Analytical description of pseudo-invariant features (PIFs)

Invariant features are needed for atmospheric normalization of images pairs. Powerful statistical approaches now exist, 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 reach 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 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.