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 -

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