Dynamic fusion of images from the visible and infrared channels of sightseeing system by complex matrix formalism

The employment of new mathematical and computer approaches for the fusion of target images from the visible and infrared channels of the sightseeing system (SSS) is one of the ways to increase the efficiency of the SSS of armored vehicles. Modern approaches to improving the efficiency of image fusion are aimed to increase the visibility of the target via improving the quality indices of fused images. This paper proposes a fundamentally new approach to image fusion, namely dynamic image fusion, at which the target is observed in the mode of a video clip composed of a sequence of stationary fused images obtained at different parameters of fusion, in contrast to traditional stationary image fusion, at which the decision is made from one fused image. Unlike stationary image fusion, aimed to increase the visibility of the target, the dynamic image fusion allows one to enhance the conspicuity of the target. The principle of dynamic image fusion proposed in this paper is based on matrix formalism, in which the fused image is constructed in the form of a complex vector function, which by its mathematical form is analogous to the Jones vector of elliptically polarized light wave, which in turn opens the possibility of matrix transformation of the complex vector of the fused image and consequently its parameterization by analogy with the Jones matrix formalism for the light wave. The article presents mathematical principles of matrix formalism, which is the basis for dynamic image fusion, gives examples of stationary and dynamic image fusion by the method of complex vector function and compares with the corresponding images, fused by algorithms of weight addition in the field of real and complex scalars. It is shown that by selecting weight coefficients, the general form of a complex amplitude vector image can be reduced to the algorithms of weight and averaged addition in the field of real scalars, weight amplitude and RMS-image in the field of complex scalar numbers, and geometric-mean image in the field of complex vectors, which, thereby, are partial cases of the general form of the complex amplitude image in the field of complex vectors. The animated images obtained by the method of complex vector function illustrate the increase of conspicuity of the object of observation due to the dynamic change of the fusion parameters.