Abstract
Recent advancements in 3D scanning technologies have inspired the development of effective methods for matching and retrieving 3D objects. A common pre-processing stage of these retrieval methods is to normalize the position, size, and orientation of the objects based on PCA. It aligns an object’s orientation based on PCA eigenvectors, and normalizes its size uniformly in all 3 spatial dimensions based on the variance of the object points. However, orientation alignment by PCA is not robust, and objects with similar shape can be misaligned. Uniform scaling of the objects is not ideal because it does not take into account the differences in the objects’ 3D aspect ratios, resulting in misalignment that can exaggerate the shape difference between the objects. This paper presents a method for computing 3D objects’ bilateral symmetry planes (BSPs) and BSP axes and extents, and a method for normalizing 3D objects based on BSP axes and extents. Compared to normalization methods based on PCA and minimum volume bounding box, our BSP-based method can normalize and align similar objects in the same category in a semantically more meaningful manner, such as aligning the objects’ heads, bodies, legs, etc.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Proc. Eurographics Symp. on Geometry Proc. (2003)
Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Matching 3D models with shape distribution. In: Proc. SMI (2001)
Paquet, E., Rioux, M., Murching, A., Naveen, T., Tabatabai, A.: Description of shape information for 2-D and 3-D objects. Signal Processing: Image Communication 16, 103–122 (2000)
Tangelder, J.W.H., Veltkamp, R.C.: Polyhedral model retrieval using weighted point sets. In: Proc. SMI (2003)
Vranic, D.V., Saupe, D.: 3D shape descriptor based on 3D Fourier transform. In: Proc. Conf. Digital Signal Proc. Multimedia Comm. and Services, pp. 271–274 (2001)
Yu, M., Atmosukarto, I., Leow, W.K., Huang, Z., Xu, R.: 3D model retrieval with morphing-based geometric and topological feature maps. In: Proc. IEEE CVPR, pp. II–656–II–661 (2003)
Atmosukarto, I., Leow, W.K., Huang, Z.: Feature combination and relevance feedback for 3D model retrieval. In: Proc. MMM, pp. 334–339 (2005)
Barequet, G., Har-Peled, S.: Efficiently approximating the minimum-volume bou- nding box of a point set in three dimensions. J. Algorithms 38, 91–109 (2001)
Alt, H., Mehlhorn, K., Wagener, H., Welzl, E.: Congruence, similarity and symmetries of geometric objects. Discrete Computational Geometry, 237–256 (1988)
Wolter, J.D., Woo, T.C., Volz, R.A.: Optimal algorithms for symmetry detection in two and three dimensions. Visual Computer 1, 37–48 (1985)
Jiang, X.Y., Bunke, H.: A simple and efficient algorithm for determining the symmetries of polyhedra. CVGIP: Graphical Models & Image Proc 54, 91–95 (1992)
Jiang, X., Yu, K., Bunke, H.: Detection of rotational and involutional symmetries and congruity of polyhedra. Visual Computer 12, 193–201 (1996)
Brass, P., Knauer, C.: Computing the symmetries of non-convex polyhedral objects in 3-space. In: Proc. European Workshop on Comp. Geometry (2002)
Brass, P., Knauer, C.: Testing congruence and symmetry for general 3-dimensional objects. Comp. Geometry: Theory and Applications 27, 3–11 (2004)
Zabrodsky, H., Peleg, S., Avnir, D.: Symmetry as a continuous feature. IEEE Trans. PAMI 17, 1154–1165 (1995)
Minovic, P., Ishikawa, S., Kato, K.: Symmetry identification of a 3d object represented by octree. IEEE Trans. PAMI 15, 507–514 (1993)
Sun, C., Sherrah, J.: 3D symmetry detection using the extended gaussian image. IEEE Trans. PAMI 19, 164–169 (1997)
Jiang, X.Y., Bunke, H.: Determination of the symmetries of polyhedra and an application to object recognition. In: Bieri, H., Noltemeier, H. (eds.) CG-WS 1991. LNCS, vol. 553, pp. 113–121. Springer, Heidelberg (1991)
Kazhdan, M., Chazelle, B., Dobkin, D., Finkelstein, A., Funkhouser, T.: A Reflective Symmetry Descriptor. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 642–656. Springer, Heidelberg (2002)
Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Symmetry descriptors and 3D shape matching. In: Proc. Eurographics Symp. on Geometry Proc, pp. 115–123 (2004)
Utrecht Univeristy Object Database, www.cs.uu.nl/centers/give/imaging/3drecog/3dmatching.html
Princeton University Object Database, shape.cs.princeton.edu/benchmark
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tedjokusumo, J., Leow, W.K. (2006). Normalization and Alignment of 3D Objects Based on Bilateral Symmetry Planes. In: Cham, TJ., Cai, J., Dorai, C., Rajan, D., Chua, TS., Chia, LT. (eds) Advances in Multimedia Modeling. MMM 2007. Lecture Notes in Computer Science, vol 4351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69423-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-69423-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69421-2
Online ISBN: 978-3-540-69423-6
eBook Packages: Computer ScienceComputer Science (R0)