Newton's method on Riemannian manifolds and a geometric model for the human spine

Roy L. Adler; Jean Pierre Dedieu; Joseph Y. Margulies; Marco Martens; Mike Shub

doi:10.1093/imanum/22.3.359

Newton's method on Riemannian manifolds and a geometric model for the human spine

Roy L. Adler
, Jean Pierre Dedieu
, Joseph Y. Margulies
, Marco Martens
, Mike Shub

Mathematics

IBM
Laboratoire Evolution et Diversité Biologique, CNRS, Université Paul Sabatier
Orthopaedic Spine Surgeon

Research output: Contribution to journal › Article › peer-review

243 Scopus citations

Abstract

To study a geometric model of the human spine we are led to finding a constrained minimum of a real valued function defined on a product of special orthogonal groups. To take advantge of its Lie group structure we consider Newton's method on this manifold. Comparisons between measured spines and computed spines show the pertinence of this approach.

Original language	English
Pages (from-to)	359-390
Number of pages	32
Journal	IMA Journal of Numerical Analysis
Volume	22
Issue number	3
DOIs	https://doi.org/10.1093/imanum/22.3.359
State	Published - Jul 2002

Keywords

Human spine
Newton's method
Orthogonal group
Riemannian manifold

Access to Document

10.1093/imanum/22.3.359

Cite this

@article{bea236d1b9a04e718cdbbbb56c7c7a39,

title = "Newton's method on Riemannian manifolds and a geometric model for the human spine",

abstract = "To study a geometric model of the human spine we are led to finding a constrained minimum of a real valued function defined on a product of special orthogonal groups. To take advantge of its Lie group structure we consider Newton's method on this manifold. Comparisons between measured spines and computed spines show the pertinence of this approach.",

keywords = "Human spine, Newton's method, Orthogonal group, Riemannian manifold",

author = "Adler, \{Roy L.\} and Dedieu, \{Jean Pierre\} and Margulies, \{Joseph Y.\} and Marco Martens and Mike Shub",

year = "2002",

month = jul,

doi = "10.1093/imanum/22.3.359",

language = "English",

volume = "22",

pages = "359--390",

journal = "IMA Journal of Numerical Analysis",

issn = "0272-4979",

number = "3",

}

TY - JOUR

T1 - Newton's method on Riemannian manifolds and a geometric model for the human spine

AU - Adler, Roy L.

AU - Dedieu, Jean Pierre

AU - Margulies, Joseph Y.

AU - Martens, Marco

AU - Shub, Mike

PY - 2002/7

Y1 - 2002/7

N2 - To study a geometric model of the human spine we are led to finding a constrained minimum of a real valued function defined on a product of special orthogonal groups. To take advantge of its Lie group structure we consider Newton's method on this manifold. Comparisons between measured spines and computed spines show the pertinence of this approach.

AB - To study a geometric model of the human spine we are led to finding a constrained minimum of a real valued function defined on a product of special orthogonal groups. To take advantge of its Lie group structure we consider Newton's method on this manifold. Comparisons between measured spines and computed spines show the pertinence of this approach.

KW - Human spine

KW - Newton's method

KW - Orthogonal group

KW - Riemannian manifold

UR - https://www.scopus.com/pages/publications/0345447647

U2 - 10.1093/imanum/22.3.359

DO - 10.1093/imanum/22.3.359

M3 - Article

AN - SCOPUS:0345447647

SN - 0272-4979

VL - 22

SP - 359

EP - 390

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 3

ER -

Newton's method on Riemannian manifolds and a geometric model for the human spine

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this