1. An image-processing apparatus comprising: a storage device, configured to store image data having color information in a three-dimensional color space; a CPU, configured to: generate a two-dimensional distribution of two dimensions of the color information of image data having color information in a three-dimensional color space; calculate a correlation coefficient related to the two-dimensional distribution; determine whether the image data constitutes color convertible image data based on the calculated correlation coefficient; if the image data is determined to constitute color convertible image data, convert the image data having color information in a three-dimensional color space to one of image data having black-and-white information or image data having gray scale information; and cause the converted image data to be stored in the storage device, whereby a storage size necessary to store the image data is reduced, while maintaining legibility, for mage data for an image without a chromatic color or with a small chromatic color.