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.