An Elastic Riemannian Framework for Shape of Curves and Tree-Like Structures

Algorithmic Advances in Riemannian Geometry and Applications - Advances in Computer Vision and Pattern Recognition ◽

10.1007/978-3-319-45026-1_8 ◽

2016 ◽

pp. 187-205

Author(s):

Adam Duncan ◽

Zhengwu Zhang ◽

Anuj Srivastava

Keyword(s):

Riemannian Framework

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A nonparametric Riemannian framework for processing high angular resolution diffusion images (HARDI)

2009 IEEE Conference on Computer Vision and Pattern Recognition ◽

10.1109/cvprw.2009.5206843 ◽

2009 ◽

Cited By ~ 2

Author(s):

A. Goh ◽

C. Lenglet ◽

P.M. Thompson ◽

R. Vidal

Keyword(s):

Angular Resolution ◽

High Angular Resolution ◽

Riemannian Framework

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Diffeomorphism Invariant Riemannian Framework for Ensemble Average Propagator Computing

Lecture Notes in Computer Science - Medical Image Computing and Computer-Assisted Intervention – MICCAI 2011 ◽

10.1007/978-3-642-23629-7_13 ◽

2011 ◽

pp. 98-106 ◽

Cited By ~ 3

Author(s):

Jian Cheng ◽

Aurobrata Ghosh ◽

Tianzi Jiang ◽

Rachid Deriche

Keyword(s):

Ensemble Average ◽

Ensemble Average Propagator ◽

Riemannian Framework

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Statistics on Lie groups: A need to go beyond the pseudo-Riemannian framework

10.1063/1.4905963 ◽

2015 ◽

Author(s):

Nina Miolane ◽

Xavier Pennec

Keyword(s):

Lie Groups ◽

Riemannian Framework

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A Riemannian Framework for Statistical Shape Analysis of the Corpus Callosum.

NeuroImage ◽

10.1016/s1053-8119(09)71176-0 ◽

2009 ◽

Vol 47 ◽

pp. S123

Author(s):

SH Joshi ◽

KL Narr ◽

RP Woods ◽

OR Phillips ◽

KH Nuechterlein ◽

...

Keyword(s):

Corpus Callosum ◽

Shape Analysis ◽

Statistical Shape Analysis ◽

Statistical Shape ◽

Riemannian Framework

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A nonparametric Riemannian framework on tensor field with application to foreground segmentation

2011 International Conference on Computer Vision ◽

10.1109/iccv.2011.6126218 ◽

2011 ◽

Cited By ~ 10

Author(s):

Rui Caseiro ◽

Joao F. Henriques ◽

Pedro Martins ◽

Jorge Batista

Keyword(s):

Tensor Field ◽

Foreground Segmentation ◽

Riemannian Framework

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A Novel Riemannian Framework for Shape Analysis of Annotated Surfaces

Procedings of the Proceedings of the 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories 2015 ◽

10.5244/c.29.diffcv.3 ◽

2015 ◽

Cited By ~ 2

Author(s):

Jiaqi Zaetz ◽

Sebastian Kurtek

Keyword(s):

Shape Analysis ◽

Riemannian Framework

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Thermodynamic and Kinetic Characterization of Protein Conformational Dynamics within a Riemannian Framework

10.1101/2021.01.19.427358 ◽

2021 ◽

Author(s):

Curtis Goolsby ◽

Ashkan Fakharzadeh ◽

Mahmoud Moradi

Keyword(s):

Free Energy ◽

Transition Rate ◽

Conformational Dynamics ◽

Diffusion Constant ◽

Minimum Free Energy ◽

Umbrella Sampling ◽

Potential Of Mean Force ◽

Collective Variable ◽

Bayesian Estimator ◽

Riemannian Framework

AbstractWe have formulated a Riemannian framework for describing the geometry of collective variable spaces of biomolecules within the context of molecular dynamics (MD) simulations. The formalism provides a theoretical framework to develop enhanced sampling techniques, path-finding algorithms, and transition rate estimators consistent with a Riemannian treatment of the collective variable space, where the quantities of interest such as the potential of mean force (PMF) and minimum free energy path (MFEP) remain invariant under coordinate transformation. Specific algorithms within this framework are discussed such as the Riemannian umbrella sampling, the Riemannian string method, and a Riemannian-Bayesian estimator of free energy and diffusion constant, which can be used to estimate the transition rate along an MFEP.

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