“Layered analysis of irregular facades via symmetry maximization” by Zhang, Xu, Lin, Cohen-Or and Chen

  • ©Hao Zhang, Kai Xu, Jinjie Lin, Daniel Cohen-Or, and Baoquan Chen




    Layered analysis of irregular facades via symmetry maximization

Session/Category Title: Structures, Faces & Building




    We present an algorithm for hierarchical and layered analysis of irregular facades, seeking a high-level understanding of facade structures. By introducing layering into the analysis, we no longer view a facade as a flat structure, but allow it to be structurally separated into depth layers, enabling more compact and natural interpretations of building facades. Computationally, we perform a symmetry-driven search for an optimal hierarchical decomposition defined by split and layering operations applied to an input facade. The objective is symmetry maximization, i.e., to maximize the sum of symmetry of the substructures resulting from recursive decomposition. To this end, we propose a novel integral symmetry measure, which behaves well at both ends of the symmetry spectrum by accounting for all partial symmetries in a discrete structure. Our analysis results in a structural representation, which can be utilized for structural editing and exploration of building facades.


    1. Aliaga, D. G., Rosen, P. A., and Bekins, D. R. 2007. Style grammars for interactive visualization of architecture. IEEE Trans. Vis. & Comp. Graphics 13, 4, 786–797. Google ScholarDigital Library
    2. Bokeloh, M., Wand, M., and Seidel, H.-P. 2010. A connection between partial symmetry and inverse procedural modeling. ACM Trans. on Graph 29, 4, 104:1–104:10. Google ScholarDigital Library
    3. Bokeloh, M., Wand, M., Seidel, H.-P., and Koltun, V. 2012. An algebraic model for parameterized shape editing. ACM Trans. on Graph 31, 4, 78:1–78:10. Google ScholarDigital Library
    4. Buffart, H., Leeuwenberg, E., and Restle, F. 1983. Analysis of ambiguity in visual pattern completion. Journal of Experimental Psychology: Human Perception and Performance, 9980–1000.Google ScholarCross Ref
    5. Chao, Y., Tian, H., Long, Q., and Tai, C.-L. 2012. Parsing facade with rank-one approximation. In Proc. of CVPR. Google ScholarDigital Library
    6. Findlay, J. M. 1995. Visual search: eye movements and peripheral vision. Optometry and Vision Science 72, 461–466.Google ScholarCross Ref
    7. Graham, J. H., Raz, S., Hel-Or, H., and Nevo, E. 2010. Fluctuating asymmetry: Methods, theory, and applications. Symmetry 2, 2, 466–540.Google ScholarCross Ref
    8. Harada, M., Witkin, A., and Baraff, D. 1995. Interactive physically-based manipulation of discrete/continuous models. In Proc. of SIGGRAPH, 199–208. Google ScholarDigital Library
    9. Hochstein, S., and Ahissar, M. 2002. View from the top: Hierarchies and reverse hierarchies in the visual system. Neuron, 5, 791–804.Google ScholarCross Ref
    10. Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S. 2004. Symmetry descriptors and 3D shape matching. Symp. on Geom. Proc., 115–123. Google ScholarDigital Library
    11. Lazebnik, S., Schmid, C., and Ponce, J. 2006. Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In Proc. of CVPR, 2169–2178. Google ScholarDigital Library
    12. Lin, J., Cohen-Or, D., Zhang, H., Cheng, L., Sharf, A., Deusson, O., and Chen, B. 2011. Structure-preserving retargeting of irregular 3D architecture. ACM Trans. on Graph 30, 6, Article 183. Google ScholarDigital Library
    13. Liu, G.-H., Li, Z.-Y., Zhang, L., and Xu, Y. 2011. Image retrieval based on micro-structure descriptor. Pattern Recognition 44, 9, 2123–2133. Google ScholarDigital Library
    14. Martinet, A. 2007. Structuring 3D Geometry based on Symmetry and Instancing Information. PhD thesis, INP Grenoble.Google Scholar
    15. Mitra, N. J., Pauly, M., Wand, M., and Ceylan, D. 2012. Symmetry in 3D geometry: Extraction and applications. In Proc. of Eurographics STAR Report.Google Scholar
    16. Musialski, P., Wonka, P., Aliaga, D. G., Wimmer, M., van Gool, L., and Purgathofer, W. 2012. A survey of urban reconstruction. In Eurographics State-of-the-art Report.Google Scholar
    17. Palmer, S. E. 1977. Hierarchical structure in perceptual representation. Cognitive Psychology 9, 4, 441–474.Google ScholarCross Ref
    18. Parish, Y. I. H., and Müller, P. 2001. Procedural modeling of cities. In Proc. of SIGGRAPH, 301–308. Google ScholarDigital Library
    19. Pauly, M., Mitra, N. J., Wallner, J., Pottmann, H., and Guibas, L. 2008. Discovering structural regularity in 3D geometry. ACM Trans. on Graph 27, 3, 43:1–11. Google ScholarDigital Library
    20. Podolak, J., Shilane, P., Golovinskiy, A., Rusinkiewicz, S., and Funkhouser, T. 2006. A planar-reflective symmetry transform for 3D shapes. ACM Trans. on Graph 25, 3, 549–559. Google ScholarDigital Library
    21. Shen, C.-H., Huang, S.-S., Fu, H., and Hu, S.-M. 2011. Adaptive partitioning of urban facades. ACM Trans. on Graph 30, 6, 184:1–184:9. Google ScholarDigital Library
    22. Simari, P., Kalogerakis, E., and Singh, K. 2006. Folding meshes: hierarchical mesh segmentation based on planar symmetry. Symp. on Geom. Proc., 111–119. Google ScholarDigital Library
    23. Stava, O., Benes, B., Mech, R., Aliga, D., and Kristof, P. 2010. Inverse procedural modeling by automatic generation of L-systems. Computer Graphics Forum (Eurographics) 29, 2, 665–674.Google ScholarCross Ref
    24. Teboul, O., Kokkinos, I., Simon, L., Koutsourakis, P., and Paragios, N. 2011. Shape grammar parsing via reinforcement learning. In Proc. of CVPR. Google ScholarDigital Library
    25. Torsello, A., Hidovic-Rowe, D., and Pelillo, M. 2005. Polynomial-time metrics for attributed trees. IEEE Trans. Pat. Ana. & Mach. Int. 27, 7, 1087–1099. Google ScholarDigital Library
    26. Wang, Y., Xu, K., Li, J., Zhang, H., Shamir, A., Liu, L., Cheng, Z., and Xiong, Y. 2011. Symmetry hierarchy of man-made objects. Computer Graphics Forum (Eurographics) 30, 2, 287–296.Google ScholarCross Ref
    27. Wertheimer, M. 1923. Untersuchungen zur lehre von der gestalt. ii. Psychologische Forschung 4, 301–350.Google ScholarCross Ref
    28. Wonka, P., Wimmer, M., Sillion, F., and Ribarsky, W. 2003. Instant architecture. ACM Trans. on Graph 22, 3, 669–677. Google ScholarDigital Library
    29. Wu, H., Wang, Y., Feng, K.-C., Wong, T.-T., Lee, T.-Y., and Heng, P.-A. 2010. Resizing by symmetry-summarization. ACM Trans. on Graph 29, 6, 159:1–10. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: