Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration

Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match shapes by aligning their embeddings in virtue of their invarian...

Full description

Saved in:
Bibliographic Details
Published in:2008 IEEE Conference on Computer Vision and Pattern Recognition pp. 1 - 8
Main Authors: Mateus, Diana, Horaud, Radu, Knossow, David, Cuzzolin, Fabio, Boyer, Edmond
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2008
Subjects:
Clustering algorithms
Eigenvalues and eigenfunctions
Fellows
Graph theory
Histograms
Kernel
Laplace equations
Noise shaping
Shape
Topology
ISBN:9781424422425, 1424422426
ISSN:1063-6919, 1063-6919
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match shapes by aligning their embeddings in virtue of their invariance to change of pose. Classical graph isomorphism schemes relying on the ordering of the eigenvalues to align the eigenspaces fail when handling large data-sets or noisy data. We derive a new formulation that finds the best alignment between two congruent K-dimensional sets of points by selecting the best subset of eigenfunctions of the Laplacian matrix. The selection is done by matching eigenfunction signatures built with histograms, and the retained set provides a smart initialization for the alignment problem with a considerable impact on the overall performance. Dense shape matching casted into graph matching reduces then, to point registration of embeddings under orthogonal transformations; the registration is solved using the framework of unsupervised clustering and the EM algorithm. Maximal subset matching of non identical shapes is handled by defining an appropriate outlier class. Experimental results on challenging examples show how the algorithm naturally treats changes of topology, shape variations and different sampling densities.
AbstractList Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match shapes by aligning their embeddings in virtue of their invariance to change of pose. Classical graph isomorphism schemes relying on the ordering of the eigenvalues to align the eigenspaces fail when handling large data-sets or noisy data. We derive a new formulation that finds the best alignment between two congruent K-dimensional sets of points by selecting the best subset of eigenfunctions of the Laplacian matrix. The selection is done by matching eigenfunction signatures built with histograms, and the retained set provides a smart initialization for the alignment problem with a considerable impact on the overall performance. Dense shape matching casted into graph matching reduces then, to point registration of embeddings under orthogonal transformations; the registration is solved using the framework of unsupervised clustering and the EM algorithm. Maximal subset matching of non identical shapes is handled by defining an appropriate outlier class. Experimental results on challenging examples show how the algorithm naturally treats changes of topology, shape variations and different sampling densities.
Author Horaud, Radu
Boyer, Edmond
Cuzzolin, Fabio
Mateus, Diana
Knossow, David
Author_xml – sequence: 1
  givenname: Diana
  surname: Mateus
  fullname: Mateus, Diana
  email: diana.mateus@inrialpes.fr
  organization: INRIA Rhone-Alpes, 655 avenue de l'Europe- Montbonnot, 38 334 Saint Ismier Cedex France
– sequence: 2
  givenname: Radu
  surname: Horaud
  fullname: Horaud, Radu
  organization: INRIA Rhone-Alpes, 655 avenue de l'Europe- Montbonnot, 38 334 Saint Ismier Cedex France
– sequence: 3
  givenname: David
  surname: Knossow
  fullname: Knossow, David
  organization: INRIA Rhone-Alpes, 655 avenue de l'Europe- Montbonnot, 38 334 Saint Ismier Cedex France
– sequence: 4
  givenname: Fabio
  surname: Cuzzolin
  fullname: Cuzzolin, Fabio
  organization: INRIA Rhone-Alpes, 655 avenue de l'Europe- Montbonnot, 38 334 Saint Ismier Cedex France
– sequence: 5
  givenname: Edmond
  surname: Boyer
  fullname: Boyer, Edmond
  organization: INRIA Rhone-Alpes, 655 avenue de l'Europe- Montbonnot, 38 334 Saint Ismier Cedex France
BookMark eNpVUE1LAzEUjFpBrf0B4iV_YGu-NpscS_ELCooUb1Jek5c20qbLJiv4722xB53DzGFmHo-5IoO0S0jIDWdjzpm9m76_vo0FY2asatPU0pyQkW0MV0IpIZQUp-SSMy0rbbk9--eJevDHuyCjnD_ZHqqWmutL8jHpSnT9Bgp6mtfQIt1CceuYVrTPB55BuwEXIVGMK0yhT67EXcoUkqd9yn2L3VfM-3q7i6nQDlcxlw4OoWtyHmCTcXTUIZk_3M-nT9Xs5fF5OplVa25FqUAj2Bp4ExrDeOOYV8Jwiw4N8xyU8daGZrkUxgevHHdah_3_qGVQgEwOye3v2YiIi7aLW-i-F8et5A_KL1zt
ContentType Conference Proceeding
DBID 6IE
6IH
CBEJK
RIE
RIO
DOI 10.1109/CVPR.2008.4587538
DatabaseName IEEE Electronic Library (IEL) Conference Proceedings
IEEE Proceedings Order Plan (POP) 1998-present by volume
IEEE Xplore All Conference Proceedings
IEEE Electronic Library (IEL)
IEEE Proceedings Order Plans (POP) 1998-present
DatabaseTitleList
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Xplore
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
Computer Science
EISBN 9781424422432
1424422434
EISSN 1063-6919
EndPage 8
ExternalDocumentID 4587538
Genre orig-research
GroupedDBID 23M
29F
29O
6IE
6IH
6IK
ABDPE
ACGFS
ALMA_UNASSIGNED_HOLDINGS
CBEJK
IPLJI
M43
RIE
RIO
RNS
ID FETCH-LOGICAL-h192t-a6ea95a17f78017c0d42819ece80d1a48d99f7bb28dfd4c1c66f536e63f4ae03
IEDL.DBID RIE
ISBN 9781424422425
1424422426
ISSN 1063-6919
IngestDate Wed Aug 27 02:44:16 EDT 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed false
IsScholarly true
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-h192t-a6ea95a17f78017c0d42819ece80d1a48d99f7bb28dfd4c1c66f536e63f4ae03
OpenAccessLink https://inria.hal.science/inria-00590251
PageCount 8
ParticipantIDs ieee_primary_4587538
PublicationCentury 2000
PublicationDate 2008-06
PublicationDateYYYYMMDD 2008-06-01
PublicationDate_xml – month: 06
  year: 2008
  text: 2008-06
PublicationDecade 2000
PublicationTitle 2008 IEEE Conference on Computer Vision and Pattern Recognition
PublicationTitleAbbrev CVPR
PublicationYear 2008
Publisher IEEE
Publisher_xml – name: IEEE
SSID ssj0000453616
ssj0023720
ssj0003211698
Score 2.1522505
Snippet Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph...
SourceID ieee
SourceType Publisher
StartPage 1
SubjectTerms Clustering algorithms
Eigenvalues and eigenfunctions
Fellows
Graph theory
Histograms
Kernel
Laplace equations
Noise shaping
Shape
Topology
Title Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration
URI https://ieeexplore.ieee.org/document/4587538
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07a8MwEBZJ6NApbZPSNxo61o0fkmyNJTR0KCGUULKUIEvnJosTYru_vzr5UQpdulkHQkY6-z50391HyL2GSPNMRp6SAfPQQ7xEpqEX8hS7cQUs5caJTcTzebJayUWPPHS1MADgyGfwiI8ul292usKrsgnjiK6TPunHsahrtbr7FAtNItFAHRxHdiEhu4xCiGosLvMpIk_IQLZFXiHGqLb3UzPmTfoz8OVk-r54qymXzeq_ZFhcFJoN__f-J2T8U85HF12gOiU9yM_IsMGftPm6C2tqJR5a24h8PB1cdw6LSA0tNmoP1EJcx7-kSJn_pK8KaV3WyShgY0-Mk86VqcoNrfKi2uPfqLDT97ttXlJUgmh79Y7Jcva8nL54jSKDt7FIsPSUACW5CuIstpEt1r5hmIgDDYlvAsUSI2UWp2mYmMwwHWghMnssIKKMKfCjczLIdzlcEJql3M9MyBKlBfMhsdO4DiHQjKfKcHVJRrh_633dc2PdbN3V3-ZrclzzOPB25IYMykMFt-RIf5Xb4nDnHOUbjfm33Q
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEA7rA_S0PvFtDh6t9pGkzVHEZcV1WWQRL7KkydT10l22W3-_mWxaEbx4awZCaDLtfGS-mY-QKw2J5oVMAiUjFqCHBJnM4yDmOXbjiljOjRObSIfD7O1Njjrkuq2FAQBHPoMbfHS5fDPTNV6V3TKO6DpbIxuonOWrtdobFQtOEuHBDo4Tu5SQbU4hRj0Wl_sUSSBkJJsyrxijVNP9yY-5T4BGoby9fx29rEiXfv1fQiwuDvW6_3uDHXLwU9BHR22o2iUdKPdI1yNQ6r_vypoakYfGtk_e7xauP4fFpIZWUzUHakGuY2BSJM1_0IFCYpd1MwrY2hMjpXNmqkpD67Kq5_g_quz0-eyzXFLUgmi69R6Qce9hfN8PvCZDMLVYcBkoAUpyFaVFamNbqkPDMBUHGrLQRIplRsoizfM4M4VhOtJCFPZYQCQFUxAmh2S9nJVwRGiR87AwMcuUFiyEzE7jOoZIM54rw9Ux2cf9m8xXXTcmfutO_jZfkq3--HkwGTwOn07J9orVgXclZ2R9uajhnGzqr-VntbhwTvMNU0W7Jg
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=proceeding&rft.title=2008+IEEE+Conference+on+Computer+Vision+and+Pattern+Recognition&rft.atitle=Articulated+shape+matching+using+Laplacian+eigenfunctions+and+unsupervised+point+registration&rft.au=Mateus%2C+Diana&rft.au=Horaud%2C+Radu&rft.au=Knossow%2C+David&rft.au=Cuzzolin%2C+Fabio&rft.date=2008-06-01&rft.pub=IEEE&rft.isbn=9781424422425&rft.issn=1063-6919&rft.eissn=1063-6919&rft.spage=1&rft.epage=8&rft_id=info:doi/10.1109%2FCVPR.2008.4587538&rft.externalDocID=4587538
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1063-6919&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1063-6919&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1063-6919&client=summon