1. An image compression method of compressing a color image, comprising: an index conversion step of converting each pixel of the color image into an index assigned in correspondence with a color value and generating color information containing the number of pixels for each indexed color and an index image obtained by converting each of the pixels into an index; a background determination step of determining a color value corresponding to a predetermined index in the index image as a background color of the color image; an order determination step of determining, on the basis of the color information and the background color, an order in which the color image is compressed for each index; a binary image generating step of generating a binary image for each index from the index image; a compression step of compressing the binary image according to the order; and a generating step of generating compressed image data by integrating background data containing a size of the color image and a color value of the background color and compressed data of the binary image for each of the indexes.