On the algorithm for reconstruction of polyhedral objects from a single line drawing

This paper presents a new level-by-level 3D reconstruction method from a single axonometric wireframe drawing with or without hidden edges of a planar object. This method solves a 3D reconstruction problem in stepwise fashion via face propagation, and allows a detailed relative importance study of key regularities and their usages for reconstruction rules establishment, which is the focus of this paper. Based on the proposed reconstruction method, two new trustfulness measures in terms of form and size distortions have been devised to evaluate regularities and their limitations. As a result of adapting the existing concepts of the MSDA [5] and the MSDSM [9] into a stepwise system, two new localized regularities have been developed in terms of the localized minimizing standard deviation of angles (L-MSDA) and the localized minimizing standard deviation of segment magnitudes (L-MSDSM). The proposed method and the identified key regularity have been tested with many cases. A range of weightings for the combination of L-MSAD and L-MSDSM regularities have been identified for practical use. The test results show that (1) the level-by-level reconstruction method is useful to 3D reconstruction, (2) the combined usage of localized key regularities L-MSDA and L-MSDSM, can produce satisfactory results with the proposed method, and (3) the demonstrated success of the combined usage of L-MSDA and L-MSDSM suggests that the concept of combining MSDA and MSDSM should be utilized in any optimization-based reconstruction approaches to improve their accuracy.