The approach of using element type representation to describe 3-D surface is encouraged for many applications such as machine vision, 3-D visualization, scene understanding, finite-element engineering analysis, and etc. In this paper, a new method for 3-D surface tessellation from a perspective 2.5-D range map is proposed. Mathematical morphology operations are applied to conduct the surface tessellation on a frame-by-frame basis. The perspective 2.5-D range map which describes the surface altitude in a 3-D orthographic projection model can be either acquired from a range finder or generated from a true 3-D voxel data set. The surface tessellation method is achieved by applying the Delaunary triangulation method to the intrinsic images. The intrinsic information, gradients of point on the surface, can are directly computed from the range map using neighborhood operation. Based on the differential geometry, the directional derivatives along two orthogonal axes in the image are used as the intrinsic images. The lines of curvature along with the principle directions can be detected from these intrinsic images by a sequence of boolean lattice mathematical morphology operations, dilation and image algebra operations. Using the lines of curvature images, a set of seed points can be obtained by intersecting the lines of curvature along the principle directions with maximum and minimum normal curvature. Finally, a set of triangular elements may be resulted by applying the Delaunay triangulation method to those seed points.