1. An image processing system comprising: a first extracting portion that extracts a repeating pattern from an image by determining a repetition period of the repeating pattern in the image by transforming pixel values in the image into frequency coefficients; a second extracting portion that extracts the repeating pattern by: constructing an image pyramid that is constructed as a set of images with different resolutions, from a high resolution image to a low resolution image; calculating a higher order local autocorrelation feature value at each pixel of a deepest layer image of the image pyramid to calculate an autocorrelation coefficient between a reference pixel area and each subject pixel area based on the calculated, higher order local autocorrelation feature values; performing such calculation of higher order local autocorrelation feature values and autocorrelation coefficients for an image of a layer that is shallower by one level than the layer of the preceding calculation, wherein, in each repetition, the calculation is performed for every subject pixel area of the current layer that corresponds to the subject pixel area whose autocorrelation coefficient was a local maximum value in the image of the layer that is deeper by one level than the layer of the current layer; repeating the preceding calculation step a predetermined number of times; and using a local maximum value of autocorrelation coefficients of a shallowest layer to determine the repetition period of the repeating pattern in the image; and a creating portion that creates an arbitrary repeating pattern, wherein: when a repeating pattern whose number of repetitions is equal to or greater than a predetermined number is extracted as a result of extraction of a repeating pattern by the first extracting portion, the repeating pattern extracted by the first extracting portion is output; and when no repeating pattern is extracted by the first extracting portion, or when no repeating pattern whose number of repetitions is equal to or greater than the predetermined number is extracted by the first extracting portion, extraction of a repeating pattern is performed by the second extraction portion, and, if a repeating pattern is extracted by the second extraction portion, the repeating pattern is output, and if no repeating pattern is extracted by the second extracting portion, the arbitrary repeating pattern is created by the creating portion and output.