Reverse engineering (RE) deals with an enormous number of irregular and scattered digitized points that require intensive processing in order to reconstruct the surfaces of an object. Surface reconstruction of freeform objects is based on geometrical and topological criteria. Current fitting methods reconstruct an object using a bottom-up approach, from points to a dense mesh, and finally into smoothed connected freeform sub-surfaces. This type of reconstruction, however, can cause topological problems that lead to undesired surface fitting results. Such problems are particularly common with concave shapes. To avoid problems of this type, the paper proposes a new method that automatically detects the topological structure of an object as a base for surface fitting. The topological reconstruction method described in the paper is based on two stages: (1) creating 3D non-self-intersecting iso-curves from a 3D triangular mesh and (2) extracting a topological graph. The feasibility of the proposed topological reconstruction method is demonstrated on several examples using freeform objects with complex topologies.