Abstract A new vector coding for natural image, which has acompressive algorithm, is presented and images' features showed in this method are described. In this paper, the pixel-value-boundary contours on RGB or YCrCb planes of natural images are expressed by function approximation and then their contour shapes are predicted .from similar contours in the decoder side. The proposed vector coding method has two main merits: the one is to meet the demands of expansion and reduction of images, the second is to suit content distribution because images can be kept their quality even under the repetition of editing. These are due to representation of function approximation. In spite of these merits on vector coding, any applications to natural have never been studied for its considerably increase of data. To put vector coding for natural images to practical use, we try to compress the data by using characteristics in three-dimensional representation of images.