research-article

Seamless surface mappings

Authors:

Yaron LipmanAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 34, Issue 4

Article No.: 72, Pages 1 - 13

https://doi.org/10.1145/2766921

Published: 27 July 2015 Publication History

Abstract

We introduce a method for computing seamless bijective mappings between two surface-meshes that interpolates a given set of correspondences.

A common approach for computing a map between surfaces is to cut the surfaces to disks, flatten them to the plane, and extract the mapping from the flattenings by composing one flattening with the inverse of the other. So far, a significant drawback in this class of techniques is that the choice of cuts introduces a bias in the computation of the map that often causes visible artifacts and wrong correspondences.

In this paper we develop a surface mapping technique that is indifferent to the particular cut choice. This is achieved by a novel type of surface flattenings that encodes this cut-invariance, and when optimized with a suitable energy functional results in a seamless surface-to-surface map.

We show the algorithm enables producing high-quality seamless bijective maps for pairs of surfaces with a wide range of shape variability and from a small number of prescribed correspondences. We also used this framework to produce three-way, consistent and seamless mappings for triplets of surfaces.

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Cited By

Morreale LAigerman NKim VMitra N(2024)Neural Semantic Surface MapsComputer Graphics Forum10.1111/cgf.1500543:2Online publication date: 17-Apr-2024
https://doi.org/10.1111/cgf.15005
Várady TSalvi PVaitkus M(2024)Genuine multi-sided parametric surface patches – A surveyComputer Aided Geometric Design10.1016/j.cagd.2024.102286110:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.cagd.2024.102286
Raganato APasi GMelzi S(2023)Attention And Positional Encoding Are (Almost) All You Need For Shape MatchingComputer Graphics Forum10.1111/cgf.1491242:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14912
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Index Terms

Seamless surface mappings
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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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 34, Issue 4

August 2015

1307 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2809654

Issue’s Table of Contents

Copyright © 2015 ACM.

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Publication History

Published: 27 July 2015

Published in TOG Volume 34, Issue 4

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Cited By

Morreale LAigerman NKim VMitra N(2024)Neural Semantic Surface MapsComputer Graphics Forum10.1111/cgf.1500543:2Online publication date: 17-Apr-2024
https://doi.org/10.1111/cgf.15005
Várady TSalvi PVaitkus M(2024)Genuine multi-sided parametric surface patches – A surveyComputer Aided Geometric Design10.1016/j.cagd.2024.102286110:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.cagd.2024.102286
Raganato APasi GMelzi S(2023)Attention And Positional Encoding Are (Almost) All You Need For Shape MatchingComputer Graphics Forum10.1111/cgf.1491242:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14912
Schmidt PPieper DKobbelt L(2023)Surface Maps via Adaptive TriangulationsComputer Graphics Forum10.1111/cgf.1474742:2(103-117)Online publication date: 23-May-2023
https://doi.org/10.1111/cgf.14747
Hu BYe CSu JLiu L(2023)Manifold-Constrained Geometric Optimization via Local ParameterizationsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.311289629:2(1318-1329)Online publication date: 1-Feb-2023
https://doi.org/10.1109/TVCG.2021.3112896
Sun MMao SJiang POvsjanikov MHuang R(2023)Spatially and Spectrally Consistent Deep Functional Maps2023 IEEE/CVF International Conference on Computer Vision (ICCV)10.1109/ICCV51070.2023.01333(14451-14461)Online publication date: 1-Oct-2023
https://doi.org/10.1109/ICCV51070.2023.01333
Abulnaga SStein OGolland PSolomon J(2022)Symmetric Volume Maps: Order-invariant Volumetric Mesh Correspondence with Free BoundaryACM Transactions on Graphics10.1145/357289742:3(1-20)Online publication date: 29-Nov-2022
https://dl.acm.org/doi/10.1145/3572897
Fargion GWeber O(2022)Globally Injective Flattening via a Reduced Harmonic SubspaceACM Transactions on Graphics10.1145/3550454.355544941:6(1-17)Online publication date: 30-Nov-2022
https://dl.acm.org/doi/10.1145/3550454.3555449
Takayama K(2022)Compatible intrinsic triangulationsACM Transactions on Graphics10.1145/3528223.353017541:4(1-12)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530175
Hertz APerel OGiryes RSorkine‐Hornung OCohen‐Or D(2022)Mesh Draping: Parametrization‐Free Neural Mesh TransferComputer Graphics Forum10.1111/cgf.1472142:1(72-85)Online publication date: 30-Nov-2022
https://doi.org/10.1111/cgf.14721
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