A New Image Compression Method Based on Fractal Equations

A new image compression technique is proposed, based on the affine transformations (ATs) that define an iterated function system. Previous related research in the field has shown that an image may be approximated by iteratively subjecting a set of sub-regions to a group of ATs. In this case, it suffices to save the AT coefficients at issue and the corners of the regions; despite this advantage, the technique is computationally intensive, because both the sub-regions and the corresponding ATs have to be looked for. Here, a new form of similarity is proposed, based on the successive points generated by the iteration of affine transformations. By understanding an AT as a discrete dynamical system, with each image point represented by an iteration of the AT, the method captures similarities between these points, namely, those with the same color in the image; by saving the starting point and the transformations´ coefficients, the points can be iterated back, to reconstruct the original image. This results in lighter computational effort, and promising results, since the comparison is made point by point, instead of region by region.