A method for extracting a 3D terrain model for identifying at least buildings and terrain from LIDAR data is disclosed, comprising the steps of generating a point cloud representing terrain and buildings mapped by LIDAR; classifying points in the point cloud, the point cloud having ground and non-ground points, the non-ground points representing buildings and clutter; segmenting the non-ground points into buildings and clutter; and calculating a fit between at least one building segment and at least one rectilinear structure, wherein the fit yields the rectilinear structure with the fewest number of vertices. The step of calculating further comprises the steps of (a) calculating a fit of a rectilinear structure to the at least one building segment, wherein each of the vertices has an angle that is a multiple of 90 degrees; (b) counting the number of vertices; (c) rotating the at least one building segment about an axis by a predetermined increment; and (d) repeating steps (a)-(c) until a rectilinear structure with the least number of vertices is found.