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Abstraction of man-made shapes

Published: 01 December 2009 Publication History

Abstract

Man-made objects are ubiquitous in the real world and in virtual environments. While such objects can be very detailed, capturing every small feature, they are often identified and characterized by a small set of defining curves. Compact, abstracted shape descriptions based on such curves are often visually more appealing than the original models, which can appear to be visually cluttered. We introduce a novel algorithm for abstracting three-dimensional geometric models using characteristic curves or contours as building blocks for the abstraction. Our method robustly handles models with poor connectivity, including the extreme cases of polygon soups, common in models of man-made objects taken from online repositories. In our algorithm, we use a two-step procedure that first approximates the input model using a manifold, closed envelope surface and then extracts from it a hierarchical abstraction curve network along with suitable normal information. The constructed curve networks form a compact, yet powerful, representation for the input shapes, retaining their key shape characteristics while discarding minor details and irregularities.

References

[1]
Arnheim, R. 1956. Art and Visual Perception: A Psychology of the Creative Eye. Faber and Faber.
[2]
Attene, M., Falcidieno, B., and Spagnuolo, M. 2006. Hierarchical mesh segmentation based on fitting primitives. The Visual Computer 22, 3, 181--193.
[3]
Attneave, F. 1954. Some informational aspects of visual perception. Psychological review 61, 3, 183--193.
[4]
Bengtsson, A., and Eklundh, J.-O. 1991. Shape representation by multiscale contour approximation. IEEE Trans. on PAMI 13, 1 (Jan), 85--93.
[5]
Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., and Taubin, G. 1999. The ball-pivoting algorithm for surface reconstruction. IEEE Trans. on Visualization and Computer Graphics 5, 4, 349--359.
[6]
Besl, P. J., and McKay, N. D. 1992. A method for registration of 3-d shapes. IEEE Trans. on PAMI 14, 2, 239--256.
[7]
Biasotti, S., Falcidieno, B., and Spagnuolo, M. 2002. Shape abstraction using computational topology techniques. From geometric modeling to shape modeling, 209--222.
[8]
Bischoff, S., Pavic, D., and Kobbelt, L. 2005. Automatic restoration of polygon models. ACM Trans. Graph. 24, 4.
[9]
Bokeloh, M., Berner, A., Wand, M., Seidel, H.-P., and Schilling, A. 2009. Symmetry detection using line features. Computer Graphics Forum, Proc. of Eurographics 28, 2, 697--706.
[10]
Brown, G., Forte, P., Malyan, R., and Barnwell, P. 1993. A non-linear shape abstraction technique. In CAIP, 223--230.
[11]
Cohen, J., Varshney, A., Manocha, D., Turk, G., Weber, H., Agarwal, P., Brooks, F., and Wright, W. 1996. Simplification envelopes. In Proc. SIGGRAPH, 119--128.
[12]
Cohen-Steiner, D., Alliez, P., and Desbrun, M. 2004. Variational shape approximation. ACM SIGGRAPH Trans. Graph., 905--914.
[13]
Cole, F., Golovinskiy, A., Limpaecher, A., Barros, H. S., Finkelstein, A., Funkhouser, T., and Rusinkiewicz, S. 2008. Where do people draw lines? ACM SIGGRAPH Trans. Graph. 27, 3, #88, 1--11.
[14]
Costa, L., and Cesar, R. M. 2001. Shape Analysis and Classification: Theory and Practice. CRC Press.
[15]
DeCarlo, D., Finkelstein, A., Rusinkiewicz, S., and Santella, A. 2003. Suggestive contours for conveying shape. ACM SIGGRAPH Trans. Graph. 22, 3 (July), 848--855.
[16]
Demirci, M., Shokoufandeh, A., and Dickinson, S. J. 2009. Skeletal shape abstraction from examples. IEEE Trans. on PAMI 31, 5, 944--952.
[17]
Falcidieno, B., and Spagnuolo, M. 1998. A shape abstraction paradigm for modelling geometry and semantics. In Computer Graphics International, 646--656.
[18]
Gal, R., Sorkine, O., Popa, T., Sheffer, A., and Cohen-Or, D. 2007. 3d collage: expressive non-realistic modeling. In Proc. of NPAR, ACM, New York, NY, USA, 7--14.
[19]
Gal, R., Sorkine, O., Mitra, N. J., and Cohen-Or, D. 2009. iwires: An analyze-and-edit approach to shape manipulation. ACM SIGGRAPH Trans. Graph. 28, 3, #33, 1--10.
[20]
Garland, M., and Heckbert, P. S. 1997. Surface simplification using quadric error metrics. In Proc. SIGGRAPH, 209--216.
[21]
Grabler, F., Agrawala, M., Sumner, R. W., and Pauly, M. 2008. Automatic generation of tourist maps. ACM SIGGRAPH Trans. Graph. 27, 3, 1--11.
[22]
Hou, S., and Ramani, K. 2008. Structure-oriented contour representation and matching for engineering shapes. Computer Aided Design 40, 1, 94--108.
[23]
Julius, D., Kraevoy, V., and Sheffer, A. 2005. D-charts: Quasi-developable mesh segmentation. In Computer Graphics Forum, Proc. of Eurographics, vol. 24, 581--590.
[24]
Koenderink, J. J., and van Doorn, A. J. 1979. The internal representation of solid shape with respect to vision. Journal Biological Cybernetics 32, 4, 211--216.
[25]
Kraevoy, V., Sheffer, A., Shamir, A., and Cohen-Or, D. 2008. Non-homogeneous resizing of complex models. ACM SIGGRAPH Trans. Graph. 27, 5, 1--9.
[26]
Kruskal, J. B., and Wish, M. 1978. Multidimensional scaling. Sage University Paper series on Quantitative Application in the Social Sciences 07--011.
[27]
Merrell, P., and Manocha, D. 2008. Continuous model synthesis. ACM Trans. Graph. 27, 5, 1--7.
[28]
Mitra, N. J., Guibas, L., and Pauly, M. 2006. Partial and approximate symmetry detection for 3d geometry. In ACM SIGGRAPH Trans. Graph., vol. 25, 560--568.
[29]
Mitra, N. J., Guibas, L., and Pauly, M. 2007. Symmetrization. In ACM SIGGRAPH Trans. Graph., vol. 26, #63, 1--8.
[30]
Na, K., Jung, M., Lee, J., and Songa, C. G. 2005. Redeeming valleys and ridges for line-drawing. In Advances in Mulitmedia Information Processing, 327--338.
[31]
Nackman, L., and Pizer, S. 1985. Three-dimensional shape description using the symmetric axis transform. IEEE Trans. on PAMI 7, 2, 187--201.
[32]
Nealen, A., Igarashi, T., Sorkine, O., and Alexa, M. 2007. Fibermesh: designing freeform surfaces with 3d curves. ACM SIGGRAPH Trans. Graph. 26, 3, 41.
[33]
Orzan, A., Bousseau, A., Winnemöller, H., Barla, P., Thollot, J., and Salesin, D. 2008. Diffusion curves: A vector representation for smooth-shaded images. In ACM SIGGRAPH Trans. Graph., vol. 27.
[34]
Pauly, M., Mitra, N. J., Wallner, J., Pottmann, H., and Guibas, L. 2008. Discovering structural regularity in 3D geometry. ACM SIGGRAPH Trans. Graph. 27, 3, #43, 1--11.
[35]
Poggio, T., Torre, V., and Koch, C. 1985. Computational vision and regularization theory. Nature 317, 314--319.
[36]
Popa, T., Julius, D., and Sheffer, A. 2006. Material-aware mesh deformations. In SMI, 22.
[37]
Sharf, A., Lewiner, T., Shamir, A., Kobbelt, L., and Cohen-Or, D. 2006. Competing fronts for coarse-to-fine surface reconstruction. Computer Graphics Forum, Proc. of Eurographics 25, 3, 389--398.
[38]
Sheffer, A., Lévy, B., Mogilnitsky, M., and Bogomyakov, A. 2005. Abf++: fast and robust angle based flattening. ACM Trans. Graph. 24, 2, 311--330.
[39]
Shen, C., O'Brien, J. F., and Shewchuk, J. R. 2004. Interpolating and approximating implicit surfaces from polygon soup. In ACM SIGGRAPH Trans. Graph., ACM Press, 896--904.
[40]
Shewchuk, J. 1996. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In Applied Computational Geometry: Towards Geometric Engineering, vol. 1148. Springer-Verlag, 203--222.
[41]
Sorkine, O., Lipman, Y., Cohen-Or, D., Alexa, M., Rössl, C., and Seidel, H.-P. 2004. Laplacian surface editing. In Proc. of Symp. of Geometry Processing, 179--188.
[42]
Sumner, R. W., and Popović, J. 2004. Deformation transfer for triangle meshes. In ACM SIGGRAPH Trans. Graph., 399--405.
[43]
Surazhsky, V., and Gotsman, C. 2003. Explicit surface remeshing. In Proc. of Symp. of Geometry Processing, 17--28.
[44]
Theobalt, C., Rössl, C., de Aguiar, E., and Seidel, H.-P. 2007. Animation collage. In Proc. of Symp. of Computer Animation, 271--280.
[45]
Toledo, S., Chen, D., and Rotkin, V., 2003. Taucs: A library of sparse linear solvers. http://www.tau.ac.il/stoledo/taucs/.
[46]
Várady, T., and Martin, R. R. 2002. Reverse engineering. In Handbook of Computer Aided Geometric Design, G. Farin, J. Hoschek, and M. S. Kim, Eds. Springer, 651--681.
[47]
Wu, J., and Kobbelt, L. 2005. Structure recovery via hybrid variational surface approximation. Computer Graphics Forum, Proc. of Eurographics 24, 3, 277--284.
[48]
Yan, D. M., Liu, Y., and Wang, W. 2006. Quadric surface extraction by variational shape approximation. In Geometric Modeling and Processing, 73--86.

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Published In

cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 28, Issue 5
December 2009
646 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/1618452
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 2009
Published in TOG Volume 28, Issue 5

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Author Tags

  1. NPR
  2. curve network
  3. perception
  4. shape analysis

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