A method for correcting radiometric disturbances of airborne push-broom hyperspectral images

Abstract

The present invention discloses a method for correcting radiation disturbances of airborne push-broom hyperspectral images. The method collects airborne hyperspectral images and other auxiliary data; performs radiation calibration and geometric correction on the hyperspectral images; establishes a radiation attenuation model to correct the radiance at different field angles to the center of the push-broom unit; constructs a semi-empirical BRDF model based on the incident-observation geometric relationship to correct the BRDF effect of the hyperspectral data; and, based on the fact that the reflectances of pixels with the same name in adjacent flight bands should be equal, lists an error equation to calculate the correction coefficient of each flight band and adjusts the reflectance. The present invention eliminates the influence of radiation attenuation differences and BRDF effects on the reflectance of a single hyperspectral flight band, and adjusts the radiation differences between multiple flight bands based on the fact that the reflectances of pixels with the same name in adjacent flight bands should be equal. The method has the characteristics of fast running time, clear physical meaning, and high precision, and realizes seamless mosaicking of airborne hyperspectral images. The method provides an effective method for correcting radiation disturbances of airborne hyperspectral images and for the large-scale application of hyperspectral images.

Description

Technical Field

[0001] The present invention relates to a method for correcting image radiation disturbance, and in particular to a method for correcting airborne push-broom hyperspectral image radiation disturbance. Background Art

[0002] Over the past few decades, hyperspectral remote sensing technology has played an increasingly important role in land use classification, quantitative estimation of surface parameters, biodiversity detection, and other fields. However, the hyperspectral imaging process is affected by some factors that interfere with the measurement signal and reduce the accuracy of parameter extraction. Therefore, accurate image preprocessing is a key step in qualitative and quantitative remote sensing. Satellite remote sensing image preprocessing usually includes steps such as radiometric calibration, atmospheric correction, and geometric correction. Unlike satellite remote sensing images, airborne hyperspectral data are usually mosaicked from multiple flight strips. Due to differences in acquisition time, observation angle, and other factors, there is a radiation brightness gradient at the edges of adjacent flight strips, which destroys the spatial integrity of the mosaicked results.

[0003] Differences in radiation paths are one of the main causes of this phenomenon. Previous studies have only considered the effects of sensor altitude and ground elevation, ignoring the effects of changes in sensor attitude and field of view. Bidirectional reflectance distribution function (BRDF) effects can also cause brightness gradients between adjacent flight strips. Semiempirical kernel-driven bidirectional reflectance models have the advantages of computational simplicity and clear physical meaning, making them widely used in practical remote sensing image processing. Many studies assume flat terrain when constructing kernel functions, ignoring the fact that terrain can alter the radiative transfer process of solar radiation between the sun, the ground, and the sensor. For sensors with a wide field of view, changes in field of view and attitude angle lead to different observation angles, which in turn alter pixel reflectance. Therefore, it is necessary to construct a BRDF correction model that integrates terrain factors (slope, aspect), sensor angle, field of view angle, and sun angle. The above two steps primarily correct for radiation perturbations within a single flight strip. Further correction is necessary to account for radiation differences between multiple flight strips to generate hyperspectral imagery with good radiometric consistency. Summary of the Invention

[0004] In response to the problems existing in the above-mentioned prior art, the present invention provides a method for correcting radiation disturbances of airborne push-broom hyperspectral images, which can eliminate the reflectivity differences between multiple flight strips caused by different imaging times and lighting conditions, and realize seamless mosaicking of airborne hyperspectral images.

[0005] To achieve the above-mentioned object, the present invention provides the following technical solution: a method for correcting radiometric disturbances of airborne push-broom hyperspectral images, comprising the following steps:

[0006] S1: Collect airborne hyperspectral images and other auxiliary data;

[0007] S2: Radiometric calibration and geometric correction of hyperspectral images;

[0008] S3: Establish a radiation attenuation model to calibrate the radiance at different field angles to the center of the push-broom unit;

[0009] S4: Construct a semi-empirical BRDF model based on the incident-observation geometry relationship to correct the BRDF effect of hyperspectral data;

[0010] S5: Based on the fact that the reflectance of pixels with the same name in adjacent flight strips should be equal, an error equation is established to calculate the correction coefficient of each flight strip and adjust the reflectance.

[0011] Furthermore, the specific method in step S1 is to use a drone equipped with an integrated sensor system to collect hyperspectral images and combined navigation data in clear, cloudless and windless weather, and at the same time obtain the local DEM for geometric correction of the hyperspectral data; the integrated sensor system includes a hyperspectral sensor, a DPU and an integrated navigation system.

[0012] Furthermore, the specific method in step S2 is to perform radiometric calibration on the dark pixels collected by the hyperspectral sensor in combination with the laboratory calibration parameter file provided by the manufacturer, and finally obtain radiance image data; according to the position, attitude data and DEM elevation information recorded by the integrated navigation system, the ground true coordinates corresponding to the pixels are calculated by the collinearity equation.

[0013] Furthermore, the specific method in step S3 is that, according to the Bouguer-Lambert transmission law, the radiance of the center point of the hyperspectral sensor and the pixel i away from it satisfies the following relationship:

[0014] E i (λ)=E ⊥ (λ)e -K(λ)*ΔH (1);

[0015] In formula (1), E i (λ) is the radiance of the pixel i from the center of the hyperspectral sensor, E ⊥ (λ) is the radiance at the center of the hyperspectral sensor, ΔH is the radiation transmission path difference between the i-th pixel and the center point, K(λ) is the radiation attenuation coefficient, and λ is the wavelength;

[0016] The radiation transmission path difference is a function of the roll angle, pitch angle, field of view angle, and the height difference between the hyperspectral sensor and the ground, and can be calculated by formula (2):

[0017]

[0018] In formula (2), H is the height difference between the hyperspectral sensor and the ground, θ p is the pitch angle, θ ris the roll angle, θ i is the field of view angle;

[0019] Ten thousand lines of inertial navigation data are selected to calculate the radiation transmission path difference corresponding to different field of view angles. After calculating the average value, the relationship between the field of view angle and the radiation transmission path difference is fitted into a one-variable quadratic regression curve, which can be expressed as: Where a0, a1, and a2 are the radiation transmission path difference ΔH and the field of view angle θ i Therefore, -K(λ)*ΔH in formula (1) can also be expressed as a function of the field of view angle, that is, formula (3):

[0020]

[0021] In formula (3), b0, b1, and b2 are -K(λ)*ΔH and the field of view angle θ i The regression coefficient between

[0022] According to the radiation uniformity assumption, the least squares model is established using the average radiance at different field angles to solve b0, b1, and b2, and the radiance is corrected to the center of the push-broom unit.

[0023] Furthermore, the specific method in step S4 is to perform atmospheric correction on the hyperspectral image to obtain reflectance data, then comprehensively consider the sun angle, hyperspectral sensor attitude angle, field angle and terrain factors to construct a corrected incident-observation geometric relationship, divide the multi-angle observation data set into different types of ground objects, and use the semi-empirical kernel to drive the bidirectional reflectance model, that is, formula (4)

[0024]

[0025] To simulate the bidirectional reflection effect of different ground objects, the kernel combination is the volume scattering kernel Li-Transit-Reciprocal and the geometric optics kernel Ross-Thick-Maignan;

[0026] In formula (4), f iso is the Lambertian reflection coefficient, k vol 、f vol are the volume scattering kernel and the corresponding volume scattering coefficient, k geo 、f geo are the geometrical optics kernel and the corresponding geometrical optics coefficient respectively; θ′ v is the observation zenith angle, θ′ s is the solar incidence angle, is the relative azimuth angle between the sun and the hyperspectral sensor, λ is the wavelength, and c is the land use type;

[0027] The stratified sampling method is used to determine the number of pixels involved in the modeling, and the least squares method is used to fit the BRDF coefficients. Then, the RMSE between the fitted reflectivity and the actual reflectivity is calculated, and the coefficient combination with the smallest RMSE is selected as the BRDF coefficient. Finally, a multiplication normalization factor is used to normalize the directional reflectivity at multiple angles to the specified incident-observation direction.

[0028] Furthermore, the specific method in step S5 is to adjust the reflectivity consistency using formula (18),

[0029] ρ′ i =a*ρ i +b (18);

[0030] In formula (18), ρ i and ρ′ i are the reflectances before and after correction respectively, a and b are the correction coefficients; the minimum reflectance difference means that the difference in the standard deviation and mean of the reflectance are both minimized; at the same time, the difference in the standard deviation and mean of the image before and after correction should be minimized; the error equation is listed with the above rules as constraints, and the least squares method is used to calculate the correction coefficient and adjust the image reflectance.

[0031] Compared with the existing technology, the present invention eliminates the influence of radiation attenuation difference and BRDF effect on the reflectivity of a single hyperspectral flight strip, and then adjusts the radiation difference between multiple flight strips based on the fact that the reflectivity of pixels with the same name in adjacent flight strips should be equal; it has the characteristics of fast running time, clear physical meaning, high precision, etc., and realizes the seamless mosaicking of airborne hyperspectral images; the present invention provides an effective method for correcting radiation disturbances in airborne hyperspectral images, and provides technical support for the large-scale application of hyperspectral images. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of the method of the present invention;

[0033] Figure 2 is a radiation path difference curve diagram of the present invention;

[0034] Figure 3 The volume scattering kernel function and geometric optics kernel function images of the present invention;

[0035] Figure 4 The outline and seam lines of the hyperspectral mosaic image of the present invention, and the true color composite images before and after correction;

[0036] Figure 5 The root mean square error diagram of the reflectance of trees, shrubs, grass and bare soil of the same-name pixels in adjacent flight strips of the present invention;

[0037] Figure 6 This is the reflectivity transition diagram of adjacent flight strips of the present invention. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] The present invention provides a technical solution: Figure 1 As shown in the figure, it includes S1: collecting airborne hyperspectral images and other auxiliary data; S2: radiometric calibration and geometric correction of hyperspectral images; S3: establishing a radiation attenuation model to correct the radiance of different field angles to the center of the push-broom unit; S4: constructing a semi-empirical BRDF (bidirectional reflectance distribution function) model based on the incident-observation geometric relationship to correct the BRDF effect of hyperspectral data; S5: listing the error equation based on the fact that the reflectance of the same-name pixels in adjacent flight strips should be equal, calculating the correction coefficient of each flight strip and adjusting the reflectance.

[0040] Example:

[0041] Shenmu City, Yulin City, Shaanxi Province, was selected as the study area. Airborne hyperspectral imagery was collected from 10:00 AM to 12:30 PM on July 19, 2020, using a DJI Rowind 4 drone equipped with an integrated sensor system. The integrated sensor system consists of a SPECIM FX10 imaging spectrometer, a DPU (control system), and an integrated navigation system. The DPU allows for configuration of flight routes, acquisition frequency, and exposure time. The integrated navigation system records the position and attitude of the imaging spectrometer. The SPECIM FX10 acquires hyperspectral imaging data with a high signal-to-noise ratio (SNR). Its spectral range is 397–1003 nm, and its field of view is 38°. The hyperspectral sensor was used in 2×1 binning mode, and the platform was flown at an altitude of 404 m above the ground. The spectral and spatial resolutions were 5.5 nm and 0.55 m, respectively. Due to the long time span of hyperspectral imagery acquisition and the significant variations in solar radiation, zenith angle, and azimuth, significant brightness gradients were observed between hyperspectral bands. In addition to acquiring hyperspectral images, a DJI Phantom 4 RTK drone was used to collect digital photos, and a DSM (digital surface model) was generated using Pix4Dmapper. Then, a filtering algorithm was used to obtain a DEM (digital elevation model).

[0042] Using CaliGeoPro software, radiometric calibration was performed to obtain radiance image data, combining the dark pixels captured by the SPECIM FX10 (dark current data is automatically recorded at the end of each hyperspectral image acquisition) with the manufacturer's provided laboratory calibration parameter file. The ground truth coordinates corresponding to the pixels were then calculated using collinearity equations based on the position and attitude data recorded by the integrated navigation system and the DEM elevation information.

[0043] A push-broom hyperspectral sensor's scanning angle gradually increases from the center of the push-broom unit toward the sides, and the radiation transmission path also gradually increases from the center toward the sides. Due to atmospheric attenuation, the energy received by the hyperspectral sensor decreases from the center toward the sides, resulting in a difference in radiance between the image edge and the center. According to the Bougner-Lambert transmission law, the radiance at the center of the hyperspectral sensor and the pixel i away from it satisfies the following relationship:

[0044] E i (λ)=E ⊥ (λ)e -K(λ)*ΔH (1);

[0045] In formula (1), E i (λ) is the radiance of the pixel i from the center of the hyperspectral sensor, E ⊥ (λ) is the radiance at the center of the hyperspectral sensor, ΔH is the radiation transmission path difference between the i-th pixel and the center point, K(λ) is the radiation attenuation coefficient, and λ is the wavelength.

[0046] Through analysis, it can be seen that the radiation transmission path difference is a function of the roll angle, pitch angle, field of view angle, and the height difference between the hyperspectral sensor and the ground, and can be calculated by formula (2):

[0047]

[0048] In formula (2), H is the height difference between the hyperspectral sensor and the ground, θ p is the pitch angle, θ r is the roll angle, θ i is the field of view angle.

[0049] Since the pitch and roll angles of each scan line are known, the relationship between the field of view angle and the radiation transmission path difference can be fitted. Ten thousand lines of inertial navigation data are selected to calculate the radiation transmission path differences corresponding to different field of view angles. After calculating the average value, the relationship between the field of view angle and the radiation transmission path difference is fitted into a quadratic regression curve, as shown in the following figure. Figure 2 As shown; can be expressed as Where a0, a1, and a2 are the radiation transmission path difference ΔH and the field of view angle θ iTherefore, -K(λ)*ΔH in formula (1) can also be expressed as a function of the field of view angle, that is, formula (3):

[0050]

[0051] In formula (3), b0, b1, and b2 are -K(λ)*ΔH and the field of view angle (θ i ) is the regression coefficient between .

[0052] According to the radiation uniformity assumption, the least squares model is established using the average radiance at different field angles to solve b0, b1, and b2, and the radiance is corrected to the center of the push-broom unit.

[0053] After atmospheric correction of the hyperspectral image to obtain reflectance data, the corrected incidence-observation geometric relationship is constructed by integrating the sun angle, hyperspectral sensor attitude angle, field of view angle and terrain factors. The multi-angle observation data set of different ground object types is divided. The semi-empirical kernel-driven BRDF correction method is used to decompose the bidirectional reflectance of the ground object into the weighted sum of isotropic reflectance, volume scattering and geometric reflectance. The function is:

[0054]

[0055] In formula (4), f iso is the Lambertian reflection coefficient, k vol 、f vol are the volume scattering kernel and the corresponding volume scattering coefficient, k geo 、f geo are the geometrical optics kernel and the corresponding geometrical optics coefficient respectively; θ′ v is the observation zenith angle, θ′ s is the solar incidence angle, is the relative azimuth angle between the sun and the hyperspectral sensor, λ is the wavelength, and c is the land use type.

[0056] The Li-Transit-Reciprocal kernel is used as the volume scattering kernel and the Ross-Thick-Maignan kernel is used as the geometric optics kernel. The kernel function of a single flight strip is as follows: Figure 3 a and Figure 3 The present invention introduces the hyperspectral sensor attitude angle, field of view angle, sun angle and terrain to jointly construct the kernel function.

[0057]

[0058]

[0059]

[0060] cos(θ′ v)=cos(θ r +θ i )cos(θ p ) (8);

[0061]

[0062]

[0063]

[0064] B=sec(θ′ s )+sec(θ′ v )-O (12);

[0065]

[0066]

[0067]

[0068] Where θ s is the solar zenith angle, α is the slope, θ′ s is the solar incidence angle, θ′ v is the observation zenith angle, is the hyperspectral sensor azimuth, θ h is the heading angle, θ r is the roll angle, θ p is the pitch angle, θ i is the instantaneous field of view, is the relative angle between the slope aspect and the solar azimuth, is the relative angle between the solar azimuth and the hyperspectral sensor observation azimuth. A constant of ξ0 = 1.5° is used to represent the hotspot half-width for most targets. The Li-Transit-Reciprocal kernel requires parameters for plant canopy geometry. Based on field measurements, h / b = 2 for trees and shrubs and 1.5 for grasses.

[0069] Airborne hyperspectral images usually contain a large number of pixels. In order to determine the effective BRDF coefficient, after classifying the hyperspectral image, all ground objects are divided into four types: trees, shrubs, grass, and bare soil. The stratified sampling method is used to determine the number of pixels involved in the modeling and the least squares method is used to fit the BRDF coefficient. The RMSE (root mean square error) between the fitted reflectivity and the actual reflectivity is then calculated, and the coefficient combination with the smallest RMSE is selected as the BRDF coefficient. Finally, the multiplication normalization factor, i.e., Equation (16), is used to normalize the directional reflectivity at multiple angles to the specified incident-observation direction.

[0070]

[0071]

[0072] Where, is the simulated reflectivity of the point below the machine, θ s_fixed and represents the fixed sun position, ρ BOA is the spectral reflectance after atmospheric correction.

[0073] According to the fact that the reflectance of pixels with the same name in adjacent flight strips should be equal, the reflectance is adjusted for consistency using formula (18).

[0074] ρ′ i =a*ρ i +b (18);

[0075] In formula (18), ρ i and ρ′ i are the reflectance before and after correction, respectively, and a and b are the correction coefficients.

[0076] The reflectivity difference of the pixels with the same name between adjacent flight strips is minimized, that is, the differences in the mean and standard deviation of the overlapping areas between images are minimized; at the same time, the differences in the standard deviation and mean of the images before and after correction should be minimized; the error equation is listed with the above rules as constraints, and the least squares method is used to calculate the correction coefficient and adjust the image reflectivity.

[0077]

[0078] In formula (19), a and b are correction coefficients, M and V are the mean and standard deviation of the image before correction, and ε is the error term.

[0079] Mosaic the hyperspectral images before and after correction. Figure 4 a to Figure 4 As shown in c, the hyperspectral image before correction has obvious brightness gradients at the edges of adjacent flight strips, which destroys the integrity of the mosaic result. After correction, there is almost no radiation difference in the image, and seamless mosaicking of multiple flight strips is achieved. The root mean square errors of the reflectance of trees, shrubs, grass, and bare soil in the same pixels of adjacent flight strips are shown as follows: Figure 5 a to Figure 5 d. It can be seen that the root mean square error before correction is large, indicating that there are obvious radiation differences between adjacent flight strips; the root mean square error after correction is significantly reduced, which means that adjacent flight strips show more similar reflectivity values in the overlapping area. The reflectivity excess between the two flight strips on the far right is shown in Figure 4. Figure 6 As shown in the figure, the reflectivity of the image before correction increases sharply at the horizontal coordinate of 0, indicating that the mosaic result has a radiation brightness gradient on both sides of the edge line, and the image is divided into two pieces. After correction, the gradient of the image at the horizontal coordinate of 0 decreases, and the integrity is improved.

[0080] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any minor modifications, equivalent replacements, and improvements made to the above embodiments based on the technical essence of the present invention shall be included in the scope of protection of the technical solution of the present invention.

Claims

1. A method for correcting radiometric disturbances of airborne push-broom hyperspectral images, characterized in that: The following steps are involved: S1: Collect airborne hyperspectral images and other auxiliary data; S2: Radiometric calibration and geometric correction of hyperspectral images; S3: Establish a radiation attenuation model to calibrate the radiance at different field angles to the center of the push-broom unit; The specific method in step S3 is that according to the Bouguer-Lambert transmission law, the radiance of the center point of the hyperspectral sensor and the pixel i away from it satisfies the following relationship: （1）； In formula (1), is the radiance of the pixel i from the center of the hyperspectral sensor, is the radiance at the center of the hyperspectral sensor, is the radiation transmission path difference between the i-th pixel and the center point, is the radiation attenuation coefficient, λ is the wavelength; The radiation transmission path difference is a function of the roll angle, pitch angle, field of view angle, and the height difference between the hyperspectral sensor and the ground, and can be calculated by formula (2): (2); In formula (2), H is the height difference between the hyperspectral sensor and the ground, is the pitch angle, is the roll angle, is the field of view angle; Ten thousand lines of inertial navigation data are selected to calculate the radiation transmission path difference corresponding to different field of view angles. After calculating the average value, the relationship between the field of view angle and the radiation transmission path difference is fitted into a one-variable quadratic regression curve, which can be expressed as: ,in 、 、 The radiation transmission path difference △H and field of view θ i The regression coefficient between Therefore, in formula (1) It can also be expressed as a function of the field of view angle, that is, formula (3): （3）； In formula (3), b 0 、 b 1 、 b 2 for -K(λ)*△H and field of view θ i The regression coefficient between Based on the radiation uniformity assumption, the least squares model is established using the average radiance at different field angles. b 0 、 b 1 、 b 2 , correct the radiance to the center of the push-broom unit; S4: Construct a semi-empirical BRDF model based on the incident-observation geometry relationship to correct the BRDF effect of hyperspectral data; The specific method in step S4 is: After atmospheric correction of the hyperspectral image to obtain reflectance data, the corrected incident-observation geometric relationship is constructed by integrating the sun angle, hyperspectral sensor attitude angle, field of view angle and terrain factors. The multi-angle observation data set of different ground object types is divided and the semi-empirical kernel is used to drive the bidirectional reflectance model, that is, Equation (4) （4）； To simulate the bidirectional reflection effect of different ground objects, the kernel combination is the volume scattering kernel Li-Transit-Reciprocal and the geometric optics kernel Ross-Thick-Maignan; In formula (4), is the Lambertian reflection coefficient, 、 are the volume scattering kernel and the corresponding volume scattering coefficient, 、 are the geometrical optics kernel and the corresponding geometrical optics coefficients respectively; is the observation zenith angle, is the solar incidence angle, is the relative azimuth angle between the sun and the hyperspectral sensor, is the wavelength, c is the land use type; The stratified sampling method is used to determine the number of pixels involved in the modeling and the least squares method is used to fit the BRDF coefficients. The RMSE between the fitted reflectivity and the actual reflectivity is then calculated, and the coefficient combination with the smallest RMSE is selected as the BRDF coefficient. Finally, a multiplication normalization factor is used to normalize the directional reflectivity at multiple angles to the specified incident-observation direction. S5: Based on the fact that the reflectance of pixels with the same name in adjacent flight strips should be equal, an error equation is established to calculate the correction coefficient of each flight strip and adjust the reflectance.

2. The method for correcting radiometric disturbances of airborne push-broom hyperspectral images according to claim 1, characterized in that: The specific method in step S1 is to use a drone equipped with an integrated sensor system to collect hyperspectral images and integrated navigation data in clear, cloudless and windless weather, and at the same time obtain the local DEM for geometric correction of the hyperspectral data; the integrated sensor system includes a hyperspectral sensor, a DPU and an integrated navigation system.

3. The method for correcting radiometric disturbances of airborne push-broom hyperspectral images according to claim 1, characterized in that: The specific method in step S2 is to perform radiometric calibration on the dark pixels collected by the hyperspectral sensor in combination with the laboratory calibration parameter file provided by the manufacturer, and finally obtain radiance image data; based on the position and attitude data recorded by the integrated navigation system and the DEM elevation information, the ground true coordinates corresponding to the pixels are calculated through the collinearity equation.

4. The method for correcting radiometric disturbances of airborne push-broom hyperspectral images according to claim 1, characterized in that: The specific method in step S5 is: Use Equation (18) to adjust the reflectivity for consistency. （18）； In formula (18), and are the reflectances before and after correction respectively, a and b are the correction coefficients; the minimum reflectance difference means that the difference in the standard deviation and mean of the reflectance are both minimized; at the same time, the difference in the standard deviation and mean of the image before and after correction should be minimized; the error equation is listed with the above rules as constraints, and the least squares method is used to calculate the correction coefficient and adjust the image reflectance.

Images