Better analysis of hyperspectral images by correcting reflectance anisotropy

Reflectance anisotropy, defined by the bidirectional-reflectance distribution function (BRDF) of materials (i.e., direction-dependent intensity of reflected light), is a source of radiometric bias that hampers qualitative and, more importantly, quantitative analysis. Correcting reflectance anisotropy improves the accuracy, quality, and reliability of information layers extracted from hyperspectral remote sensing for applications involving identification of materials or approximation of material concentrations. As a result, all processing and modeling based on such spatial information layers can benefit from this enhancement. The improved quality will propagate into, for example, geographical-information systems and image simulators.

The Israeli Goniometric Facility (IGF) at the remote-sensing laboratory of Tel Aviv University (Israel) was designed and built to facilitate the definition of BRDF and to solve the problem (see Figure 1). The goniospectrometer enables manual positioning of a handheld Analytical Spectral Devices (ASD) FieldSpec Pro-FR spectrometer that measures reflected energy with an illumination source radiating energy, at a range of wavelengths, on a virtual hemisphere, at a high angular resolution of 2.5^° in both the ϕ (azimuth) and θ (inclination) directions. The apparatus consists of two sliding arcs with a radius of 75cm and a base ring. Targets are illuminated with stabilized diffuse light from an ASD Pro-Lamp. Diffusion is obtained using a glass plate. Incident illumination in the research reported here was set to azimuth ϕ_i = 90^° and inclination θ_i∊{25^°, 45^°, 65^°}.

Figure 1. (a) The Israeli Goniometric Facility (IGF). (b) Concept of reflectance anisotropy and related angles and radiometric quantities. E_i: Illumination source radiating energy. E_v: Reflected energy. λ: Wavelength. N: North. φ_i, φ_v: Azimuth of illumination, reflectance. θ_i, θ_v: Inclination of illumination, reflectance.

The IGF radius permits a ground instantaneous field of view from nadir of about 9cm across, using an 8^° fore optic at the end of the spectrometer's optical fiber. For each illumination position, over 100 radiance measurements were taken on the hemisphere. Once divided by counterpart radiance measurements of an ASD calibrated, Lambertian, white reference plate (Spectralon^®), we obtained a bidirectional-reflectance factor (BRF) that approximates directional spectral reflectance from a certain image pixel.¹

We normalized all BRFs to the value at the nadir (normal to the reflection plane) to obtain a reflectance-anisotropy factor (ANIF, α) that represents, at each wavelength, the deviation of reflectance from that measured at the nadir. Albedo (i.e., the mean hemispherical reflectance) provides another basis for normalization. In either case, the reciprocal of α, (1/α), can be applied to correct reflectance anisotropy such that the corrected BRF value (BRF′), using either normalization base, is defined as BRF′ = BRF /α.^2,3

A soil sample (Alfisol, according to the USDA taxonomic classification⁴) collected from a field exhibited roughness of up to 0.5cm in diameter. The angular distribution of the sample's anisotropy factor α (see Figure 2) is the nadir-normalized BRF value at wavelength 400nm. The sample—illuminated from ϕ, θ = 90^°, 45^°—emphasizes the strong backscatter effect of the rough soil surface, and also exhibits a relatively symmetrical distribution. In compiling such maps for longer wavelengths, we observed the expected clear decrease in the amplitude of extreme values as more illumination became available on the sample, increasing multiple scattering and acting as countereffect to reflectance anisotropy.

Figure 2. Angular distribution of the anisotropy factor (ANIF, α) of an Alfisol soil sample at wavelength 400nm, based on goniometer data.

Figure 3. Effect of reflectance-anisotropy correction on imaging-spectroscopy data from an initial (red) to a final state (blue), distributed symmetrically across the flight line (nadir, dashed) and along most of the visible to near-IR spectral range. CASI: Compact Airborne Spectral Imager.

Generally, computation of the relative angles between the sun or the sensor and the surface can be carried out if the coordinate system is rotated so that the surface normal for a given pixel points upwards. Because rotation is an angle-preserving transformation, the sensor and sun directions, following rotation, will fit the quantities measured by the goniometer, provided those measurements are performed on samples laid horizontally. This transformation can be implemented by inversely rotating the respective ϕand θ angles for each image pixel. We mapped the relative influence of slope and aspect in each pixel, and generated new angle maps of sensor position and solar illumination.⁵ We extracted slopes and aspects from a digital terrain model corresponding to the imaged area generated from an airborne-laser scanner (i.e., light detection and ranging). As a result, linkage to angle-based spectral data from the goniometer was straightforward and spectral-anisotropy factors could be calculated and inverted.

Following intensive use of the spectrogoniometer, we assembled a database of over 42 million spectral BRF values for a selection of test materials, including soil, concrete, asphalt, and meadow grass, and calculated their respective spectral αvalues. Surprisingly, even surfaces perceived as visually smooth show a considerable degree of backscatter because of a forward-scatter component. Table 1 compares typical α ranges of surfaces measured at 400nm (higher Δα values indicate rougher surfaces).

We then proceeded to correct reflectance anisotropy in hyperspectral data from the Compact Airborne Spectral Imager (CASI) and compared the effect of correction with this approach to original data by visualizing spectral anisotropy before and after the process.⁶ Testing the method on meadows showed it to be quite effective (see Figure 3) after decreasing anisotropy from its precorrection state (red) by a factor of approximately two (blue) from both sides of the nadir (i.e., flight) line in the 400–1000nm spectral range. Because CASI is a line-scanning imaging spectrometer, at each image line the α of the flight line at the time of acquisition equals exactly 1 (dashed line). Thus, in this case anisotropy correction enabled us to improve potential quantitative mapping of the imaged area, for example, for vegetation-stress or chlorophyll-concentration maps.

The combination of airborne-laser scanning, imaging spectroscopy (IS), and goniometer data facilitates successful correction of anisotropy in IS data and makes quantitative interpretation of such imagery more accurate. In addition, the suggested method is suitable as a standard procedure in a radiometric-atmospheric-anisotropic preprocessing chain of IS data, following the construction of BRDF libraries for various natural and manmade materials. We established such a library for this work using the IGF at the remote-sensing laboratory. Our next step will be to further develop this method for operational image processing by combining standard BRDF models with field measurements.

Many thanks to Juval Portugali from Tel Aviv University, Rudolf Richter and Andreas Muller from the German Space Agency, the Sapir fund of the Pais Foundation (Israel), and the German Academic Exchange Service for their support.