“O‐Snap: Optimization‐Based Snapping for Modeling Architecture” by Arikan, Schwärzler, Flöry and Malerhofer

  • ©Murat Arikan, Michael Schwärzler, Simon Flöry, and Stefan Malerhofer




    O‐Snap: Optimization‐Based Snapping for Modeling Architecture


Session Title: Structures, Faces & Building



    In this article, we introduce a novel reconstruction and modeling pipeline to create polygonal models from unstructured point clouds. We propose an automatic polygonal reconstruction that can then be interactively refined by the user. An initial model is automatically created by extracting a set of RANSAC-based locally fitted planar primitives along with their boundary polygons, and then searching for local adjacency relations among parts of the polygons. The extracted set of adjacency relations is enforced to snap polygon elements together, while simultaneously fitting to the input point cloud and ensuring the planarity of the polygons. This optimization-based snapping algorithm may also be interleaved with user interaction. This allows the user to sketch modifications with coarse and loose 2D strokes, as the exact alignment of the polygons is automatically performed by the snapping. The generated models are coarse, offer simple editing possibilities by design, and are suitable for interactive 3D applications like games, virtual environments, etc. The main innovation in our approach lies in the tight coupling between interactive input and automatic optimization, as well as in an algorithm that robustly discovers the set of adjacency relations.


    1. Alliez, P., Cohen-Steiner, D., Tong, Y., and Desbrun, M. 2007. Voronoi-Based variational reconstruction of unoriented point sets. In Proceedings of the 5th Eurographics Symposium on Geometry Processing. Eurographics Association, 39–48.
    2. Atkinson, A. C. and Riani, M. 2000. Robust Diagnostic Regression Analysis. Springer.
    3. Avron, H., Sharf, A., Greif, C., and Cohen-Or, D. 2010. ℓ1-sparse reconstruction of sharp point set surfaces. ACM Trans. Graph. 29, 135:1–135:12.
    4. Boissonnat, J.-D. and Oudot, S. 2005. Provably good sampling and meshing of surfaces. Graph. Models 67, 405–451.
    5. Botsch, M., Pauly, M., Gross, M., and Kobbelt, L. 2006. Primo: coupled prisms for intuitive surface modeling. In Proceedings of the 4th Eurographics Symposium on Geometry Processing. 11–20.
    6. Cazals, F., Giesen, J., Pauly, M., and Zomorodian, A. 2005. Conformal alpha shapes. In Proceedings of the Eurographics/IEEE VGTC Symposium on Point-Based Graphics 0, 55–61.
    7. Chen, J. and Chen, B. 2008. Architectural modeling from sparsely scanned range data. Int. J, Comput. Vis. 78, 2–3, 223–236.
    8. Cignoni, P., Rocchini, C., and Scopigno, R. 1996. Metro: Measuring error on simplified surfaces. Tech. rep., Paris, France.
    9. Cohen-Steiner, D., Alliez, P., and Desbrun, M. 2004. Variational shape approximation. ACM Trans. Graph. 23, 905–914.
    10. Davis, T. A. 2011. Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization. ACM Trans. Math. Softw. 38, 1.
    11. Debevec, P. E., Taylor, C. J., and Malik, J. 1996. Modeling and rendering architecture from photographs: A hybrid geometry- and image-based approach. In Proceedings of SIGGRAPH 96. 11–20.
    12. Demaine, E. and O’Rourke, J. 2007. Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press.
    13. Edelsbrunner, H. and Mücke, E. P. 1994. Three-Dimensional alpha shapes. ACM Trans. Graph. 13, 43–72.
    14. Fleishman, S., Cohen-Or, D., and Silva, C. T. 2005. Robust moving least-squares fitting with sharp features. ACM Trans. Graph. 24, 544–552.
    15. Furukawa, Y., Curless, B., Seitz, S. M., and Szeliski, R. 2009. Manhattan-world stereo. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 1422–1429.
    16. Gal, R., Sorkine, O., Mitra, N. J., and Cohen-Or, D. 2009. iWIRES: An analyze-and-edit approach to shape manipulation. ACM Trans. Graph. 28, 3, #33, 1–10.
    17. Garland, M. and Heckbert, P. S. 1997. Surface simplification using quadric error metrics. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques. 209–216.
    18. Graphite. 2010. http://alice.loria.fr/index.php/software.html.
    19. Jolliffe, I. T. 2002. Principal Component Analysis 2nd Ed. Springer, New York.
    20. Kazhdan, M., Bolitho, M., and Hoppe, H. 2006. Poisson surface reconstruction. In Proceedings of the 4th Eurographics Symposium on Geometry Processing. Eurographics Association, 61–70.
    21. Kelley, C. T. 1999. Iterative Methods for Optimization. SIAM, Philadephia, PA.
    22. Kilian, M., Flöry, S., Chen, Z., Mitra, N. J., Sheffer, A., and Pottmann, H. 2008. Curved folding. ACM Trans. Graph. 27, 3, #75, 1–9.
    23. Kobbelt, L. P., Botsch, M., Schwanecke, U., and Seidel, H.-P. 2001. Feature sensitive surface extraction from volume data. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques. ACM, New York, 57–66.
    24. Li, Y., Wu, X., Chrysanthou, Y., Sharf, A., Cohen-Or, D., and Mitra, N. J. 2011. GlobFit: Consistently fitting primitives by discovering global relations. ACM Trans. Graph. 30, 4, Article 52.
    25. MeshLab. 2008. MeshLab:/An open=source 3D mesh processing System. http://meshlab.sourceforge.net.
    26. Musialski, P., Wonka, P., Aliaga, D. G., Wimmer, M., van Gool, L., and Purgathofer, W. 2012. A survey of urban reconstruction. In EUROGRAPHICS 2012 State of the Art Reports, Eurographics Association, 1–28.
    27. Nan, L., Sharf, A., Zhang, H., Cohen-Or, D., and Chen, B. 2010. SmartBoxes for interactive urban reconstruction. ACM Trans. Graph. 29, 93:1–93:10.
    28. Pauly, M., Mitra, N. J., Wallner, J., Pottmann, H., and Guibas, L. 2008. Discovering structural regularity in 3D geometry. ACM Trans. Graph. 27, 3, #43, 1–11.
    29. Pointools Ltd. 2011. Pointools plugin for sketchup. http://www.pointools. com/pointools-plug-in-for-sketchup.php.
    30. Pottmann, H., Huang, Q.-X., Yang, Y.-L., and Hu, S.-M. 2006. Geometry and convergence analysis of algorithms for registration of 3D shapes. Int. J. Comput. Vis. 67, 277–296.
    31. Rousseeuw, P. J. and Leroy, A. M. 1987. Robust Regression and Outlier Detection. John Wiley&Sons, New York.
    32. Salman, N., Yvinec, M., and Merigot, Q. 2010. Feature preserving mesh generation from 3D point clouds. Comput. Graph. Forum 29, 5, 1623–1632.
    33. Schindler, K. and Bauer, J. 2003. A model-based method for building reconstruction. In Proceedings of the 1st IEEE International Workshop on Higher-Level Knowledge in 3D Modeling and Motion Analysis. 74– 82.
    34. Schnabel, R., Degener, P., and Klein, R. 2009. Completion and reconstruction with primitive shapes. Comput. Graph. Forum 28, 2, 503–512.
    35. Schnabel, R., Wahl, R., and Klein, R. 2007. Efficient RANSAC for point-cloud shape detection. Comput. Graph. Forum 26, 2, 214–226.
    36. Sinha, S. N., Steedly, D., Szeliski, R., Agrawala, M., and Pollefeys, M. 2008. Interactive 3D architectural modeling from unordered photo collections. ACM Trans. Graph. 27, 159:1–159:10.
    37. Strecha, C., von Hansen, W., Gool, L. J. V., Fua, P., and Thoennessen, U. 2008. On benchmarking camera calibration and multi-view stereo for high resolution imagery. In Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR).
    38. van den Hengel, A., Dick, A., Thormählen, T., Ward, B., and Torr, P. H. S. 2007. VideoTrace: Rapid interactive scene modelling from video. ACM Trans. Graph. 26.
    39. Vanegas, C. A., Aliaga, D. G., and Benes, B. 2010. Building reconstruction using Manhattan-world grammars. In Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR). 358–365.
    40. Werner, T. and Zisserman, A. 2002. New techniques for automated architectural reconstruction from photographs. In Proceedings of European Conference on Computer Vision (ECCV). 541–555.

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