In the visualization of three-dimensional (3D) images, specific isosurfaces are usually extracted from 3D images and used to represent (approximate) boundary surfaces of certain structures within 3D images. In order to well approximate the boundary surfaces of these structures, it is important to determine a good isosurface for each boundary surface. An isosurface is said to be a good isosurface of a boundary surface if it can approximate the boundary surface with the smallest error under certain error measuring criteria. The mathematical model describing the approximation problem of a boundary surface by isosurfaces is constructed and studied. The method used to deduce good isosurfaces for the boundary surfaces within 3D discrete images is presented. The proposed method is illustrated by examples with different real 3D biomedical images.