A two-dimensional (two-color) statistical structure is formulated that is applicable to pattern recognition, discrimination, and detection problems occurring in infrared signal-processing systems. The methodology relates physical quantities such as the temperature T of an object, its projected area A, emissivity ∊, range R from the sensor, and noise equivalent flux density (NEFD) to the geometry of a local orthogonal coordinate system where the coordinate axes correspond to the apparent radiant intensity J in each micron bandwidth. The bivariate distribution, correlation, and transformation properties attendant to this framework are discussed in detail. Additional insight into the structure of the problem is achieved by investigating the two-color system in terms of a nonorthogonal local coordinate system. The various results presented in the paper may be extended to three-, four-, or five-color systems by direct analogies.
Richard Clow and Frank McNolty, "Bivariate Distribution, Correlation, and Transformation Properties of Two-Color Infrared Systems," Appl. Opt. 13, 1238-1247 (1974)