On Image Contours of Projective Shapes - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2014

On Image Contours of Projective Shapes


This paper revisits classical properties of the outlines of solid shapes bounded by smooth surfaces, and shows that they can be established in a purely projective setting, without appealing to Euclidean measurements such as normals or curvatures. In particular, we give new synthetic proofs of Koenderink's famous theorem on convexities and concavities of the image contour, and of the fact that the rim turns in the same direction as the viewpoint in the tangent plane at a convex point, and in the opposite direction at a hyperbolic point. This suggests that projective geometry should not be viewed merely as an analytical device for linearizing calculations (its main role in structure from motion), but as the proper framework for studying the relation between solid shape and its perspective projections. Unlike previous work in this area, the proposed approach does not require an oriented setting, nor does it rely on any choice of coordinate system or analytical considerations.
Fichier principal
Vignette du fichier
ponce2014b.pdf (968.61 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01053677 , version 1 (01-08-2014)


  • HAL Id : hal-01053677 , version 1


Jean Ponce, Martial Hebert. On Image Contours of Projective Shapes. ECCV - European Conference on Computer Vision, Sep 2014, Zurich, Switzerland. ⟨hal-01053677⟩
222 View
169 Download


Gmail Facebook Twitter LinkedIn More