We describe a new method for building 3D surface meshes from volumetric images, as are created in Magnetic Resonance Imaging (MRI). The method works by first extracting the contours from the MRI data, and then using modified polygon boolean operations to find difference polygons. The last step is performed by applying a Constrained Delauny Triangulation (CDT) algorithm to build a surface mesh. Since it is based on CDT, the mesh quality is usually very good. Moreover, the resulting triangular surface mesh is the optimal one for surface interpolation. In case of undersampled images, the mesh quality can be improved dramatically by inserting new Steiner points in to the mesh. Thus the mesh can be made suitable for use in scientific computation. Our method has the advantages of combining the generation and optimization of the mesh in one step compared with other methods. These advantages are illustrated. Also UMIACS-TR-2003-11