We deal with the applications of a class of nonlinear dynamic systems to image transformation and encoding whereby the nonlinear system presents a chaotic or hyperchaotic attractor. Several ways are possible to encode or transform the image using chaos. We develop algorithms for image encoding based on the permutation of the pixel value, position, or both. This approach enables the fast decorrelation of relations among pixels in the initial image in a random-like fashion. We illustrate the use of 1-D, 2-D, and 3-D maps for this purpose. We also use chaotic dynamical systems with a single or two outputs. A discussion of the sensitivity of the algorithms to the keys is followed by the illustration of the algorithms using example images.
In this paper, a new strategy is presented to map the pixel space from infrared (IR) image to the pixel space of optical images. This is done by utilizing the usual technique of system identification using the input-output measurements and trying to fit a parametric model under a given fitness criterion. In this case, the IR image is taken as the input data and a similar image taken simultaneously by a normal CCD camera is taken as the output data. The acquired data are then fitted with an autoregressive moving average (ARMA) model in 1D under the H∞ criterion which is the most robust and statistically less-dependent fitness criterion. The well known LMS algorithm can reach the H∞ bounds under certain impositions. By structuring the given data to suite these impositions, the LMS algorithm is used to reach the optimal bound. This implies a faster convergence with better performance. The results have shown remarkable enhancement in the images and appears to be promising for the real-time applications.
We describe an application of nonlinear dynamical systems to image transformation and encoding. Our approach is different from the classical one where affine discrete maps are used. Similarly to classical fractal image compression, nonlinear maps use the redundancy in the image for compression. Furthermore, compression speed is enhanced whenever nonlinear maps have more than one attractor. Nonlinear maps having strange chaotic attractors can also be used to encode the image. In this case, the image will take the shape of the strange attractor when mapped under the nonlinear system. The procedure needs some precautions for chaotic maps, because of the sensitivity to initial conditions. Another possibility is to use strange attractors to hide the initial image using various schemes. For example, it is possible to hide the image using position permutation, value permutation, or both position and value permutations. We develop an algorithm to show that chaotic maps can be used successfully for this purpose. We also show that the sensitivity to initial conditions of chaotic maps forms the basis of the encryption strategy.