Abstract
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 language | English (US) |
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Pages (from-to) | 65-83 |
Number of pages | 19 |
Journal | International Journal of Computer Vision |
Volume | 63 |
Issue number | 1 |
DOIs | |
State | Published - Jun 2005 |
Keywords
- Differential invariants
- Frontier points
- Local shape
- Oriented projective geometry
- Projective differential geometry
ASJC Scopus subject areas
- Software
- Computer Vision and Pattern Recognition
- Artificial Intelligence