Integral invariants for robust geometry processing

Helmut Pottmann, Johannes Wallner*, Qi Xing Huang, Yong Liang Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

164 Scopus citations


Differential invariants of curves and surfaces such as curvatures and their derivatives play a central role in Geometry Processing. They are, however, sensitive to noise and minor perturbations and do not exhibit the desired multi-scale behavior. Recently, the relationships between differential invariants and certain integrals over small neighborhoods have been used to define efficiently computable integral invariants which have both a geometric meaning and useful stability properties. This paper considers integral invariants defined via distance functions, and the stability analysis of integral invariants in general. Such invariants proved useful for many tasks where the computation of shape characteristics is important. A prominent and recent example is the automatic reassembling of broken objects based on correspondences between fracture surfaces.

Original languageEnglish (US)
Pages (from-to)37-60
Number of pages24
JournalComputer Aided Geometric Design
Issue number1
StatePublished - Jan 1 2009


  • 3D shape understanding
  • Curvature
  • Geometry processing
  • Integral invariant
  • Stability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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