The local projective shape of smooth surfaces and their outlines

Svetlana Lazebnik, Jean Ponce

Research output: Contribution to journalArticlepeer-review


This article examines projectively-invariant local geometric properties of smooth curves and surfaces. Oriented projective differential geometry is proposed as a general framework for establishing such invariants and characterizing the local projective shape of surfaces and their outlines. It is applied to two problems: (1) the projective generalization of Koenderink's famous characterization of convexities concavities and inflections of the apparent contours of solids bounded by smooth surfaces and (2) the image-based construction of rim meshes which provide a combinatorial description of the arrangement induced on the surface of an object by the contour generators associated with multiple cameras observing it.

Original languageEnglish (US)
Pages (from-to)65-83
Number of pages19
JournalInternational Journal of Computer Vision
Issue number1
StatePublished - Jun 2005


  • Differential invariants
  • Frontier points
  • Local shape
  • Oriented projective geometry
  • Projective differential geometry

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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