1. An image information compressing method of performing feature extraction and coding on an original image, comprising the steps of: converting a two-dimensional or three-dimensional original image into one-dimensional original data by pseudo-Hilbert scan; extracting first feature information by generating first feature data by approximating said one-dimensional original data by a step function which changes step by step every predetermined interval; coding said first feature information, thereby obtaining first feature coded data; extracting second feature information by subtracting said first feature information from said original image; and developing said second feature information to a space constructed by base vectors by using base vectors stored in a base vector table, and coding a part of a component value of said second feature information for a predetermined base vector in the space constructed by said base vectors, thereby obtaining second feature coded data, wherein the step function for approximating said one-dimensional original data is a step function in which a data value of said first feature data in each of said intervals is equal to an average value in the interval of said one-dimensional original data, and made by a series of data divided into said intervals so that a cumulative error in all of the intervals between said one-dimensional original data and said first feature data becomes the minimum or a step function in which a data value of said first feature data in each of said intervals is equal to an average value in the interval of said one-dimensional original data, and made by a series of data divided into said intervals so that a cumulative error in each of the intervals between said one-dimensional original data and said first feature data becomes equal to or less than a predetermined threshold.