Authors: Chunyuan Li [email protected]

Visualization of Different Spectral Descriptors

Heat Kernel Signature (HKS)	Wave Kernel Signature (WKS)	Spectral Graph Wavelet Signature (SGWS)

Please see more details in my Slides and Master Thesis, or Wikipedia

Citation

If you use this code for your research, please cite our papers

Spectral Graph Wavelet Signature:

@article{li2013multiresolution,
  title={A multiresolution descriptor for deformable 3D shape retrieval},
  author={Li, Chunyuan and Hamza, A Ben},
  journal={The Visual Computer},
  volume={29},
  number={6-8},
  pages={513--524},
  year={2013},
  publisher={Springer}
}

Empirical Comparison of Spectral Descriptors

@article{li2014spatially,
  title={Spatially aggregating spectral descriptors for nonrigid 3D shape retrieval: a comparative survey},
  author={Li, Chunyuan and Hamza, A Ben},
  journal={Multimedia Systems},
  volume={20},
  number={3},
  pages={253--281},
  year={2014},
  publisher={Springer}
}

If you are are interested in spatial pyramid matching on 3D surfaces, please check out Intrinsic SPM

How to use the code

1. Open 'demo_spectral_descriptor.m'.

2. Set the type of spectral descriptor by spectifying the variable 'DescriptorType'. Global Point Signature (GPS) [1], Heat Kernel Signature (HKS) [2] [3], Wave Kernel Signature (WKS) [4], Scale Invariant Heat Kernel Signature (SIHKS) [5], Heat mean signature (HMS) [6], Spectral Graph Wavelet Signature (SGWS) [7]

3. Set the parameters of the spectral descriptor in 'PARAMETERS_test.m'. We provide a list of the parameters for the SHREC'11 nonrigid dataset [9] in 'PARAMETERS_SS_shrec2011_nonrigid.m' for your reference.

4. Run 'demo_spectral_descriptor.m', 'desc' is the resulted spectral descritptor, and one dimension is visualied in the demo.

If you use the software package, please cite the pespective papers and our review paper [8] associated with the package. If you use 'sgwt_toolbox', please also cite [10].

References

[1] Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of symposium on geometry processing, pp. 225–233 (2007)

[2] Sun, J., Ovsjanikov, M., Guibas, L.J.: A concise and provably informative multi-scale signature based on heat diffusion. Comput. Graph. Forum 28(5), 1383–1392 (2009)

[3] K. Gebal, J. A. Bærentzen, H. Aanæs, and R. Larsen. Shape analysis using the auto diffusion function. In Computer Graphics Forum, volume 28, pp 1405–1413 (2009).

[4] Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: Proceedings of computational methods for the innovative design of electrical devices, pp. 1626–1633 (2011)

[5] Kokkinos, I., Bronstein, M.M., Yuille, A.: Dense scale-invariant descriptors for images and surfaces. Research Report, INRIA RR-7914 (2012)

[6] Fang, Y., Sun, M., Kim, M., Ramani, K.: Heat-mapping: a robust approach toward perceptually consistent mesh segmentation. In: Proc. CVPR, pp. 2145–2152 (2011)
[7] Li, Chunyuan, and A. Ben Hamza. "A multiresolution descriptor for deformable 3D shape retrieval." The Visual Computer 29.6-8 (2013): 513-524.

[8] Li, Chunyuan, and A. Ben Hamza. "Spatially aggregating spectral descriptors for nonrigid 3D shape retrieval: a comparative survey." Multimedia Systems: 1-29.

[9] Lian, Z., Godil, A., et al.: SHREC'11 track: Shape retrieval on non-rigid 3D watertight meshes. In Proc. of Eurographics on 3DOR, 2011.

[10] Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmon. Anal. 30(2), 129–150 (2011)