This paper proposes a procedure enabling the extraction of view-dependent triangular approximations from a height map. In general, procedures to approximate a height map use tree hierarchies. These methods, however, have a limitation in terms of accuracy, because they depend on tree hierarchy than terrain features. To overcome the difficult, we apply the simplification method for triangular meshes to a height map. The proposed procedure maintains full decimation procedure to support multiresolution. The maintenance of decimation procedure results in creation of the groups (trees), each of which consists of vertices that can be merged into one vertex (root node). As the groups have tolerance which is determined by some tests, they support the generation of view-dependent arbitrary triangular meshes.