Jones formalism for image fusion

We suggest a novel approach for the fusion of visible (u) and infrared (upsilon) images, basing on analogy between the mathematical forms of a Jones vector of elliptically polarized light wave and a complex 2D vector (psi) over right arrow (0) composed of the images u and upsilon. Since there is no restriction on which of the two images should be chosen as a real (or imaginary) component, one can construct (psi) over right arrow (0) in the two forms, (psi) over right arrow (0)(neg) = (1/root 2) [u, i upsilon](Tr) or (psi) over right arrow pos(0) = (1/root 2) [upsilon, iu](Tr), where the superscript "Tr" denotes the operation of transposing, i.e. (psi) over right arrow (0) represents a column vector. Following the analogy with the Jones vector of light wave, the vector (psi) over right arrow (0)(pos,neg) can be transformed as (psi) over right arrow = J (psi) over right arrow (0)(neg,pas), with J being a complex 2 x 2-matrix, an analogue of the Jones matrix for optically anisotropic medium. The above analogy with the Jones formalism allows one to synthesize the fused images using three types of the fusion algorithms, 'amplitude', 'azimuth' and 'ellipticity' ones. Varying the components of the J matrix with time, one can synthesize the fused image in a dynamic mode, thus animating the images fused under smoothly varying parameters, which are combinations of the J matrix components.