1. An image processing apparatus for classifying an image into a plurality of classes in accordance with a property thereof and for executing processes corresponding to the respective classes, comprising: generating means for generating, from the image, a compressed image having a smaller number of pixels than the image, wherein the generating means generates, as the compressed image, a decimated image obtained by decimating pixels of the image and a reduced image obtained by eliminating peripheral pixels of the image; calculating means for calculating self-similarity of the image based on the compressed image, wherein the calculating means comprises: first extracting means for extracting pixels that constitute the decimated image and arranged in a given direction; second extracting means for extracting pixels that constitute the reduced image and arranged in the given direction; and operating means for calculating, as the self-similarity in the given direction, a norm of vectors having, as components, pixel values of the pixels extracted by the first and second extracting means, respectively; classifying means for determining a class of the image from among the plurality of classes based on the calculated self-similarity; and processing means for executing a process corresponding to the determined class on the image.