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Hyperspectral recovery from RGB images using Gaussian Processes

Naveed Akhtar, Ajmal Mian

arXiv:1801.04654v2cs.CV

TL;DR

Recovering detailed spectra from RGB is under-constrained, and the approach assumes hyperspectral training data. The paper models spectral sources with Gaussian Processes and combines them with RGB patch codes; it reports up to 30.75% lower RMSE than.

  • Problem

    RGB measurements can correspond to multiple spectral signatures, making recovery of detailed spectra under-constrained.

    Source: §3 · p. 4

  • Method

    The method learns clustered sets of Gaussian Processes from hyperspectral training patches, modeling reflectance smoothness and non-negativity, then combines RGB patch codes with the original processes.

    Source: §1 · pp. 1–2, §5.1 · p. 5

  • Results

    Up to 30.75% reduction in RMSE for spectral recovery versus is reported, with evaluation across three hyperspectral datasets.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The results demonstrate effective extraction of spectral details from RGB images using the proposed approach.

    Source: §1 · p. 2, §8 · p. 13

    The approach assumes hyperspectral training data and prefers training from the same or similar scene domains for appropriate recovery.

    Source: §4 · p. 4, §7.2 · p. 9

Abstract

from arXiv · show

We propose to recover spectral details from RGB images of known spectral quantization by modeling natural spectra under Gaussian Processes and combining them with the RGB images. Our technique exploits Process Kernels to model the relative smoothness of reflectance spectra, and encourages non-negativity in the resulting signals for better estimation of the reflectance values. The Gaussian Processes are inferred in sets using clusters of spatio-spectrally correlated hyperspectral training patches. Each set is transformed to match the spectral quantization of the test RGB image. We extract overlapping patches from the RGB image and match them to the hyperspectral training patches by spectrally transforming the latter. The RGB patches are encoded over the transformed Gaussian Processes related to those hyperspectral patches and the resulting image is constructed by combining the codes with the original Processes. Our approach infers the desired Gaussian Processes under a fully Bayesian model inspired by Beta-Bernoulli Process, for which we also present the inference procedure. A thorough evaluation using three hyperspectral datasets demonstrates the effective extraction of spectral details from RGB images by the proposed technique.

1 INTRODUCTION

Hyperspectral imaging preserves spectral detail, but specialized cameras have limits in exposure time, spatial resolution, and cost. This work recovers spectral detail from RGB images by modeling reflectance properties with Gaussian Processes and reports lower RMSE than Arad and Ben-Shahar.

1 INTRODUCTION

  • Hyperspectral cameras capture many narrow spectral bands but generally require longer exposures, have lower spatial resolution, and are expensive.The stated resolution trade-off arises because increasing sensor resolution further reduces photon density in already narrow spectral bands.Source: §1 · p. 1
  • Unlike spectral-recovery methods that rely on extra hardware, the approach focuses on reflectance smoothness, non-negativity, and spatial and spectral self-similarity.Gaussian Process kernels model spectral smoothness, while the method also exploits non-negativity and self-similarity.Source: §1 · p. 1
  • The method learns Gaussian Process sets from clustered spatio-spectrally correlated hyperspectral patches, transforms their means to match RGB quantization, and combines RGB patch codes with the original processes.The processes are inferred under a Beta-Bernoulli-inspired Bayesian representation model with non-negativity encouragement.Source: §1 · p. 2, Figure 1 · p. 2
  • Up to 30.75% reduction in RMSE for spectral recovery versus is reported for the proposed approach.The evaluation covers more than 35 indoor, outdoor, and object scenes across CAVE, iCVL, and Harvard datasets.Source: §1 · p. 2

2 RELATED WORK

Prior hyperspectral-recovery approaches use specialized acquisition hardware, illumination, or training data, while this work emphasizes modeling intrinsic spectral attributes. Earlier direct RGB methods include basis-and-code approaches and learned mappings from RGB to multiple spectral channels.

2 RELATED WORK

  • Specialized acquisition approaches use scanning, filters, computational imaging, foveal sampling, illumination, or kaleidoscope geometries, often retaining hardware or scene-coverage constraints.The cited examples include computed tomography imaging spectrometers,,, fovea systems,, and active illumination,,,,,.Source: §2 · pp. 2–3
  • Direct RGB spectral recovery includes radial-basis-function estimation, sparse spectral and convolutional features, and hyperspectral bases used to encode RGB images.Arad and Ben-Shahar combine RGB sparse codes with the original hyperspectral basis to recover scene reflectance.Source: §2 · p. 3
  • Other training-data methods learn RGB-to-spectrum mappings with deep networks, shallow regression, or generative adversarial networks.Wu et al. proposed an improvement over based on adjusted anchored neighborhood regression.Source: §2 · p. 3
  • The proposed approach distinguishes itself by exploiting intrinsic spectral-signature attributes in a principled manner, which the authors say existing approaches lack.The paper situates this emphasis amid growing research interest and the NTIRE spectral-reconstruction challenge at CVPR 2018.Source: §2 · p. 3

3 PROBLEM FORMULATION

The task is to infer a higher-spectral-resolution image from RGB measurements, whose channels are formed by a known spectral transformation. The formulation assumes hyperspectral training data and uses Gaussian Processes to represent smooth, non-negative natural spectra.

3 PROBLEM FORMULATION

  • The target is a hyperspectral image with L > 3 channels, with the stated spectral-resolution increase limited to L ≤ 10 × 3.The mapping M(.) integrates the target hyperspectral channels to form the RGB image.Source: §3 · p. 4
  • For each pixel, the RGB observation is modeled as y = TΦα, where T is the known spectral transformation and Φ contains material signatures.The transformation is assumed known a priori and can be estimated from camera spectral response.Source: §3 · p. 4
  • Given a hyperspectral training prior, the method estimates signatures with Gaussian Processes that account for natural spectral smoothness and reflectance non-negativity.The formulation represents hyperspectral pixels as combinations of material signatures.Source: §3 · p. 4

4 SPECTRAL RECOVERY FROM RGB SIGNALS

Recovering detailed spectra from three-channel RGB is under-constrained because metameric spectra can produce matching sensed colors. Prior evidence supports recoverability under conditions on the spectral-signal manifold and metamer frequency, but the approach assumes a useful hyperspectral training prior.

4 SPECTRAL RECOVERY FROM RGB SIGNALS

  • RGB-to-hyperspectral recovery is under-constrained because metamerism allows multiple spectral signatures to correspond to one RGB pixel.The passage frames recovery of roughly 30-dimensional signatures from three-dimensional RGB signals as an open question.Source: §4 · p. 4
  • Prior work argues detailed recovery is possible when encountered spectra lie on a relatively low-dimensional manifold and metamers are infrequent there.Reported evidence places natural-scene metamer-pair frequency at 10^-4 to 10^-6.Source: §4 · p. 4
  • The method assumes an available prior in the form of hyperspectral training data.The passage notes several public hyperspectral image databases, including CAVE.Source: §4 · p. 4

5 PROPOSED APPROACH

The approach learns cluster-specific Gaussian Processes (GPs) from hyperspectral patches, then uses transformed GP means to encode RGB patches and reconstruct spectra. Its Bayesian representation models spectral smoothness and encourages non-negativity in reflectance estimates.

5 PROPOSED APPROACH

  • GPs learned from hyperspectral training data model spectral smoothness and non-negativity, and transformed GP means provide bases for recovering spectra from RGB patches.The approach combines these representations with the RGB image and accounts for self-similarity among hyperspectral patches.Source: §5 · p. 4

5.1 Training

  • K-means groups hyperspectral patches into clusters, each represented by a set of GPs whose posterior means are transformed to match the RGB camera’s spectral quantization.Clusters are motivated by within-cluster similarity and reduced frequency of metamers.Source: §5.1 · p. 5

5.1.1 Representation Model

  • The representation uses GP kernels for spectral correlation and Beta-Bernoulli coefficients, with non-zero mean priors promoting non-negativity in basis vectors and coefficients.The model places Gamma hyper-priors on kernel parameters to adapt them to training data.Source: §5.1.1 · pp. 5–6

5.1.2 Bayesian Inference

  • A fully conjugate model enables Gibbs sampling to iteratively infer posterior distributions over its parameters.The sampler uses analytical posterior expressions and iterates until convergence.Source: §5.1.2 · p. 6

5.1.3 Prior distribution parameter computation

  • Non-negative sparse optimization supplies prior means for the GP basis vectors and representation weights, while posterior means can differ from those priors and remain non-negative.The reported posterior means are smoother functions of wavelength than the corresponding prior means.Source: §5.1.3 · p. 6, Figure 2 · p. 7

5.2 Testing

  • At test time, each RGB patch is assigned to a cluster using Euclidean distances to transformed-patch centroids, then encoded over that cluster’s transformed GP means to reconstruct its spectra.The hyperspectral patches are transformed and clustered offline; overlapping RGB patches are processed and their spectral estimates combined by expectation.Source: §5.2 · pp. 6–7

6 IMPLEMENTATION DETAILS

The implementation uses sparse-optimization solvers and empirically selected parameters. The authors report that results remain fairly robust across nearby parameter initializations.

6 IMPLEMENTATION DETAILS

  • SPAMS implements the online dictionary-learning and non-negative LARS solvers; the experiments set δ to 0.01 and δ1 to 10^-21.The authors note that low RGB SNR should be accounted for with a larger δ1.Source: §6 · p. 7
  • Most Gamma hyper-prior parameters were set to 10^-6, while K was determined automatically from cluster size and initialization values were chosen from model interpretations.The noise precision was set to 10^6, and the GP kernel parameter ℓ was set to 3.Source: §6 · p. 7
  • Results remained fairly robust when the model was tested with nearby alternative initial parameter values.The authors characterize this robustness as typical for a Bayesian approach.Source: §6 · pp. 7–8

7 EXPERIMENTAL EVALUATION

The evaluation compares the proposed method with Arad and A+ [74] on CAVE, iCVL, and Harvard data, and tests real-world color-chart recovery and computational time. Across these experiments, the reported results favor the proposed method over the baselines, while cross-domain recovery and runtime have practical qualifications.

7.1 CAVE images

  • On CAVE, the proposed method reduces average RMSE by 16.35% and average SAM by 9.39% versus Arad, and by 11.98% and 5.85% versus A+ [74].Table 1 reports CAVE results; the DL variant, which omits Gaussian Processes, performs less well.Source: Table 1 · p. 8, §7.1 · p. 8

7.2 iCVL images

  • On domain-specific iCVL tests, average relative RMSE and SAM improve over Arad by 18.62% and 23.35%, and over A+ [74] by 12.31% and 16.78%.Training used remaining scenes from the same domain; results improve with training/test spectral-source similarity.Source: §7.2 · p. 9, Table 2 · p. 9
  • Cross-domain iCVL recovery degrades compared with domain-specific results, but remains acceptable despite substantial differences in spectral sources.The experiments recover Floral scenes using training data from the Outdoor or Green house domains.Source: §7.2 · p. 9
  • For exhaustive iCVL testing, average relative RMSE and SAM were 0.0601 and 2.49, versus 0.0814 and 3.64 for Arad and 0.0673 and 2.95 for A+ [74].Source: §7.2 · p. 10

7.3 Harvard images

  • On Harvard scenes, the proposed method improves average RMSE by 30.75% and average SAM by 9.85% over Arad.Table 4 reports results for Indoor and Outdoor test scenes.Source: Table 4 · p. 11, §7.3 · p. 11

7.4 Real-world experiments

  • For Macbeth chart swatches, average SAM and RMSE were 6.1 and 6.9 using Gaussian Processes learned from CAVE data.The spectral transformation was approximated for the acquired RGB images, yet the authors report useful recovery of spectral details.Source: §7.4 · p. 11

7.5 Computational time

  • Sampling 1% of pixels per training patch cut inference time by nearly two orders of magnitude; training took 7.32 minutes on CAVE, 39.63 on Harvard, and 54.98 on iCVL.For 512 × 512 images, testing took 3.96, 3.81, and 7.44 minutes on CAVE, Harvard, and iCVL; Arad was nearly twice as fast in these experiments, while the proposed method improved recovery.Source: §7.5 · pp. 11–13

8 CONCLUSION

The paper recovers hyperspectral images from RGB images of known spectral quantization using clustered training patches and Gaussian Processes that incorporate reflectance properties. Across 37 images, results show reasonable spectral recovery and up to 30.75% lower RMSE and 20.93% lower SAM than.

8 CONCLUSION

  • Up to 30.75% reduction in RMSE and 20.93% reduction in SAM were achieved against for reconstructed images.The evaluation recovered 37 hyperspectral images from RGB images of Objects, Indoor, and Outdoor scenes.Source: §8 · p. 13
  • The method estimates a scene's hyperspectral image from an RGB image with known spectral quantization, using hyperspectral training data as a prior.It clusters similar patches to compute Gaussian Process sets, with kernels and non-negative mean priors encoding spectral attributes.Source: §8 · p. 13
  • RGB patches are matched to transformed training patches, encoded over transformed Gaussian Processes, then combined with the original Processes to construct the hyperspectral image.The Gaussian Processes are inferred with a Bayesian representation model and its proposed inference scheme.Source: §8 · p. 13
  • The authors report reasonable recovery of detailed spectra across the evaluated images.Source: §8 · p. 13
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