 10

Evaluation setup

  • The comparison uses four solvers on the same ROI, with 1 m candidate-distance spacing for TEDA, arPLS, and per-range joint inversion.Because hyperspectral and LiDAR data are only approximately registered, quantitative comparisons use locally homogeneous patches rather than pixelwise error metrics.Source: D. Real Data Results · pp. 10–11

Selected-scene range map

  • The selected scene contains rolling grassland, a foreground tree, and background forest; TEDA reproduces their principal range ordering against LiDAR.Pixels dominated by reflected downwelling radiance, including the checkerboard targets, are masked rather than assigned distances.Source: D. Real Data Results · p. 11, Figure 7 · p. 11

Selected-scene comparison

  • 8.19 s for TEDA versus 24,076.50 s for per-range joint inversion on the 256 × 256 ROI, with similar range layering.The foreground-tree patch is closer to the LiDAR reference and has lower spread with TEDA; the grass patch is closest with per-range joint inversion, and the background-tree patch lacks a valid LiDAR reference.Source: Table IV · p. 11, D. Real Data Results · p. 11, Figure 8 · p. 12

Additional acquisitions

  • TEDA preserves the foreground-to-background range structure across three additional acquisitions, with estimates qualitatively agreeing with LiDAR references.The acquisitions use the same fixed hyperparameters without per-scene adjustment; local differences are not treated as pixelwise errors because the sensors are only approximately registered.Source: D. Real Data Results · pp. 11–12

VI. DISCUSSION AND CONCLUSION

TEDA reformulates passive LWIR hyperspectral ranging as transmittance recovery followed by distance alignment, avoiding repeated temperature–emissivity fitting. Simulations report lower distance RMSE than the comparison method at all three tested temperature differences, while the real-data evaluation is limited by reflective-surface effects.

Method

  • TEDA recovers transmittance before range alignment, using closed-form baseline branches and an observation-derived gate to preserve atmospheric absorption structure.This separates baseline estimation from distance search and avoids fitting temperature and emissivity at every candidate distance.Source: §VI · p. 12

Additional measured scenes

  • The additional DARPA scenes show qualitative agreement with LiDAR and are processed with fixed hyperparameters without per-scene tuning.The figure presents three additional acquisitions, each as spectral-mean imagery, LiDAR references, and TEDA estimates.Source: Figure 9 · p. 13

Simulation results

  • 1.571 s for TEDA versus 943.02 s for per-range joint inversion in the complete simulation batch; TEDA also attains lower distance RMSE at all three tested target–air temperature differences.The sensor-domain transmittance model is evaluated at each candidate distance to address the finite-spectral-response dependence of effective attenuation.Source: §VI · pp. 12–13

Scope and limitation

  • Strongly reflective surfaces can introduce absorption structure not determined solely by line-of-sight transmittance, so the real-data experiments exclude pixels dominated by reflected downwelling radiance.The authors identify reflected-environmental-radiance modeling or downwelling-radiance estimation and compensation as possible ways to broaden the applicable emissivity range.Source: §VI · p. 13
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