When the B-spline surface is used in the image representation, it suffices only to apply the image processing to the polygon vertices to derive the same result as in the processing of the whole original surface. If a compression method is established in which the points on the B-spline surface are considered as the original image data and polygon vertices are regarded as coding data, the image processing can directly be applied to the compressed data, i.e., the polygon vertices. This results in more efficient storage, transmission, and display of the image. However, no study has been made concerning the application of the B-spline to the compression coding of the surface. This paper considers the application of the B-spline with the, forementioned features to the compression coding of the image and discusses the application techniques and performances. As a result of simulation, it is seen that by adaptively determining the parameters for the surface generation and the number of polygon vertices according to the context of the image, a performance equivalent to or better than the performance of the conventional discrete cosine transform (DCT) can be realized. In other words, the B-spline surface can well be applied to the compression coding.