Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

Tao Liao; Hao-Chih Lee; Ge Yang; Yongjie Jessica Zhang

Molecular Based Mathematical Biology (2015)

  • Volume: 3, Issue: 1
  • ISSN: 2299-3266

Abstract

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The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the order of modes. An initial correspondence is built based on the distribution of a shape diameter, which matches similar surface features in different shapes and guides the eigenfunction computation. A two-step scheme is developed to determine the final correspondence. The first step utilizes volumetric eigenfunctions to correct the assignment of boundary nodes that disobeys the main structures. The second step minimizes the distortion induced by deforming one shape to the other. As a result, a dense point correspondence is constructed between the two given shapes, based on which we approximate and predict the shape deformation, as well as quantitatively measure the detailed shape differences.

How to cite

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Tao Liao, et al. "Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions." Molecular Based Mathematical Biology 3.1 (2015): null. <http://eudml.org/doc/275856>.

@article{TaoLiao2015,
abstract = {The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the order of modes. An initial correspondence is built based on the distribution of a shape diameter, which matches similar surface features in different shapes and guides the eigenfunction computation. A two-step scheme is developed to determine the final correspondence. The first step utilizes volumetric eigenfunctions to correct the assignment of boundary nodes that disobeys the main structures. The second step minimizes the distortion induced by deforming one shape to the other. As a result, a dense point correspondence is constructed between the two given shapes, based on which we approximate and predict the shape deformation, as well as quantitatively measure the detailed shape differences.},
author = {Tao Liao, Hao-Chih Lee, Ge Yang, Yongjie Jessica Zhang},
journal = {Molecular Based Mathematical Biology},
keywords = {shape correspondence; biomolecular shape; volumetric eigenfunction; joint graph; deformation approximation; shape comparison},
language = {eng},
number = {1},
pages = {null},
title = {Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions},
url = {http://eudml.org/doc/275856},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Tao Liao
AU - Hao-Chih Lee
AU - Ge Yang
AU - Yongjie Jessica Zhang
TI - Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions
JO - Molecular Based Mathematical Biology
PY - 2015
VL - 3
IS - 1
SP - null
AB - The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the order of modes. An initial correspondence is built based on the distribution of a shape diameter, which matches similar surface features in different shapes and guides the eigenfunction computation. A two-step scheme is developed to determine the final correspondence. The first step utilizes volumetric eigenfunctions to correct the assignment of boundary nodes that disobeys the main structures. The second step minimizes the distortion induced by deforming one shape to the other. As a result, a dense point correspondence is constructed between the two given shapes, based on which we approximate and predict the shape deformation, as well as quantitatively measure the detailed shape differences.
LA - eng
KW - shape correspondence; biomolecular shape; volumetric eigenfunction; joint graph; deformation approximation; shape comparison
UR - http://eudml.org/doc/275856
ER -

References

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  1.  
  2. [1] M. Carcassoni and E. Hancock. Correspondence matching with modal clusters. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(12):1609–1615, 2003. [Crossref] 
  3. [2] F. Chung. Spectral graph theory. American Mathematical Soc., 1997. Zbl0867.05046
  4. [3] S. Dong, S. Kircher, and M. Garland. Harmonic functions for quadrilateral remeshing of arbitrarymanifolds. Computer aided geometric design, 22(5):392–423, 2005. Zbl1205.65116
  5. [4] Z. Gao, Z. Yu, and X. Pang. A compact shape descriptor for triangular surface meshes. Computer-Aided Design, 53:62–69, 2014. [WoS] 
  6. [5] M. Hilaga, Y. Shinagawa, T. Kohmura, and T. Kunii. Topologymatching for fully automatic similarity estimation of 3D shapes. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pages 203–212, 2001. 
  7. [6] V. Jain and H. Zhang. Robust 3D shape correspondence in the spectral domain. In Shape Modeling and Applications 2006, pages 19–32, 2006. 
  8. [7] O. Van Kaick, H. Zhang, G. Hamarneh, and D. Cohen-Or. A survey on shape correspondence. Computer Graphics Forum, 30(6):1681–1707, 2011. [Crossref][WoS] 
  9. [8] H.-C. Lee and G. Yang. Integrating dimension reduction with mean-shift clustering for biological shape classification. In IEEE 11th International Symposium on Biomedical Imaging (ISBI), pages 254–257, 2014. 
  10. [9] Z. Li, S. Qin, Z. Yu, and Y. Jin. Skeleton-based shape analysis of protein models. Journal ofMolecular Graphics andModelling, 53:72–81, 2014. 
  11. [10] Z. Lian, A. Godil, B. Bustos, M. Daoudi, J. Hermans, S. Kawamura, Y. Kurita, G. Lavoué, H. Van Nguyen, and R. Ohbuchi. A comparison of methods for non-rigid 3D shape retrieval. IEEE Transactions on Pattern Recognition, 46(1):449–461, 2013. [Crossref][WoS] 
  12. [11] T. Liao, G. Xu, and Y. Zhang. Structure-aligned guidance estimation in surface parameterization using eigenfunction-based cross field. Graphical Models, 76:691–705, 2014. 
  13. [12] T. Liao, Y. Zhang, P. Kekenes-Huskey, Y. Cheng, A. Michailova, A.D. McCulloch, M. Holst, and J.A. McCammon. Multi-core CPU or GPU-accelerated multiscale modeling for biomolecular complexes. Molecular Based Mathematical Biology, 1:164–179, 2013. Zbl1276.92030
  14. [13] H. Lombaert, L. Grady, J. Polimeni, and F. Cheriet. Fast brain matching with spectral correspondence. In Information Processing in Medical Imaging, pages 660–673, 2011. 
  15. [14] H. Lombaert, L. Grady, J. Polimeni, and F. Cheriet. Focusr: Feature oriented correspondence using spectral regularization – a method for precise surface matching. Pattern Analysis and Machine Intelligence, 35(9):2143–2160, 2013. [WoS] 
  16. [15] H. Lombaert, J. Sporring, and K. Siddiqi. Diffeomorphic spectral matching of cortical surfaces. In Information Processing in Medical Imaging, pages 376–389, 2013. 
  17. [16] D. Mateus, R. Horaud, D. Knossow, F. Cuzzolin, and E. Boyer. Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration. IEEE Conference on Computer Vision and Pattern Recognition, pages 1–8, 2008. 
  18. [17] D. Mateus, R. Horaud, D. Knossow, F. Cuzzolin, and E. Boyer. Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration. In IEEE Conference on Computer Vision and Pattern Recognition, pages 1–8, 2008. 
  19. [18] M. Niethammer, M. Reuter, F. Wolter, S. Bouix, N. Peinecke, M. Koo, and M. Shenton. Global medical shape analysis using the Laplace-Beltrami spectrum. In Medical Image Computing and Computer-Assisted Intervention – MICCAI, pages 850–857. 2007. 
  20. [19] M. Reuter. Hierarchical shape segmentation and registration via topological features of Laplace-Beltrami eigenfunctions. International Journal of Computer Vision, 89(2-3):287–308, 2010. [WoS][Crossref] 
  21. [20] M. Reuter, F. Wolter, and N. Peinecke. Laplace-spectra as fingerprints for shape matching. In Proceedings of the ACM symposium on solid and physical modeling, pages 101–106, 2005. 
  22. [21] M. Reuter, F. Wolter, and N. Peinecke. Laplace-Beltrami spectra as "Shape-DNA" of surfaces and solids. Computer-Aided Design, 38(4):342–366, 2006. [Crossref] 
  23. [22] G. Scott and H. C. Longuet-Higgins. An algorithm for associating the features of two images. Proceedings of the Royal Society of London. Series B: Biological Sciences, 244(1309):21–26, 1991. 
  24. [23] L. Shapiro and J. Michael Brady. Feature-based correspondence: an eigenvector approach. Image and Vision Computing, 10(5):283–288, 1992. [Crossref] 
  25. [24] O. Sorkine and M. Alexa. As-rigid-as-possible surface modeling. In ACM International Conference Proceeding Series, volume 257, pages 109–116, 2007. 
  26. [25] S. Umeyama. An eigendecomposition approach to weighted graph matching problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(5):695–703, 1988. [Crossref][WoS] Zbl0678.05049
  27. [26] Y. Zhang, C. L. Bajaj, and B. Sohn. 3D finite element meshing from imaging data. Computer Methods in Applied Mechanics and Engineering, 194(48–49):5083–5106, 2005. Zbl1093.65019

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