1. An image processing method for performing fractal transformation on an input image of a first size, and generating an output image of a second size, greater than the first size, said image processing method comprising using a processor to perform the steps of: dividing the input image into L sets of first regions, defined by boundaries, using L division patterns, so that at least one of boundaries of the first regions, corresponding to one of the L division patterns, is different from the boundaries of each first region in the other L division patterns, L being an integer equal to or greater than 2; generating scaled-down images by performing, using parameters for each of the L sets of first regions in the input image, respectively, contractive affine transformation on reference regions, each respective reference region being included in the input image and being greater in size than a first region that refers to the respective reference region, and calculating L sets of fractal parameters used for the fractal transformation on an input image of the first size by calculating, for each first region in the L sets of first regions, a corresponding one of the fractal parameters in the L sets of fractal parameters, the contractive affine transformation being performed for each possible combination of the reference region and the parameter, each fractal parameter in the L sets of fractal parameters being fractal information indicating (i) the parameter used to generate, for a corresponding one of the first regions in the L sets of first regions, a scaled-down image having a highest correlation with the corresponding first region and (ii) a position of the reference region used in combination with the parameter; modifying the L sets of fractal parameters into respective L sets of modified fractal parameters for the fractal transformation on an image of the second size; and generating the output image of the second size by performing the fractal transformation on a target image, the fractal transformation including the contractive affine transformation performed on the reference regions, included in the target image and indicated by the L sets of modified fractal parameters, and performed using the parameters indicated by the L sets of modified fractal parameters for each modified fractal parameter in the L sets of modified fractal parameters.