Detection of Critical Direction for Feature Line Extraction on Meshes Based on Local Integral Invariants

  • Qiqi GaoEmail author
  • Yasushi YamaguchiEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)


The extraction of feature lines on surfaces approximated by dense polygon meshes provides an effective one dimensional visual cue for the understanding of 3D shapes. Detection of directions over meshes is a crucial prerequisite for the extraction of such feature lines as it determines where and how the lines should be generated on meshes. While the majority of the feature lines proposed so far are defined based on classical definition of curvature in a discrete differential geometry context, extraction of curvature information from an integral invariant viewpoint has been proposed comparatively recently. This paper provides a systematic discussion over various critical directions including but not limited to principal directions of curvature, based on integral invariants defined over local neighborhoods on meshes. We categorize the critical directions with our framework, address their implementation, and present the result of implementation and observation from the viewpoints of effectiveness, robustness and computational costs.


Neighborhood Critical direction Integral invariants 



We would like to thank Prof. Yong-Liang Yang, Dr. Yu-Kun Lai and Prof. Johannes Wallner for sharing the details of their implementation, Prof. Otto Röschel and Prof. Hans-Peter Schröcker for valuable discussions and anonymous reviewers for their constructive feedback.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.The University of TokyoTokyoJapan

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