Year: 2016
Author: Weihua Tong, Xuecheng Tai
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 1 : pp. 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 $\mathcal{Γ}$-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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1510-m4510
Journal of Computational Mathematics, Vol. 34 (2016), Iss. 1 : pp. 87–112
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Feature lines Variational approach Polygonal meshes The Mumford-Shah model Discrete operators Valleys of functions.
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