Intrinsic Spatial Pyramid Matching

This is the package to demonstrate ISPM. It can

1. Visualize the functions and partitions on 3D meshed surfaces;
2. Perform the Intrinsic Spatial Pyramid Matching of shapes.

Why ISPM?	2nd Eigenfunction performs Intrinsic Cuts	Invariant to Shape Deformation

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

Citation

If you use this code for your research, please cite our paper: Intrinsic Spatial Pyramid Matching

@article{li2013intrinsic,
  title={Intrinsic spatial pyramid matching for deformable 3d shape retrieval},
  author={Li, Chunyuan and Hamza, A Ben},
  journal={International Journal of Multimedia Information Retrieval},
  volume={2},
  number={4},
  pages={261--271},
  year={2013},
  publisher={Springer}
}

Instructions:

Data: The first 4 shapes in shrec2011 nonrigid dataset [9] are used in this package.

1. Visualize the partition of 2nd eigenfunction 

Step 1. Please open 'demo_visualize_isocontours.m'; Step 2. To set the number of isocontours, change 'Nlines''; Step 3. Run the demo, it will visualize both the values and isocontours of 2nd eigenfunction.

2. Intrinsic Spatial Pyramid Matching (ISPM)

Step 1. Please open 'demo_ISPM.m'; Step 2. Set the parameters of in 'setting_up.m', including the pyramid paritions 'pyramid'. Step 3. Run 'demo_ISPM.m', it will perform ISPM and display the distances with different combinations.

Note that any of the following local descriptors can be incorporated as the input of ISPM, we use SGWS [7] in this demo. We surveyed the performance of these descriptors in [8], and found GPS [1] is not compatible with ISPM due to the sgin flip.

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].

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.