This paper proposes a new method of describing spatiotemporal images based on the concept of structured abstract index images. In spatiotemporal images, each region in an image sequence forms a tube. An original image sequence can be reconstructed by cutting out the sequence of cross sections from the group of tubes in these images. That is, a moving image sequence can be described compactly by the group of tubes. This paper first discusses the method of approximating static contours by Bezier curves. Approximation of surface tubes by Bezier surface is examined in detail. A problem with this method is that it does not work well if shape of the cross section changes considerably along the time axis. This problem can be solved by growing a new Bezier surface from passing points of Bezier curve and by combining the different Bezier surfaces.
