a new method for correction of bidirectional effects in hyperspectral ...

International Workshop on Spectroscopy Application in Precision Farming, Freising - Weihenstephan, 2001

A NEW METHOD FOR CORRECTION OF BIDIRECTIONAL EFFECTS IN HYPERSPECTRAL IMAGERY Ulrich Beisl1,2 1

DLR Oberpfaffenhofen 82230 Wessling, Germany phone: +49-8153-28-1161 Email: [email protected] 2

Remote Sensing Laboratories, Dept of Geography, University of Zurich Winterthurerstr. 190 8057 Zurich, Switzerland

KEY WORDS: BRDF, hyperspectral, bidirectional, inversion, correction ABSTRACT During the DAISEX 99 campaign hyperspectral multiangular images have been taken with the airborne imaging spectrometer HyMap at the Barrax test site in Spain. In order to remove the effects of angular dependent path radiance and atmospheric transmittance, the image data are atmospherically corrected. Using classification and a statistical approach, the directional behaviour of the reflectance for each class is derived from a single image. Three multiplicative BRDF correction methods are applied independently to two images of the same target taken from different flight directions and the result is discussed. 1 INTRODUCTION Most current multi- and hyperspectral airborne imaging sensors (e.g., DAIS7915, HyMap, MIVIS) are designed to acquire wide-FOV images, unless a very high spatial resolution is required. The reflectance of most ground surfaces shows anisotropic behaviour already in the angular range of wide-FOV imaging sensors (–30 degrees). For line scanner systems this is most prominent if the flight direction is perpendicular to the sun-target-observer plane (so-called principal plane, PP). Subsequently a large across track illumination gradient is observed, reducing the intercomparability of different portions of the image. To avoid this gradient in the across track direction, the flight line is usually directed towards the sun. Together with the need to optimize for a high signal to noise ratio (SNR) while flying at a high solar irradiance (typically at noon), the flight lines are more or less restricted to the north-south direction. Thus routines have been developed to correct the illumination gradient with an overall correction function (typically polynomials; Royer and Bonn, 1985; ENVI) which does not account for surfacetype dependent reflection anisotropy within the image. Other methods use a sampling from different images to get enough angle information to fit a semiempirical BRDF model (Chopping, 2000). The methods proposed here combine the advantages of both approaches.


2 METHOD 2.1 HyMap Image Spectra In the DAISEX 99 campaign (Berger et al., 2000) the flight lines are covered at three different times of the day (10, 14 and 17 hrs MET) in a cross-shape pattern with headings of 180 and 270 degrees respectively (cf., Figure 1). The solar position was East at 10 h MET, South at 14 h MET and West at 17 h MET.

N

4.06.99 10:01 BAR1_9

4.06.99 17:11 BAR2_15 4.06.99 16:58 BAR1_15

4.06.99 10:16 BAR2_9

BAR2_X

BAR1_X

3.06.99 14:08 BAR2_12

3.06.99 13:52 BAR1_12

Figure 1. The HyMap flight lines. The sun symbols denote the solar positions for the indicated times and images. The radiometric calibration of the image data is done by inflight calibration (IFCALI) (Richter, 1996) using the noon image and nadir ground measurements at Barrax. The resulting set of calibration coefficients is used for all scenes. The image data are atmospherically corrected using the ATCOR4 software (Richter, 2000). This compensates the effects of angle-dependent path radiance and atmospheric transmittance, as well as the adjacency effect for airborne imagery. The algorithm takes into account the different path lengths in the images of a wide FOV -sensor, but uses an isotropic ground reflectance model. The scenes are geometrically corrected and geocoded using PARGE (Schl pfer et al., 2000). 2.2 Retrieval of Angular Dependence In order to retrieve surface type specific anisotropy, a spectral classification is performed using SPECL, an add-on-program of ATCOR4. It uses spectral indices and thresholds calculated from the channels corresponding to the TM spectral bands. The classification accuracy is tested with a crosscheck of all scenes. Furthermore a SAM classification is performed to check the validity of the spectral classes. The aim is a spectral classification not a land use map.


A statistical analysis is performed for each image and each class derived by a separate classification for each image. The lines of constant view zenith angle (the image columns for the N-S flight direction, Bar1_X, and the image lines for the E-W direction, Bar2_X) are summed up for each class separately, resulting in a mean value and standard deviation for each angle and class. The statistical mean value contains reflectance variations from the inhomogeneity of the classes as well as view angle effects. The standard deviation reflects the varying pixel frequencies at certain angles as well as inhomogeneity at a constant angle. In order to separate the view angle effects from the inhomogeneity effects, an easy-to-invert BRDF model is applied. The fitted curves are then used for calculating the correction factors. The number of classes is determined by the number of spectrally separable entities. However, a statistically significant number of pixels from a wide range of view angles must be collected within each class for the following model inversion procedure to work properly. The model used (Ambrals model; Wanner et al., 1995) was developed for the MODIS BRDF and Albedo Product (Lucht et al., 2000b). A set of angle-dependent functions, so-called kernels, is used to model different angular behaviour, while the linear parameters act as weighting of the different effects. The Ambrals model is a semiempirical linear kernel based model. Semiempirical means that it is an approximation of a general radiative transfer theory, where the parameters retain some physical meaning, while being linear. Linearity leads to a fast and easy-to-use inversion process (Gauss elimination) with a well-developed theory of error estimation (weights of determination) (Lucht and Lewis, 2000a). The usefulness for inversion was demonstrated already by Wanner et al.(1997) and Hu et al.(1997). Due to the fast inversion process each spectral band can be inverted independently. However for physical consistency one set of kernels is selected for all channels with individual parameters for each channel. The best subset of kernels (apart from the isotropic kernel usually only one or two) is automatically chosen by comparison of the mean root mean square error of the different fits. 2.3 BRDF-Correction for a Line Scanner The simplest ways to correct line scanner images for bidirectional effects are the additive and the multiplicative method (Kennedy et al., 1997).

where

Additive:

ρc(θr) = ρ(θr) + (R(θc) - R(θr) )

(1)

Multiplicative:

ρc(θr) = ρ(θr) * (R(θc) / R(θr) )

(2)

ρc(θi, θr, ϕ, λ, j) corrected reflectance for wavelength λ of a pixel of class j ρ(θi, θr, ϕ, λ, j) observed reflectance R(θi, θr, ϕ, λ, j) = ∑k fjk(λ) Kjk (θi, θr, ϕ) modelled reflectance θi, θr, θc incident, reflected and correction zenith angle ϕ relative azimuth angle (assuming rotational symmetry) fjk model parameter for class j and Kernel Kjk Kjk Kernel k for class j

In the following the multiplicative method is chosen, since it performs better (Kennedy et al., 1997).


3 RESULTS 3.1 Classification Results for HyMap Data The classification with SPECL into 14 classes leads to satisfactory results from the spectral point of view. Speckles within the larger areas are supposed to be a variation in spectral signature caused by areas of sparse vegetation or varying soil moisture and texture. The difference to the SAM classification using the same classes is not larger than the difference from image to image. 3.2 Calculating an Average Angular Behaviour for Each Class In the following the statistical results for three selected classes are presented. Table 1 shows the standard deviation of the pixels of one class and one view zenith angle averaged over all bands and all view zenith angles. This gives an estimate of the variability of the classes with the angle effect removed. The standard deviations within one class are approximately the same for different images (Bright sand: 10%, bright vegetation: 17%, dry vegetation: 15%). This indicates that the classification is performing well in all scenes and managed to seperate classes of different angular behaviour. The standard deviations for the total images are with 39% much larger. Scene Bar1_9 Bar2_9 Bar1_12 Bar2_12 Bar1_15 Bar2_15

Bright sand/soil (S10) # pixel St. dev.[%] 66913 11 78379 12 96356 10 106169 8.3 79256 9.7 78588 11

Bright vegetation (V17) # pixel St. dev.[%] 52264 18 43908 19 42142 21 41653 13 56665 14 44501 15

Dry vegetation (V25) # pixel St. dev.[%] 81100 18 76334 17 96303 14 107143 12 117557 15 105771 15

Total image # pixel St. dev.[%] 436480 42 436480 42 436480 36 436480 36 436480 38 436480 40

Table 1. Number of pixels and mean standard deviation in % of mean reflectance per class. S10, V17 and V25 denote special targets within the classes. 3.3 Modelling of Angular Dependence Modelling the angular dependence means inverting the BRDF model to retrieve the model parameters and then calculating modelled reflectances with those parameters. The BRDF inversion results with the Ambrals model are shown in Table 2. Scene Bar1_9 Bar2_9 Bar1_12 Bar2_12 Bar1_15 Bar2_15

Bright sand/soil (S10) Kernel RMSE Li dense RLO 2.1 Li dense RLO 2.0 Li dense RHO 2.2 Li dense RHP 1.2 Li dense RLO 2.1 Li dense RLO 1.6

Bright vegetation (V17) Kernel RMSE Li dense RHP 4.2 Li dense RLO 2.9 Ross thick 4 Li dense RHP 3.3 Li dense RLP 4.4 Li dense RLO 2.7

Dry vegetation (V25) Kernel RMSE Li dense RLP 2.8 Li dense RLP 2.1 Li dense RLO 1.5 Li dense RHO 1.5 Li dense RLP 2.3 Li dense RLO 2.5

Total image Kernel RMSE Ross thick 3.3 Li transit 2.2 Li transit 3.9 Li dense RLP 2.6 Li dense RLP 3.8 Li transit 2.4

Table 2. Kernels and spectrally averaged inversion RMSEs [%] for the Ambrals model (RLO, etc. denote a specific kernel subtype). The comparison of the angular behaviour of the reflectance of the image data with goniometric ground measurements is shown in (Beisl et al., 2000). Taking into account the large standard deviation within each class (cf., Table 1) a good agreement of the modelled angular behaviour with goniometric ground measurements can be found.


Only scenes with large sun zenith angles (Bar1_9 and Bar2_15) show larger discrepancies. Those two were taken in the cross-principal plane. The angular dependence in the cross-principal plane has got a similar shape for all kernels and does not provide much information for inversion. Then the Ambrals inversion procedure becomes unstable and produces spurious results. This can be monitored by looking at the white sky albedo which can be easily integrated from the kernels. Since the white sky albedo is an average of the reflectances from all illumination and and viewing angles, an unphysical behaviour of the modelled BRDF in a large part of the angular range will result in an unphysical white sky albedo. 3.4 Uncorrected vs Corrected Images Applying the multiplicative correction method to the two noon images (BAR*_12) independently, a considerable improvement compared to the standard quadratic model (Royer and Bonn, 1985) can be achieved. This is best seen when overlaying small squares of the two scenes in an alternating way. The differences are most pronounced where a chessboard like pattern appears. In Figure 2 four different mosaics are discussed: the original images, the images corrected with a single ( global ) quadratic polynomial fit (e.g., ENVI cross track illumination correction ), the images corrected with a single ( global ) Ambrals fit and the images corrected with a class specific Ambrals fit. The quadratic model balances the brightness across the scene, but the two scenes do not match together in the absolute reflectance level. Furthermore the brightness peak in the so-called hot spot area (a horizontal stripe in the upper half of BAR2_12 due to backscattering) cannot be represented adequately by a quadratic polynomial. On the other hand a higher order polynomial would fit too much to in-scene variations and not to the BRDF. Therefore different fit functions are necessary for the extreme illumination geometries in southern countries. After correction with the Ambrals model, the largest reflectance differences between the two scenes can be observed in the so-called hot spot area. The differences are smaller than in the original or the quadratically corrected image, but still visible especially in average vegetation (dark red and violet areas). This is due to a large reflectance variation within those classes. In contrary the bright vegetation class (bright red) and the soil classes are rather homogeneous and show no significant differences any more. Looking at the differences between the images the class specific Ambrals correction does not perform better than the global Ambrals correction. Actually it is worse where a different classification of the same pixel occurs between the two images (e.g., in vegetation). Then a different Ambrals submodel will be applied to the same pixel in the two images which results in two different reflectances. On the other hand the angular behaviour of each individual class is represented better with the class specific method.


Bare Soil: S10

Alfalfa: V17

Ripe Barley: V25

Figure 2. A chessboard type of overlay of the two noon images (false color infrared) before (upper left) and after multiplicative correction: global quadratic model (upper right), global Ambrals model (lower left), class specific Ambrals model (lower right). 4 CONCLUSIONS In this article it is shown that the Ambrals model provides an appropriate set of modelling functions for the correction of BRDF effects. It is superior to the quadratic polynomial model for extreme illumination conditions while still being easy to invert. A multiplicative correction (2) can considerably improve the intra- and intercomparability of images taken at approximately the same solar zenith angle. It is possible to separate the in-scene variation from the angle-dependence of the reflectance by dividing up the pixels into spectrally distinct classes with low variation. This is shown explicitly for three targets: bare soil, alfalfa and dry barley. The Ambrals modelling of reflectance data from further classes, which are not shown here, suggests that this method is generally applicable. Care must be taken that the number of pixels for a wide range of view angles is sufficient. This requires a sufficiently equal distribution of the class members over the image. If this requirement cannot be


met then the global angular dependence should be taken. The resulting zenith-angle-dependence can then be used to correct the classes separately for the view angle effect. Further calculations showed that extrapolation of the model to angular ranges, where no observed data were present, is in general not possible. So far only the case of a plane terrain was considered. For rugged terrain a digital elevation model must be used to calculate the sun and view angle relative to the ground normal. This way an even larger angular sampling range can be obtained which helps to find better BRDF inversion coefficients. Unfortunately at the same time it becomes more difficult to find a correct spectral classification since the variation increases. Furthermore already Hugli and Frei (1981) discovered that plants grow vertically in sloping terrain and that therefore the anisotropic behaviour is different from that in even terrain. The correction proposed here is a step towards a more accurate quantitative analysis of wide-FOV hyperspectral data and makes it possible to compare data of different times and viewing geometry. This method will reduce flight planning restrictions and make airborne imagery more efficient. ACKNOWLEDGEMENTS Many thanks to the DLR imaging spectroscopy team (A. Hausold for processing the images, R. Richter for performing the atmospheric correction and A. M ller/U. Heiden for additional ground measurements). I am very grateful to the MODIS team (esp. W. Lucht) who provided the Ambrals code for BRDF inversion. The financial support of DLR and Astrium GmbH is acknowledged. REFERENCES Beisl, U., Strub, G., Dickerhof, C., 2000. Validation of Hyperspectral Imaging Data from the Barrax Test Site with BRDF Ground Measurements in the Reflective Wavelength Range. Proc. 2nd EARSeL Workshop on Imaging Spectroscopy, Enschede. Berger, M., Moreno, J., M ller, A., Schaepman, M., Wursteisen, P., Rast, M. Attema, E., 2000. The Digital Imaging Spectrometer Experiment — DAISEX 99.In Proc. IGARSS 2000, Hawaii, pp. 3039-3041. Chopping, M. J., 2000. Large-Scale BRDF Retrieval over New Mexico with a Multiangular NOAA AVHRR Dataset. Remote Sensing of Environment 74, pp. 163-191. ENVI, 2000. Environment for Visualizing Images, www.rsinc.com. Research Software, Inc., Boulder. Hu, B., Lucht, W., Li, X., Strahler, A.H., 1997. Validation of Kernel-Driven Semiempirical Models for the Surface Bidirectional Reflectance Distribution Function of Land Surfaces. Remote Sensing of Environment 62, pp. 201-214. Hugli, H., Frei, W., 1981. Correcting For Anisotropic Reflectances In Remotely Sensed Images From Mountainous Terrains. Machine Processing of Remotely Sensed Data Symposium, pp. 363374.


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