Abstract
This paper introduces a new method for extracting salient features from surfaces that are represented by triangle meshes. Our method extracts salient geometric feature points in the Laplace–Beltrami spectral domain instead of usual spatial domains. Simultaneously, a spatial region is determined as a local support of each feature point, which is correspondent to the “frequency” where the feature point is identified. The local shape descriptor of a feature point is the Laplace–Beltrami spectrum of the spatial region associated to the points which are stable and distinctive. Our method leads to the salient spectral geometric features invariant to spatial transforms such as translation, rotation, and scaling. The properties of the discrete Laplace–Beltrami operator make them invariant to isometric deformations and mesh triangulations as well. With the scale information transformed from the “frequency”, the local supporting region always maintains the same ratio to the original model no matter how it is scaled. This means that the spatial region is scale-invariant as well. Therefore, both global and partial matching can be achieved with these salient feature points. We demonstrate the effectiveness of our method with many experiments and applications.
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References
Bemporad, A., Mignone, D., Morari, M.: An efficient branch and bound algorithm for state estimation and control of hybrid systems. In: Proceedings of European Control Conference (1999)
Chavel, I.: Eigenvalues in Riemannian Geometry. Academic Press, San Diego (1984)
Duda, R.M., Hart, P.E.: Pattern Classification and Scene Analysis. Wiley, New York (1973)
Gal, R., Cohen-Or, D.: Salient geometric features for partial shape matching and similarity. ACM Trans. Graph. 25(1), 130–150 (2006)
Hilaga, M., Shinagawa, Y., Kohmura, T., Kunii, T.L.: Topology matching for fully automatic similarity estimation of 3D shapes. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 203–212 (2001)
Horn, B.K.P.: Extended Gaussian images. In: Proceedings of IEEE, vol. 72, pp. 1671–1686 (1984)
Hua, J., Lai, Z., Dong, M., Gu, X., Qin, H.: Geodesic distance-weighted shape vector image diffusion. IEEE Trans. Vis. Comput. Graph. 14(6), 1643–1650 (2008)
Ip, C., Lapadat, D., Sieger, L., Regli, W.C.: Using shape distributions to compare solid models. In: Proceedings of ACM Symposium on Solid Modeling and Applications, pp. 273–280 (2002)
Iyer, N., Kalyanaraman, Y., Lou, K., Jayanti, S., Ramani, K.: A reconfigurable 3D engineering shape search system: Part I: Shape representation. In: Proceedings of ASME Computers and Information in Engineering Conference, pp. 1–10 (2003)
Karni, Z., Gotsman, C.: Compression of soft-body animation sequences. Comput. Graph. 28(1), 25–34 (2004)
Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant spherical harmonic representation of 3D shape descriptors. In: Proceedings of the ACM/Eurographics Symposium on Geometry Processing, pp. 167–175 (2003)
Kendall, D.G.: The diffusion of shape. Adv. Appl. Probab. 9(3), 428–430 (1977)
Lee, C.H., Varshney, A., Jacobs, D.W.: Mesh saliency. ACM Trans. Graph. 24(3), 659–666 (2005)
Lévy, B.: Laplace–Beltrami eigenfunctions: Towards an algorithm that understand s geometry. In: Proceedings of IEEE International Conference on Shape Modeling and Applications, p. 13 (2006)
Marr, D.: Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. Freeman, New York (1982)
Meyer, M., Desbrun, M., Schröder, P., Barr, A.: Discrete differential geometry operators for triangulated 2-manifolds. In: Proceedings of the VisMath Conference, pp. 1–26 (2002)
Novotni, M., Klein, R.: 3D zernike descriptors for content based shape retrieval. In: Proceedings of ACM Symposium on Solid Modeling and Applications, pp. 216–225 (2003)
Ohbuchi, R., Takei, T.: Shape-similarity comparison of 3D models using alpha shapes. In: Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, pp. 293–302 (2003)
Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. ACM Trans. Graph. 21(4), 807–832 (2002)
Reuter, M., Wolter, F.E., Peinecke, N.: Laplace–Beltrami spectra as “Shape-DNA” of surfaces and solids. Comput. Aided Des. 38(4), 342–366 (2006)
Rustamov, R.M.: Laplace–Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the Fifth Eurographics Symposium on Geometry Processing, pp. 225–233 (2007)
Sadjadi, F.A., Hall, E.L.: Three-dimensional moment invariants. IEEE Trans. Pattern Anal. Mach. Intell. 2(2), 127–136 (1980)
Shum, H., Hebert, M., Ikeuchi, K.: On 3D shape similarity. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 526–531 (1996)
Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton based shape matching and retrieval. In: Proceedings of IEEE International Conference on Shape Modeling and Applications, pp. 130–139 (2003)
Tung, T., Schmittt, F.: Shape retrieval of noisy watertight models using aMRG. In: Proceedings of IEEE International Conference on Shape Modeling and Applications, pp. 229–230 (2008)
Zou, G., Hua, J., Dong, M., Qin, H.: Surface matching with salient keypoints in geodesic scale space. J. Comput. Animat. Virtual Worlds 19(3–4), 399–410 (2008)
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Hu, J., Hua, J. Salient spectral geometric features for shape matching and retrieval. Vis Comput 25, 667–675 (2009). https://doi.org/10.1007/s00371-009-0340-6
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DOI: https://doi.org/10.1007/s00371-009-0340-6