Skip to main content
SpringerLink
Log in

Feature-Preserved 3D Canonical Form

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

Measuring the dissimilarity between non-rigid objects is a challenging problem in 3D shape retrieval. One potential solution is to construct the models’ 3D canonical forms (i.e., isometry-invariant representations in 3D Euclidean space) on which any rigid shape matching algorithm can be applied. However, existing methods, which are typically based on embedding procedures, result in greatly distorted canonical forms, and thus could not provide satisfactory performance to distinguish non-rigid models.

In this paper, we present a feature-preserved canonical form for non-rigid 3D watertight meshes. The basic idea is to naturally deform original models against corresponding initial canonical forms calculated by Multidimensional Scaling (MDS). Specifically, objects are first segmented into near-rigid subparts, and then, through properly-designed rotations and translations, original subparts are transformed into poses that correspond well with their positions and directions on MDS canonical forms. Final results are obtained by solving nonlinear minimization problems for optimal alignments and smoothing boundaries between subparts. Experiments on two non-rigid 3D shape benchmarks not only clearly verify the advantages of our algorithm against existing approaches, but also demonstrate that, with the help of the proposed canonical form, we can obtain significantly better retrieval accuracy compared to the state of the art.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Alexa, M., Cohen-Or, D., & Levin, D. (2000). As-rigid-as-possible shape interpolation. In Proc. SIGGRAPH (pp. 157–164).

    Chapter  Google Scholar 

  • Borg, I., & Groenen, P. (1997). Modern multidimensional scaling—theory and applications. Berlin: Springer.

    MATH  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2006). Efficient computation of isometry-invariant distances between surfaces. SIAM Journal on Scientific Computing, 28(5), 1812–1836.

    Article  MathSciNet  MATH  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2008). Numerical geometry of non-rigid shapes. Berlin: Springer.

    MATH  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., Kimmel, R., Mahmoudi, M., & Sapiro, G. (2010). A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. International Journal of Computer Vision, 89(2–3), 266–286.

    Article  Google Scholar 

  • Chen, D. Y., Tian, X. P., Shen, Y. T., & Ouhyoung, M. (2003). On visual similarity based 3D model retrieval. In Proc. Eurographics 2003 (pp. 223–232).

    Google Scholar 

  • Chen, X., Golovinskiy, A., & Funkhouser, T. (2009). A benchmark for 3D mesh segmentation. ACM Transactions on Graphics, 28(3). doi:10.1145/1531326.1531379.

  • Chui, H., & Rangarajan, A. (2003). A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding, 89(2–3), 114–141.

    Article  MATH  Google Scholar 

  • Cox, M. A., & Cox, T. F. (1994). Multidimensional scaling. London/New York: Chapman and Hall.

    MATH  Google Scholar 

  • Davis, T. A. (2011). Algorithm 915, SuiteSparseQR: multifrontal multithreaded rank-revealing sparse QR factorization. ACM Transactions on Mathematical Software, 38(1). doi:10.1145/2049662.2049670.

  • Elad, A., & Kimmel, R. (2003). On bending invariant signatures for surface. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(10), 1285–1295.

    Article  Google Scholar 

  • Faloutsos, C., & Lin, K. D. (1995). A fast algorithm for indexing, data-mining and visualisation of traditional and multimedia datasets. In Proc. ACM SIGMOD (pp. 163–174).

    Google Scholar 

  • Funkhouser, T., & Shilane, P. (2006). Partial matching of 3D shapes with priority-driven search. In Proc. symposium on geometry processing (SGP’06) (pp. 131–142).

    Google Scholar 

  • Gal, R., Shamir, A., & Cohen-Or, D. (2007). Pose-oblivious shape signature. IEEE Transactions on Visualization and Computer Graphics, 13(2), 261–271.

    Article  Google Scholar 

  • Hilaga, M., Shinagawa, Y., Kohmura, T., & Kunii, T. L. (2001). Topology matching for fully automatic similarity estimation of 3D shapes. In Proc. SIGGRAPH (pp. 203–212).

    Google Scholar 

  • Huang, Q., Adams, B., Wicke, M., & Guibas, L. J. (2008). Non-rigid registration under isometric deformations. Computer Graphics Forum, 27(5), 1449–1457.

    Article  Google Scholar 

  • Jain, V., & Zhang, H. (2007). A spectral approach to shape-based retrieval of articulated 3D models. Computer Aided Design, 39(5), 398–407.

    Article  Google Scholar 

  • Johnson, A. E., & Hebert, M. (1999). Using spin images for efficient object recognition in cluttered 3D scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(5), 433–449.

    Article  Google Scholar 

  • Kazhdan, M., Funkhouser, T., & Rusinkiewicz, S. (2003). Rotation invariant spherical harmonic representation of 3D shape descriptors. In Proc. symposium on geometry processing (SGP’03) (pp. 156–164).

    Google Scholar 

  • Lai, Y., Hu, S., Martin, R. R., & Rosin, P. L. (2008). Fast mesh segmentation using random walks. In Proc. SPM’08 (pp. 183–191).

    Google Scholar 

  • Lian, Z., & Godil, A. (2011). A feature-preserved canonical form for 3D meshes. In Proc. international conference on 3D imaging, modeling, processing, visualization and transmission (3DIMPVT’11) (pp. 116–123).

    Chapter  Google Scholar 

  • Lian, Z., Godil, A., & Sun, X. (2010a). Visual similarity based 3D shape retrieval using bag-of-features. In Proc. shape modeling international (SMI’10) (pp. 25–36).

    Google Scholar 

  • Lian, Z., Godil, A., Sun, X., & Zhang, H. (2010b). Non-rigid 3D shape retrieval using multidimensional scaling and bag-of-features. In Proc. international conference on image processing (ICIP 2010) (pp. 3181–3184).

    Chapter  Google Scholar 

  • Lian, Z., Rosin, P. L., & Sun, X. (2010c). Rectilinearity of 3D meshes. International Journal of Computer Vision, 89(2–3), 130–151.

    Article  Google Scholar 

  • Liu, Y., Zha, H., & Qin, H. (2006). Shape topics: a compact representation and new algorithms for 3D partial shape retrieval. In Proc. IEEE conference on computer vision and pattern recognition (CVPR’06) (pp. 2025–2032).

    Google Scholar 

  • Lowe, D. G. (2004). Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision, 60(2), 91–110.

    Article  Google Scholar 

  • Mahmoudi, M., & Sapiro, G. (2009). Three-dimensional point cloud recognition via distributions of geometric distances. Graphical Models, 71(1), 22–31.

    Article  Google Scholar 

  • Mateus, D., Cuzzolin, F., Horaud, R., & Boyer, E. (2007). Articulated shape matching using locally linear embedding and orthogonal alignment. In Proc. international conference on computer vision (ICCV’07) (pp. 1–8).

    Google Scholar 

  • Memoli, F. (2007). On the use of Gromov-Hausdorff distances for shape comparison. In Proc. SPG’07 (pp. 81–90).

    Google Scholar 

  • Memoli, F., & Sapiro, G. (2005). A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics, 5(3), 313–347.

    Article  MathSciNet  MATH  Google Scholar 

  • Morris, D. (2006). Voxelizer: floodfilling and distance map generation for 3D surfaces. http://techhouseorg/~dmorris/projects/voxelizer/.

  • Ohbuchi, R., Osada, K., Furuya, T., & Banno, T. (2008). Salient local visual features for shape-based 3D model retrieval. In Proc. shape modeling international (SMI’08) (pp. 93–102).

    Google Scholar 

  • Osada, R., Funkhouser, T., Chazelle, B., & Dobkin, D. (2002). Shape distributions. ACM Transactions on Graphics, 21(4), 807–832.

    Article  Google Scholar 

  • Ovsjanikov, M., Bronstein, A. M., Bronstein, M. M., & Guibas, L. (2009). Shape google: a computer vision approach to isometry invariant shape retrieval. In Proc. NORDIA’09 (pp. 320–327).

    Google Scholar 

  • Philipp-Foliguet, S., Jordan, M., Najman, L., & Cousty, J. (2011). Artwork 3D model database indexing and classification. Pattern Recognition, 44(3), 588–597.

    Article  MATH  Google Scholar 

  • Reuter, M., Wolter, F. E., & Peinecke, N. (2005). Laplace-spectra as fingerprints for shape matching. In Proc. SPM’05 (pp. 101–106).

    Google Scholar 

  • Rustamov, R. M. (2007). Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In Proc. symposium on geometry processing (SGP’07) (pp. 225–233).

    Google Scholar 

  • Shilane, P., Min, P., Kazhdan, M., & Funkhouser, T. (2004). The Princeton shape benchmark. In Proc. shape modeling international (SMI’04) (pp. 167–178).

    Chapter  Google Scholar 

  • Siddiqi, K., Zhang, J., Macrini, D., Shokoufandeh, A., Bouix, S., & Dickinson, S. (2008). Retrieving articulated 3D models using medial surfaces. Machine Vision and Applications, 19(4), 261–275.

    Article  Google Scholar 

  • Sumner, R. W., & Popovic, J. (2004). Deformation transfer for triangle meshes. In Proc. SIGGRAPH (pp. 399–405).

    Google Scholar 

  • Sun, J., Ovsjanikov, M., & Guibas, L. (2009). A concise and provably informative multi-scale signature based on heat diffusion. In Proc. symposium on geometry processing (SGP’09) (pp. 1383–1392).

    Google Scholar 

  • Sundar, H., Silver, D., Gagvani, N., & Dickinson, S. (2003). Skeleton based shape matching and retrieval. In Proc. shape modeling international (SMI’03) (pp. 130–139).

    Chapter  Google Scholar 

  • Tam, G., & Lau, R. (2007). Deformable model retrieval based on topological and geometric signatures. IEEE Transactions on Visualization and Computer Graphics, 13(3), 470–482.

    Article  MathSciNet  Google Scholar 

  • Tangelder, J. W., & Veltkamp, R. C. (2008). A survey of content based 3D shape retrieval methods. Multimedia Tools and Applications, 39(3), 441–471.

    Article  Google Scholar 

  • Toldo, R., Castellani, U., & Fusiello, A. (2009). Visual vocabulary signature for 3D object retrieval and partial matching. In Proc. Eurographics workshop on 3D object retrieval (3DOR’09) (pp. 21–28).

    Google Scholar 

  • Wang, X., Liu, Y., & Zha, H. (2010). Intrinsic spin images: a subspace decomposition approach to understanding 3D deformable shapes. In Proc. international symposium on 3D data processing, visualization and transmission (3DPVT’10) (pp. 17–20).

    Google Scholar 

  • Wuhrer, S., Azouz, Z. B., & Shu, C. (2010). Posture invariant surface description and feature extraction. In Proc. IEEE conference on computer vision and pattern recognition (CVPR’10) (pp. 374–381).

    Google Scholar 

  • Zunic, J., & Rosin, P. L. (2004). A new convexity measure for polygons. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(7), 923–934.

    Article  Google Scholar 

Download references

Acknowledgements

This work has been supported by China Postdoctoral Science Foundation (Grant No.: 2012M510274), the SIMA program and the Shape Metrology IMS. We would like to thank the anonymous reviewers for their constructive comments, and Xu-Lei Wang for providing his results that have been compared in this paper.

Author information

Authors and Affiliations

  1. Institute of Computer Science and Technology, Peking University, Beijing, P.R. China

    Zhouhui Lian & Jianguo Xiao

  2. National Institute of Standards and Technology, Gaithersburg, USA

    Afzal Godil

Authors
  1. Zhouhui Lian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Afzal Godil
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianguo Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhouhui Lian.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lian, Z., Godil, A. & Xiao, J. Feature-Preserved 3D Canonical Form. Int J Comput Vis 102, 221–238 (2013). https://doi.org/10.1007/s11263-012-0548-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11263-012-0548-1

Keywords

Search

Navigation