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Near-regular structure discovery using linear programming. (English) Zbl 1322.68224

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68T10 Pattern recognition, speech recognition
90C05 Linear programming
90C10 Integer programming
90C25 Convex programming

Software:

SCAPE; CVX
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] D. Anguelov, P. Srinivasan, D. Koller, S. Thrun, J. Rodgers, and J. Davis. 2005. Scape: Shape completion and animation of people. In ACM SIGGRAPH Papers. 408–416.
[2] A. Berner, M. Wand, N. J. Mitra, D. Mewes, and H.-P. Seidel. 2011. Shape analysis with subspace symmetries. Comput. Graph. Forum 30, 2, 277–286. · doi:10.1111/j.1467-8659.2011.01859.x
[3] M. Bokeloh, M. Wand, and H.-P. Seidel. 2010. A connection between partial symmetry and inverse procedural modeling. In ACM SIGGRAPH Papers. 104:1–104:10.
[4] S. Boyd and L. Vandenberghe. 2004. Convex Optimization. Cambridge University Press, Cambridge, UK. · Zbl 1058.90049 · doi:10.1017/CBO9780511804441
[5] A. Bronstein, M. Bronstein, and R. Kimmel. 2008. Numerical Geometry of Non-Rigid Shapes 1<sup>st</sup> Ed. Springer. · Zbl 1178.68608
[6] Y. Chen and G. Medioni. 1992. Object modelling by registration ofn multiple range images. Image Vis. Comput. 10, 145–155. · doi:10.1016/0262-8856(92)90066-C
[7] H. Edelsbrunner and J. Harer. 2010. Computational Topology: An Introduction. American Mathematical Society. · Zbl 1193.55001
[8] M. S. Floater. 2003. Mean value coordinates. Comput.-Aid. Geom. Des. 20, 1, 19–27. · Zbl 1069.65553 · doi:10.1016/S0167-8396(03)00002-5
[9] R. Gal, O. Sorkine, N. J. Mitra, and D. Cohen-Or. 2009. Iwires: An analyze-and-edit approach to shape manipulation. In ACM SIGGRAPH Papers. 33:1–33:10.
[10] D. Giorgi, S. Biasotti, and L. Paraboschi. 2007. Shape retrieval contest 2007: Watertight models track. http://watertight.ge.imati.cnr.it/watertight-global.pdf.
[11] M. Grant and S. Boyd. 2011. CVX: Matlab software for disciplined convex programming. http://www.stanford.edu/-boyd/cvx/.
[12] J. Hays, M. Leordeanu, A. A. Efros, and Y. Liu. 2006. Discovering texture regularity as a higher-order correspondence problem. In Proceedings of the European Conference on Computer Vision Part II. 522–535.
[13] M. Kilian, N. J. Mitra, and H. Pottmann. 2007. Geometric modeling in shape space. In ACM SIGGRAPH Papers. 64:1–64:9.
[14] V. G. Kim, Y. Lipman, X. Chen, and T. A. Funkhouser. 2010. Mobius transformations for global intrinsic symmetry analysis. Comput. Graph. Forum 29, 5, 1689–1700. · doi:10.1111/j.1467-8659.2010.01778.x
[15] S. Krishnan, P. Y. Lee, J. B. Moore, and S. Venkatasubramanian. 2005. Global registration of multiple 3d point sets via optimization-on-a-manifold. In Proceedings of the Symposium on Geometry Processing (SGP’05).
[16] M. Li, F. C. Langbein, and R. R. Martin. 2006. Constructing regularity feature trees for solid models. In Proceedings of the Conference on Geometric Modeling and Processing. Springer, 267–286. · Zbl 1160.68634
[17] Y. Lipman and T. Funkhouser. 2009. Mobius voting for surface correspondence. In ACM SIGGRAPH Papers. 72:1–72:12.
[18] S. Liu, R. R. Martin, F. C. Langbein, and P. L. Rosin. 2007. Segmenting periodic reliefs on triangle meshes. In Proceedings of the IMA Conference on the Mathematics of Surfaces. 290–306. · Zbl 1163.68356
[19] Y. Liu, W.-C. Lin, and J. Hays. 2004. Near-regular texture analysis and manipulation. In ACM SIGGRAPH Papers. 368–376.
[20] N. J. Mitra, A. M. Bronstein, and M. M. Bronstein. 2010. Intrinsic regularity detection in 3d geometry. In Proceedings of the European Conference on Computer Vision Part III. 398–410.
[21] N. J. Mitra, L. J. Guibas, and M. Pauly. 2006. Partial and approximate symmetry detection for 3d geometry. In ACM SIGGRAPH Papers. 560–568.
[22] N. J. Mitra, M. Pauly, M. Wand, and D. Ceylan. 2012. Symmetry in 3d geometry: Extraction and applications. In Eurographics State-of-the-Art Report.
[23] N. J. Mitra, M. Wand, H. Zhang, D. Cohen-Or, and M. Bokeloh. 2013. Structure-aware shape processing. In Eurographics State-of-the-Art Report.
[24] M. Ovsianikov, Q. Merigot, F. Memoli, and L. J. Guibas. 2010. One point isometric matching with the heat kernel. Comput. Graph. Forum 29, 5, 1555–1564. · doi:10.1111/j.1467-8659.2010.01764.x
[25] M. Ovsianikov, J. Sun, and L. J. Guibas, 2008. Global intrinsic symmetries of shapes. Comput. Graph. Forum 27, 5, 1341–1348. · Zbl 05653367 · doi:10.1111/j.1467-8659.2008.01273.x
[26] M. Park, K. Brocklehurst, R. T. Collins, and Y. Liu. 2009. Deformed lattice detection in real-world images using mean-shift belief propagation. IEEE Trans. Pattern Anal. Mach. Intell. 31, 1804–1816. · doi:10.1109/TPAMI.2009.73
[27] M. Pauly, N. J. Mitra, J. Wallner, H. Pottmann, and L. J. Guibas. 2008. Discovering structural regularity in 3d geometry. In ACM SIGGRAPH Papers. 43:1–43:11.
[28] J. Podolak, P. Shilane, A. Golovinskiy, S. Rusinkiewicz, and T. Funkhouser. 2006. A planar-reflective symmetry transform for 3d shapes. In ACM SIGGRAPH Papers. 549–559.
[29] N. Ray, W. C. Li, B. Levy, A. Sheifer, and P. Alliez, 2006. Periodic global parameterization. ACM Trans. Graph. 25, 1460–1485. · Zbl 05457723 · doi:10.1145/1183287.1183297
[30] F. Schaffalitzky and A. Zisserman. 1999. Geometric grouping of repeated elements within images. In Shape, Contour and Grouping in Computer Vision, Springer, 165–181. · doi:10.1007/3-540-46805-6_10
[31] A. Schrijver. 1986. Theory of Linear and Integer Programming. John Wiley & Sons, New York. · Zbl 0665.90063
[32] O. Sorkine, D. Cohen-Or, Y. Lipman, M. Alexa, C. Rossl, and H.-P. Seidel. 2004. Laplacian surface editing. In Proceedings of the Symposium on Geometry Processing (SGP’04). 175–184.
[33] J. Sun, M. Ovsianikov, and L. Guibas. 2009. A concise and provably informative multi-scale signature based on heat diffusion. In Proceedings of the Symposium on Geometry Processing (SGP’09). 1383–1392.
[34] A. Tevs, M. Bokeloh, M. Wand, A. Schilling, and H.-P. Seidel. 2009. Isometric registration of ambiguous and partial data. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR’09). 1185–1192.
[35] D. W. Thompson. 1945. On Growth and Form. Cambridge University Press, Cambridge, UK.
[36] T. Tuytelaars, A. Turina, and L. van Gool. 2003. Noncombinatorial detection of regular repetitions under perspective skew. IEEE Trans. Pattern Anal. Mach. Intell. 25, 418–432. · Zbl 05111074 · doi:10.1109/TPAMI.2003.1190569
[37] O. van Kaick, H. Zhang, C. Hamarneh, and D. Cohen-Or. 2011. A survey on shape correspondence. Comput. Graph. Forum 30, 6, 1681–1707. · doi:10.1111/j.1467-8659.2011.01884.x
[38] M. Wand, P. Jenke, Q. Huang, M. Bokeloh, L. Guibas, and A. Schilling. 2007. Reconstruction of deforming geometry from time-varying point clouds. In Proceedings of the Symposium on Geometry Processing (SGP’07). 49–58.
[39] S.-Q. Xin and G.-J. Wang. 2009. Improving chen and han’s algorithm on the discrete geodesic problem. ACM Trans. Graph. 28, 104:1–104:8.
[40] K. Xu, H. Zhang, A. Tagliasacchi, L. Liu, C. Li, M. Meng, and Y. Xiong. 2009. Partial intrinsic reflectional symmetry of 3d shapes. In ACM SIGGRAPH Asia Papers. 138:1–138:10.
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