Analytical Description of Pseudoinvariant Features

Invariant features are needed for atmospheric normalization of image pairs. Powerful statistical approaches now exist, which are designed to isolate unchanged pixels based on quantitatively evaluating the spectral correlation of pixels in image pairs. This suggests that it should be possible to obtain similar results following an analytical path, and our hypothesis is that the derivation of an analytical procedure will yield some physical insight that is not directly accessible with a stochastic approach. In this paper, we derive an analytical formula that relates pseudoinvariant features (PIFs) to the radiometric properties of the scenes. The formula is then inverted to yield an estimate of the ratio of transmission spectra of the two images given the path radiance for each scene and a set of invariant features, The normalized spectral transmission ratio proved to be quite stable over the 700–1800 nm but was less reproducible outside of that range. The absolute (nonnormalized) values of the transmission ratio implied a disparity in the spectral transmission suggesting that the September sky was clearer in visible light, whereas the August sky was clearer in the infrared. This leads to a discussion of the sensitivity of PIF reflectance to the viewing and illumination angles, suggesting that there may be an inherent uncertainty related to the bidirectional reflectance distribution function of the targets comprising the PIF pixels.