The spectral reflectance of vegetation obtained from optical sensors provides information on their biophysical and biochemical properties. However, in remote sensing, reflectance is typically computed with respect to the top-of canopy (TOC) surface, resulting in an apparent reflectance due to the differences between the illumination conditions between the observed vegetation elements and the TOC surface. While the TOC reflectance is useful for data with coarse spatial resolution, it leads to erroneous estimates of the vegetation properties when applied to very high spatial resolution (VHR) data where individual leaves are visible. An illumination correction is required to retrieve the true leaf reflectance from the TOC reflectance. The present work investigates an illumination correction method for retrieving the true leaf reflectance from VHR hyperspectral TOC reflectance images based on the spectral invariant theory and a simple mathematical model for the leaf reflectance. The method is tested on simulated and measured data. The results show that the leaf reflectance can be accurately estimated from both data (average RMSD between 0.02 and &lt; 0.12)

Ihalainen, Olli

Juola, Jussi

Mõttus, Matti

English

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Electronic or print copies may not beoffered for sale.VTT Technical Research Centre of FinlandInversion of True Leaf Reflectance from Very High Spatial ResolutionHyperspectral ImagesIhalainen, Olli; Mõttus, Matti; Juola, JussiPublished in:IGARSS 2023 - 2023 IEEE International Geoscience and Remote Sensing SymposiumDOI:10.1109/IGARSS52108.2023.10283065Published: 01/01/2023Document VersionEarly version, also known as pre-printLink to publicationPlease cite the original version:Ihalainen, O., Mõttus, M., & Juola, J. (2023). Inversion of True Leaf Reflectance from Very High SpatialResolution Hyperspectral Images. In IGARSS 2023 - 2023 IEEE International Geoscience and Remote SensingSymposium (pp. 7579-7582). IEEE Institute of Electrical and Electronic Engineers.https://doi.org/10.1109/IGARSS52108.2023.10283065Download date: 04. Nov. 2023INVERSION OF TRUE LEAF REFLECTANCE FROM VERY HIGH SPATIAL RESOLUTIONHYPERSPECTRAL IMAGESOlli Ihalainen∗, Matti MõttusVTT Technical Research Centre of FinlandEspoo, FinlandJussi JuolaAalto UniversityDepartment of Built EnvironmentEspoo, FinlandABSTRACTThe spectral reflectance of vegetation obtained from opti-cal sensors provides information on their biophysical andbiochemical properties. However, in remote sensing, re-flectance is typically computed with respect to the top-of-canopy (TOC) surface, resulting in an apparent reflectancedue to the differences between the illumination conditionsbetween the observed vegetation elements and the TOC sur-face. While the TOC reflectance is useful for data with coarsespatial resolution, it leads to erroneous estimates of the vege-tation properties when applied to very high spatial resolution(VHR) data where individual leaves are visible. An illumina-tion correction is required to retrieve the true leaf reflectancefrom the TOC reflectance. The present work investigates anillumination correction method for retrieving the true leafreflectance from VHR hyperspectral TOC reflectance imagesbased on the spectral invariant theory and a simple mathe-matical model for the leaf reflectance. The method is testedon simulated and measured data. The results show that theleaf reflectance can be accurately estimated from both data(average RMSD between 0.02 and < 0.12).Index Terms— hyperspectral, imaging spectroscopy, re-flectance, p-theory, spectral invariant, inversion, radiativetransfer1. INTRODUCTIONThe spectral reflectance of vegetation obtained from opticalsensors enables the retrieval of their biophysical and biochem-ical properties. The hemispherical-directional reflectance fac-tor (hereafter called reflectance unless otherwise specified) ina pixel corresponding to a vegetation canopy element suchas a leaf or a tree crown is calculated as the ratio of radi-ance reflected by the canopy element towards the sensor tothe theoretical radiance reflected by a reference surface underidentical illumination and observation geometry. However, inpractice, the latter is commonly calculated using the known∗Olli Ihalainen is the corresponding author. Email: olli.ihalainen@vtt.fi.spectrum of solar radiation and radiative transfer in the atmo-sphere or taken from the reflectance of a reference panel nextto the vegetated area. Therefore, the reflectance of a pixel isnot calculated using the irradiance conditions for the elementin the pixel but using that on a top-of-canopy (TOC) surface.For spectral data recorded by traditional environmentalsatellites with a medium spatial resolution larger than 10 m,this approach produces reasonable results: reflectance factorsfor a vegetation canopy. For images with a very high spa-tial resolution taken from aircraft and drones, where the pixelsize is below 1 m, the approach becomes less justified: at suchscales, individual canopy elements such as leaves become vis-ible. The illumination conditions on the canopy elements canbe considerably different from those at the TOC [1, 2]. Hence,the reflectance calculated for a pixel with respect to the TOCsurface does not represent the true reflectance of the canopyelement in a pixel.Previous research has shown that the local illuminationconditions for vegetation elements can be accounted for bythe spectral invariant theory [3]. Indeed, the spectral in-variant theory links the TOC reflectance to the true leafreflectance via wavelength-independent parameters, whichare directly related to the illumination conditions, namely thedirect solar irradiance and diffuse ambient irradiance [4].Recently, [5] demonstrated accurate retrieval of the trueleaf reflectance from VHR hyperspectral images using thespectral invariant theory and the PROSPECT-D leaf radia-tive transfer model [6]. However, PROSPECT is ill-suitedfor this illumination correction method, as it models theleaf directional-hemispherical reflectance rather than thehemispherical-directional reflectance. Thus, an alternativemodel for the leaf reflectance is needed.The main objective of this work was to investigate us-ing a sigmoid function as a leaf reflectance model in the rededge wavelengths (710 to 790 nm) when performing illumi-nation correction on TOC reflectance with the spectral invari-ant theory. The method enables the retrieval of the true leafreflectance for visual to near-infrared wavelengths using thespectral invariants retrieved from the red edge.2. MATERIALS2.1. Simulated dataWe used eight synthetic hyperspectral TOC reflectance im-ages by [5], where the true leaf reflectance of each pixel isknown a priori. The data were generated using Monte Carloray tracing with cyclic boundary conditions such that the sim-ulated vegetation scenes had identical geometric propertiesbut varying leaf optical properties. More specifically, eachscene had of a non-reflecting forest floor and 138 randomlypositioned and oriented disk-shaped identical bi-Lambertianleaves with a 0.15 m radius within a 1 m × 1 m area. TheANGERS database was used for the leaf spectra [6]. For onehalf of the scenes, the reflectance and transmittance factors ofleaves 74, 126, 202, and 245 of the ANGERS database wereused (Fig. 1a–d). For the other half of the scenes, the corre-sponding biochemical traits of the leaves from the ANGERSdatabase were used as input for the PROSPECT-D model togenerate the leaf spectra (Fig. 1e–h). The simulated wave-lengths ranged from 450 nm to 900 nm at 5 nm intervals andthe spatial resolution was 1 cm resulting in images with 100rows and 100 columns.a) P74 b) P126 c) P202 d) P245e) A74 f) A126 g) A202 h) A245Fig. 1. RGB images of the simulated data scenes. Each leafin a given scene has the same optical properties.2.2. Measured dataFor the measured data, we used a hyperspectral image ofa Diervilla lonicera Mill. canopy located in the Otaniemicampus, Finland (60◦11′ N, 24◦49′ E) by [5]. The imagewas recorded using a Specim IQ imaging spectrometer (serialnumber 190-1100152, Specim, Oulu, Finland; 512 × 512pixels, spectral resolution 7 nm) from a nadir view geometryon a cloudless day with the Sun at a 47° zenith angle. Theinstrument was placed approx. 1 m above the canopy, result-ing in a spatial resolution of approx. 1 mm. The image wascalibrated to TOC reflectance using Spectralon white diffusereflectance standard (99%) panel placed above the canopysuch that it was visible in one corner of the image. The ref-erence reflectance spectra of two sunlit leaves visible in theimage were collected using an Avantes SensLine spectometer(AvaSpec-ULS-2048x64TEC-EVO, Avantes, Netherlands)with a bare fiber optic cable in a cross-plane geometry at 45°view zenith angle. As with the simulated data, the wave-lengths between 450 nm and 900 nm were selected.3. THEORYLet us consider a measurement of the radiance Is scatteredby a sunlit leaf within a vegetation canopy toward the in-stantaneous field of vision of a sensor above the canopy.The hemispherical-directional reflectance factor of the leaf isgiven by Rleaf = πIs/ϕ, where ϕ is the incident irradianceon the leaf [7]. Similarly, the TOC reflectance of the leaf isgiven by RTOC = πIs/ΦTOC, where ΦTOC is the irradianceon the TOC from the above. By decomposing the irradianceon the leaf into direct solar irradiance, ϕ⊙, and diffuse irradi-ance from the sky and from within the canopy, ϕA, the TOCreflectance can be written asRTOC(λ) =[ϕ⊙(λ)ΦTOC(λ)+ϕA(λ)ΦTOC(λ)]Rleaf(λ) (1)= [ρ+ pRTOC(λ)]Rleaf(λ), (2)where ϕ⊙ΦTOC = ρ andϕAΦTOC= pRTOC, and ρ and p are indepen-dent of the wavelength [1, 3, 4]. Assuming the leaf reflectancecan be parameterized by a vector ϑ⃗leaf and rearranging Eq. (2),we get a forward model for the TOC reflectanceRmodTOC(ϑ⃗TOC;λ) =ρRmodleaf (ϑ⃗leaf;λ)1− pRmodleaf (ϑ⃗leaf;λ)+ ε, (3)where ϑ⃗TOC = [p, ρ, ϑ⃗leaf]T is the model input vector and εis the measurement and model uncertainty. The present workuses a sigmoid function with three input parameters for mod-eling the leaf reflectance in the red edge wavelength region(710 to 790 nm)Rmodleaf (ϑ⃗leaf;λ) =A1 + exp[k(λ− λ0)], (4)where A is the upper right asymptote of the logistic curve, kis the logistic growth rate, and λ0 is the midpoint of the curve.The lower left asymptote of the curve is zero.4. METHODSGiven the forward model for the TOC reflectance (Eq. (3)),the parameters ϑ⃗TOC are estimated by minimizing the resid-ual sum of squares between the measured and modeled re-flectances in the red edge, λ̃⃗̂ϑTOC = argminϑ⃗TOCn∑i=0(RmeaTOC(λ̃i)−RmodTOC(ϑ⃗TOC; λ̃i))2,(5)where n is the number of measured wavelengths. The param-eter inversion (Eq. 5) was performed using the trust region re-flective algorithm implemented in the SciPy library of Python.The initial guess values and the lower and upper bounds ofϑ⃗TOC are given in Table 1.Table 1. The initial guess values and upper and lower bound-aries of parameters used in the inversion.p ρ A k λ0initial guess 0.50 0.90 0.45 0.10 715.00lower bound −∞ −∞ 0.1 0.00 670.00upper bound ∞ ∞ 1.00 0.2 790.00Given the estimated values of the spectral invariants, p̂, ρ̂,the illumination corrected leaf reflectance can be computedfor the entire observed spectral domain of the measured wave-lengths, λ, from Eq. (2) asRleaf(λ) =RTOC(λ)ρ̂+ p̂RTOC(λ). (6)The complete illumination correction algorithm thus consistsof two steps:1. Parameter inversion: estimate ⃗̂ϑTOC = [p̂, ρ̂,⃗̂ϑleaf]T us-ing wavelengths between 710 and 790 nm (Eq. (5)).2. Illumination correction: compute the true leaf re-flectance (Eq. (6)) for all observed wavelengths usingp̂, ρ̂.5. RESULTS AND DISCUSSIONOverall, the the estimated leaf reflectance spectra producedby the illumination correction algorithm were in good agree-ment with the true leaf reflectances for both the simulated andmeasured hyperspectral data. For the simulated images, wecomputed the RMSD between the estimated and the true leafreflectances for the sunlit pixels (Fig. 2). Despite a number ofoutlier values, the mean RMSDs of the scenes were between0.02 and 0.12, and the standard deviations of the RMSDswere between 0.002 and 0.01. The outliers were caused bypixels where the Monte Carlo simulation noise was high suchas pixels between the leaf edges and the black forest floor.For the measured data (Fig. 3a), the method significantlyreduced the effects of illumination conditions of the TOC re-flectance for most of the leaves in the image (Fig. 3b). ForA74 P74 A126 P126 A202 P202 A245 P245Simulated data scene0.000.050.100.15RMSDFig. 2. The distributions of the RMSD values between theestimated leaf reflectances and the true leaf reflectances ofthe simulated data scenes.the reference leaf A, the RMSD between the estimated andmeasured leaf reflectance was 0.02, (Fig. 3c), and for leaf Bthe RMSD was 0.06 (Fig. 3d).Although the results from both simulated and measureddata were promising, we found that the reflectance producedby the illumination correction algorithm is heavily dependenton the initial guess values for the parameters A and λ0 ofthe sigmoid function (Eq. (4)). In fact, the parameter inver-sion did not generally converge far from the initial valuesof A and λ0 (data not shown) meaning that variation in theRMSD values for the data can be partially attributed to howclosely the sigmoid function with the initial guess parametersmatches the true leaf reflectance at the red edge. E.g., forthe scene P74 the sigmoid curve with the initial guess valueswas already close to the true leaf reflectance, whereas for thescene P126 it was not. The non-uniqueness of the solution forEq. (5) is a hallmark of ill-posed inverse problems. A uniquesolution could be sought by imposing a other regularizationstrategies than setting upper and lower parameter bounds asdone in the present work. Alternative approaches are offeredby using Bayesian inference, where the unknown parametersare treated as random variables [8], or by training a machinelearning method on simulated data for estimating the spectralinvariants.Despite the issues caused by the ill-posedness of the in-verse problem, these results can have major implications forhyperspectral vegetation monitoring applications relying onVHR data, e.g., when taken from a unmanned aerial vehi-cle, which show strong multiple-scattering effects. In thissituation, the traditional radiative transfer models used forvegetation (e.g., SAIL [9]) are not applicable, as the vegeta-tion canopy cannot be considered to consist of infinitesimallysmall scattering elements. The theory of spectral invariantsmakes no such assumptions and can reduce the effects of thelocal illumination conditions and scale the measured canopy-level reflectance factor to that of a leaf, enabling detection ofthe true physiological signals from the canopy elements.AB(a) (b)600 800Wavelength [nm]0.00.20.40.60.81.0Reflectance(c)In situ reflectanceInverted reflectanceTOC reflectance600 800Wavelength [nm]0.00.20.40.60.81.0Reflectance(d)In situ reflectanceInverted reflectanceTOC reflectanceFig. 3. TOC reflectance image of the Diervilla lonicera Mill.canopy with the pixels corresponding to the in situ measuredarea of leaves A and B shown respectively in cyan and fuch-sia (a), an inverted reflectance RGB image (b), the situ mea-sured reflectances and the corresponding averaged TOC andinverted reflectances of leaf A (c) and leaf B (d).6. CONCLUSIONThe present work evaluated the performance of an illumina-tion correction method for retrieving the true reflectance ofsunlit leaves from very high spatial resolution hyperspectralTOC reflectance images. The method relates the TOC re-flectance to the true leaf reflectance via the spectral invari-ant theory and uses a sigmoid function to model the leaf re-flectance. The results show that the method can accuratelyretrieve the leaf reflectance under varying illumination condi-tions. The illumination corrected true leaf reflectance spec-trum enables the accurate estimation of leaf biochemical vari-ables, such as leaf chlorophyll content. However, the resultsdepend heavily on the initial guess values for the parametersinverted by the method. Hence, further research is should fo-cus on increasing the robustness of the method.7. ACKNOWLEDGMENTSThis work was funded by the Academy of Finland (grant322256).8. REFERENCES[1] Matti Mõttus, Tuure L.H. Takala, Pauline Stenberg, YuriKnyazikhin, Bin Yang, and Tiit Nilson, “Diffuse sky radi-ation influences the relationship between canopy PRI andshadow fraction,” ISPRS Journal of Photogrammetry andRemote Sensing, vol. 105, pp. 54–60, 7 2015.[2] Forrest G Hall, Thomas Hilker, Nicholas C Coops, AlexeiLyapustin, Karl F Huemmrich, Elizabeth Middleton,Hank Margolis, Guillaume Drolet, and T Andrew Black,“Multi-angle remote sensing of forest light use efficiencyby observing PRI variation with canopy shadow frac-tion,” Remote Sensing of Environment, vol. 112, no. 7,pp. 3201–3211, 2008.[3] Rocio Hernandez-Clemente, Pasi Kolari, Albert Porcar-Castell, Lauri Korhonen, and Matti Mõttus, “Trackingthe Seasonal Dynamics of Boreal Forest PhotosynthesisUsing EO-1 Hyperion Reflectance: Sensitivity to Struc-tural and Illumination Effects,” IEEE Transactions onGeoscience and Remote Sensing, vol. 54, no. 9, pp. 5105–5116, 9 2016.[4] Olli Ihalainen and Matti Mõttus, “Spectral invariants inultra-high spatial resolution hyperspectral images,” Jour-nal of Quantitative Spectroscopy and Radiative Transfer,p. 108265, 2022.[5] Olli Ihalainen, Jussi Juola, and Matti Mõttus, “Physicallybased illumination correction for sub-centimeter spatialresolution hyperspectral data,” unpublished.[6] Jean-Baptiste Feret, Christophe François, Gregory P As-ner, Anatoly A Gitelson, Roberta E Martin, Luc PR Bidel,Susan L Ustin, Guerric Le Maire, and Stéphane Jacque-moud, “PROSPECT-4 and 5: Advances in the leafoptical properties model separating photosynthetic pig-ments,” Remote sensing of environment, vol. 112, no. 6,pp. 3030–3043, 2008.[7] G. Schaepman Strub, M. E. Schaepman, T. H. Painter,S. Dangel, and J. V. Martonchik, “Reflectance quanti-ties in optical remote sensing-definitions and case stud-ies,” Remote Sensing of Environment, vol. 103, no. 1, pp.27–42, 7 2006.[8] Daniel Schraik, Petri Varvia, Lauri Korhonen, and Mi-ina Rautiainen, “Bayesian inversion of a forest re-flectance model using sentinel-2 and landsat 8 satelliteimages,” Journal of Quantitative Spectroscopy and Ra-diative Transfer, vol. 233, pp. 1–12, 2019.[9] Wouter Verhoef, “Light scattering by leaf layers withapplication to canopy reflectance modeling: The SAILmodel,” Remote sensing of environment, vol. 16, no. 2,pp. 125–141, 1984.

Inversion of True Leaf Reflectance from Very High Spatial Resolution Hyperspectral Images

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Inversion of true leaf reflectance from very high spatial resolution hyperspectral images

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