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, Variational approach, Polygonal meshes, The Mumford-Shah
model, Discrete operators, Valleys of functions.
AB - <p style="text-align: justify;">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.</p>