research-article

Map-based exploration of intrinsic shape differences and variability

Authors:

Raif M. Rustamov,

Maks Ovsjanikov,

Mirela Ben-Chen,

Frédéric Chazal,

Leonidas GuibasAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 32, Issue 4

Article No.: 72, Pages 1 - 12

https://doi.org/10.1145/2461912.2461959

Published: 21 July 2013 Publication History

Abstract

We develop a novel formulation for the notion of shape differences, aimed at providing detailed information about the location and nature of the differences or distortions between the two shapes being compared. Our difference operator, derived from a shape map, is much more informative than just a scalar global shape similarity score, rendering it useful in a variety of applications where more refined shape comparisons are necessary. The approach is intrinsic and is based on a linear algebraic framework, allowing the use of many common linear algebra tools (e.g, SVD, PCA) for studying a matrix representation of the operator. Remarkably, the formulation allows us not only to localize shape differences on the shapes involved, but also to compare shape differences across pairs of shapes, and to analyze the variability in entire shape collections based on the differences between the shapes. Moreover, while we use a map or correspondence to define each shape difference, consistent correspondences between the shapes are not necessary for comparing shape differences, although they can be exploited if available. We give a number of applications of shape differences, including parameterizing the intrinsic variability in a shape collection, exploring shape collections using local variability at different scales, performing shape analogies, and aligning shape collections.

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Cited By

Mayer JBaum DAmbellan Fvon Tycowicz C(2024)Shape-based disease grading via functional maps and graph convolutional networks with application to Alzheimer’s diseaseBMC Medical Imaging10.1186/s12880-024-01513-z24:1Online publication date: 18-Dec-2024
https://doi.org/10.1186/s12880-024-01513-z
Sundararaman RDonati NMelzi SCorman EOvsjanikov M(2024)Deformation Recovery: Localized Learning for Detail-Preserving DeformationsACM Transactions on Graphics10.1145/368796843:6(1-16)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687968
Le QBu JQu YZhu BDu T(2024)Computational Biomimetics of Winged SeedsACM Transactions on Graphics10.1145/368789943:6(1-13)Online publication date: 19-Dec-2024
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Index Terms

Map-based exploration of intrinsic shape differences and variability
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 32, Issue 4

July 2013

1215 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2461912

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Copyright © 2013 ACM.

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Publication History

Published: 21 July 2013

Published in TOG Volume 32, Issue 4

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Cited By

Mayer JBaum DAmbellan Fvon Tycowicz C(2024)Shape-based disease grading via functional maps and graph convolutional networks with application to Alzheimer’s diseaseBMC Medical Imaging10.1186/s12880-024-01513-z24:1Online publication date: 18-Dec-2024
https://doi.org/10.1186/s12880-024-01513-z
Sundararaman RDonati NMelzi SCorman EOvsjanikov M(2024)Deformation Recovery: Localized Learning for Detail-Preserving DeformationsACM Transactions on Graphics10.1145/368796843:6(1-16)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687968
Le QBu JQu YZhu BDu T(2024)Computational Biomimetics of Winged SeedsACM Transactions on Graphics10.1145/368789943:6(1-13)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687899
Leblanc LVialle RDe Farias CSaghbiny EMarturi NTamadazte B(2024)Pedicle Drilling Planning Transfer for Spine Surgery Using Functional Map Correspondences2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)10.1109/IROS58592.2024.10802159(6947-6952)Online publication date: 14-Oct-2024
https://doi.org/10.1109/IROS58592.2024.10802159
Thomas OShen HRaaum RHarcourt-Smith WPolk JHasegawa-Johnson M(2023)Automated morphological phenotyping using learned shape descriptors and functional maps: A novel approach to geometric morphometricsPLOS Computational Biology10.1371/journal.pcbi.100906119:1(e1009061)Online publication date: 19-Jan-2023
https://doi.org/10.1371/journal.pcbi.1009061
Hartwig FSassen JAzencot ORumpf MBen-Chen M(2023)An Elastic Basis for Spectral Shape CorrespondenceACM SIGGRAPH 2023 Conference Proceedings10.1145/3588432.3591518(1-11)Online publication date: 23-Jul-2023
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Magnet ROvsjanikov M(2023)Scalable and Efficient Functional Map Computations on Dense MeshesComputer Graphics Forum10.1111/cgf.1474642:2(89-101)Online publication date: 23-May-2023
https://doi.org/10.1111/cgf.14746
Attaiki SOvsjanikov M(2023)Understanding and Improving Features Learned in Deep Functional Maps2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52729.2023.00133(1316-1326)Online publication date: Jun-2023
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Mang AHe JAzencott R(2023)An operator-splitting approach for variational optimal control formulations for diffeomorphic shape matchingJournal of Computational Physics10.1016/j.jcp.2023.112463493(112463)Online publication date: Nov-2023
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Herzog VSuwelack S(2023)Bridging the Gap between Geometry and User Intent: Retrieval of CAD Models via Regions of InterestComputer-Aided Design10.1016/j.cad.2023.103573163(103573)Online publication date: Oct-2023
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