Maxim Shoshany, Ophir Almog, and Victor Alchanatis Introduction
Of those factors affecting accurate estimation of surface reflectance, the flux density effect, as represented by the cosine of the sun's incidence angle, is well established. Accounting for this effect, however, requires very detailed information regarding the surface facets' orientation across a wide range of scales (e.g., the plants' leaves, the soil aggregates' structure). Moreover, the spatial resolution of the available surface structure data (e.g., the Digital Elevation Model) is frequently lower than that of satellite and airborne imagery. Thus, reflectance estimations for these images will not fully account for flux density effects and consequently, the reflectance of the same surface material would vary, resulting in increased spectral confusion. However, utilizing normalization, band selection and ratioing, spectral angle (SAM), and derivative techniques for this purpose provide only partial solutions under unknown illumination conditions.
In this letter we introduce a novel signal processing approach, based on wavelet analysis, for reducing the effects of flux density variations at the object and pixel levels. Wavelet analysis has been frequently used mainly for dimensionality reduction , and feature extraction. Although a significant number of studies used wavelet techniques such as Discrete Wavelet Transform (DWT) energy for improving classification and estimation of surface properties, none of these studies used them for explicitly overcoming flux density effects. Furthermore, the terms 'flux density', 'illumination', and 'irradiance' are rarely mentioned in most of the existing articles dealing with wavelet analysis in this context.
The new method is assessed by comparing classifications based on raw spectral data and wavelet-transformed information using synthetic data as well as data derived from hyperspectral images acquired from semi-natural Mediterranean shrubs' scenes.
Figure 1a: Typical vegetation spectra artificially affected by flux density variations
Figure 1b: The new wavelet based R2a transformation of all flux density-affected spectra in Figure 1a.