Discovering structural regularity in 3D geometry

ACM Transactions on Graphics

Volumn 27, Issue 3, 2008, Pages

  Pauly, Mark ^a   Mitra, Niloy J ^b   Wallner, Johannes ^c   Pottmann, Helmut ^d   Guibas, Leonidas J ^e  

^a ETH ZURICH   (Switzerland)

^b INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

^c GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^d VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^e STANFORD UNIVERSITY   (United States)

Author keywords

Regular structure; Repetitive pattern; Shape analysis; Similarity transformation; Transformation group

Indexed keywords

3-D SHAPE; 3D GEOMETRY; COMPUTATIONAL FRAMEWORK; GEOMETRIC PATTERNS; GEOMETRIC STRUCTURES; LATTICE STRUCTURES; MODEL REPAIR; OPTIMIZATION METHODS; PRIOR KNOWLEDGE; REGISTRATION METHODS; REGULAR STRUCTURE; REGULAR STRUCTURES; REPETITIVE PATTERN; ROBUST ALGORITHMS; SHAPE ANALYSIS; SIMILARITY TRANSFORMATION; SIMILARITY TRANSFORMATIONS; SPATIAL DOMAINS; SPATIAL LOCATIONS; STRUCTURAL REGULARITY; TRANSFORMATION GROUP; UNIFORM GRIDS;

CHLORINE COMPOUNDS; COMPLEXATION; MODEL STRUCTURES;

THREE DIMENSIONAL;

EID: 49249104899     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/1360612.1360642     Document Type: Article

References (32)

1. BLAKEMORE, C., AND CAMPBELL, F. 1969. On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images. J. Physiol. 203, 237-260.
2. BROWN, J. C. 1991. Calculation of a constant Q spectral transform. J. Acoust. Soc. Am. 80, 425-434.
3. BUADES, A., COLL, B., AND MOREL, J.-M. 2008. Nonlocal image and movie denoising. Int. J. Computer Vision 76, 2, 123-139.
4. CAZALS, F., AND POUGET, M. 2003. Estimating differential quantities using polynomial fitting of osculating jets. In Proc. Symp. Geometry Processing. 177-187.
5. COMANICIU, D., AND MEER, P. 2002. Mean shift: A robust approach toward feature space analysis. IEEE Trans. PAMI24, 5, 603-619.
6. FISCHLER, M., AND BOLLES, R. 1981. Random Sample Consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM, 381-395.
7. GOLOVINSKIY, A., PODOLAK, J., AND FUNKHOUSER, T. 2007. Symmetry-aware mesh processing. Tech. Rep. 782-07, Princeton Univ.
8. GRÜNBAUM, B., AND SHEPHARD, G. C. 1987. Tilings and Patterns. W. H. Freeman.
9. HALL, B. C. 2003. Lie Groups, Lie algebras, and representations. An Elementary Introduction. Springer.
10. HOFER, M., ODEHNAL, B., POTTMANN, H., STEINER, T., AND WALLNER, J. 2005. 3D shape recognition and reconstruction based on line element geometry. In Int. Conference on Computer Vision. 1532-1538.
11. HORN, B. K. P. 1987. Closed form solution of absolute orientation using unit quaternions. J. Opt. Soc. A 4, 629-642.
12. HSU, J. T., LIU, L.-C., AND LI, C. 2001. Determination of structure component in image texture using wavelet analysis. In Int. Conference on Image Processing, 166-169.
13. JACQUIN, A. 1992. Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans. Image Proc. 1, 1, 18-30.
14. KORAH, T., AND RASMUSSEN, C. 2007. 2D lattice extraction from structured environments. In Int. Conference on Image Processing, 61-64.
15. LEUNG, T. K., AND MALIK, J. 1996. Detecting, localizing and grouping repeated scene elements from an image. In European Conference on Computer Vision, 546-555.
16. LI, M., LANGBEIN, F. C., AND MARTIN, R. R. 2006. Constructing regularity feature trees for solid models. Geom. Modeling Processing, 267-286.
17. LIU, Y., COLLINS, R., AND TSIN, Y. 2004. A computational model for periodic pattern perception based on frieze and wallpaper groups. IEEE Trans. PAMI26, 3, 354 - 371.
18. LIU, S., MARTIN, R. R., LANGBEIN, F. C., AND ROSIN, P. L. 2007. Segmenting periodic reliefs on triangle meshes. In Math, of Surfaces XII. Springer, 290-306.
19. MANDELBROT, B. 1982. The Fractal Geometry of Nature. W. H. Freeman & Co.
20. MARTINET, A., SOLER, C., HOLZSCHUCH, N., AND SILLION, F. X. 2006. Accurate detection of symmetries in 3d shapes. ACM Trans. Gr. 25, 2, 439-464.
21. MITRA, N. J., GUIBAS, L. J., AND PAULY, M. 2006. Partial and approximate symmetry detection for 3D geometry. ACM Trans. Gr. 25, 3, 560-568.
22. MITRA, N. J., GUIBAS, L. J., AND PAULY, M. 2007. Symmetrization. ACM Trans. Gr. 26, 3, #63.
23. MÜLLER, P., ZENG, G., WONKA, P., AND VAN GOOL, L. 2007. Image-based procedural modeling of facades. ACM Trans. Gr. 26, 3, #85.
24. PAULY, M., MITRA, N., GIESEN, J., GROSS, M., AND GUIBAS, L. 2005. Example-based 3D scan completion. In Proc. Symp. Geometry Processing, 23-32.
25. PODOLAK, J., SHILANE, P., GOLOVINSKIY, A., RUSINKIEWICZ, S., AND FUNKHOUSER, T. 2006. A planar-reflective symmetry transform for 3D shapes. ACM Trans. Gr. 25, 3, 549-559.
26. 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. Computer Vision 67, 3, 277-296.
27. RUSTAMOV, R. M. 2007. Augmented symmetry transforms. In Proc. Shape Modeling International. 13-20.
28. SCHAFFALITZKY, F., AND ZLSSERMAN, A. 1999. Geometric grouping of repeated elements within images. In Shape, Contour and Grouping in Computer Vision, 165-181.
29. SHIKHARE, D., BHAKAR, S., AND MUDUR, S. P. 2001. Compression of large 3D engineering models using automatic discovery of repeating geometric features. In Vision, Modeling, and Visualization, 233-240.
30. SIMARI, P., KALOGERAKIS, E., AND SINGH, K. 2006. Folding meshes: hierarchical mesh segmentation based on planar symmetry. In Proc. Symp. Geometry Processing. 111-119.
31. THOMPSON, D. W. 1992. On Growth and Form. Dover.
32. TUYTELAARS, T., TURINA, A., AND GOOL, L. V. 2003. Non-combinatorial detection of regular repetitions under perspective skew. IEEE Trans. PAMI25, 4, 418-432.