Volume 34, Issue 1
A Variational Approach for Detecting Feature Lines on Meshes

Weihua Tong & Xuecheng Tai

J. Comp. Math., 34 (2016), pp. 87-112.

Published online: 2016-02

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  • Abstract

Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic rendering. This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using Γ-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polynomials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.

  • Keywords

Feature lines Variational approach Polygonal meshes The Mumford-Shah model Discrete operators Valleys of functions

  • AMS Subject Headings

65D18.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

tongwh@ustc.edu.cn (Weihua Tong)

tai@mi.uib.no (Xuecheng Tai)

  • BibTex
  • RIS
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@Article{JCM-34-87, author = {Tong , Weihua and Tai , Xuecheng }, title = {A Variational Approach for Detecting Feature Lines on Meshes}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {1}, pages = {87--112}, abstract = { Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic rendering. This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using Γ-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polynomials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1510-m4510}, url = {http://global-sci.org/intro/article_detail/jcm/9784.html} }
TY - JOUR T1 - A Variational Approach for Detecting Feature Lines on Meshes AU - Tong , Weihua AU - Tai , Xuecheng JO - Journal of Computational Mathematics VL - 1 SP - 87 EP - 112 PY - 2016 DA - 2016/02 SN - 34 DO - http://doi.org/10.4208/jcm.1510-m4510 UR - https://global-sci.org/intro/article_detail/jcm/9784.html KW - Feature lines KW - Variational approach KW - Polygonal meshes KW - The Mumford-Shah model KW - Discrete operators KW - Valleys of functions AB - Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic rendering. This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using Γ-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polynomials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.
Weihua Tong & Xuecheng Tai . (2020). A Variational Approach for Detecting Feature Lines on Meshes. Journal of Computational Mathematics. 34 (1). 87-112. doi:10.4208/jcm.1510-m4510
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