research-article

Texture Mapping Using Surface Flattening via Multidimensional Scaling

Authors:

N. KiryatiAuthors Info & Claims

IEEE Transactions on Visualization and Computer Graphics, Volume 8, Issue 2

Pages 198 - 207

https://doi.org/10.1109/2945.998671

Published: 01 April 2002 Publication History

Abstract

We present a novel technique for texture mapping on arbitrary surfaces with minimal distortions by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute a geodesic distance map from a given surface point in O( n \lg n) operations, where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multidimensional scaling (MDS). MDS is a family of methods that map a set of points into a finite dimensional flat (Euclidean) domain, where the only given data is the corresponding distances between every pair of points. The MDS mapping yields minimal changes of the distances between the corresponding points. We then solve an inverse problem and map a flat texture patch onto the curved surface while preserving the structure of the texture.

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Cited By

Bulut VOnan ASenyayla B(2024)Obtaining the optimal shortest path between two points on a quasi-developable Bézier-type surface using the Geodesic-based Q-learning algorithmEngineering Applications of Artificial Intelligence10.1016/j.engappai.2024.108821136:PAOnline publication date: 1-Oct-2024
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Texture Mapping Using Surface Flattening via Multidimensional Scaling

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cover image IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics Volume 8, Issue 2

April 2002

111 pages

ISSN:1077-2626

Issue’s Table of Contents

Copyright © Copyright © 2002 IEEE. All Rights Reserved.

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IEEE Educational Activities Department

United States

Publication History

Published: 01 April 2002

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Cited By

Bulut VOnan ASenyayla B(2024)Obtaining the optimal shortest path between two points on a quasi-developable Bézier-type surface using the Geodesic-based Q-learning algorithmEngineering Applications of Artificial Intelligence10.1016/j.engappai.2024.108821136:PAOnline publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1016/j.engappai.2024.108821
Pang BZheng ZWang GWang P(2023)Learning the Geodesic Embedding with Graph Neural NetworksACM Transactions on Graphics10.1145/361831742:6(1-12)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618317
Xia QZhang JFang ZLi JZhang MDeng BHe Y(2022)GeodesicEmbedding (GE): A High-Dimensional Embedding Approach for Fast Geodesic Distance QueriesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2021.310997528:12(4930-4939)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1109/TVCG.2021.3109975
Sun KLiu X(2022)Heat method of non-uniform diffusion for computing geodesic distance on images and surfacesMultimedia Tools and Applications10.1007/s11042-021-11851-781:25(36293-36308)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s11042-021-11851-7
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Budninskiy MLiu BTong YDesbrun M(2017)Spectral Affine-Kernel EmbeddingsComputer Graphics Forum10.1111/cgf.1325036:5(117-129)Online publication date: 1-Aug-2017
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Patané GMadeira JPatow G(2016)STARProceedings of the 37th Annual Conference of the European Association for Computer Graphics: State of the Art Reports10.5555/3059330.3059334(599-624)Online publication date: 9-May-2016
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Sahillioğlu YKavan L(2016)Detail-Preserving Mesh Unfolding for Nonrigid Shape RetrievalACM Transactions on Graphics10.1145/289347735:3(1-11)Online publication date: 20-May-2016
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