# Problèmes classiques en vision par ordinateur et en géométrie algorithmique revisités via la géométrie des droites

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications, INRIA Lorraine
Abstract : Systematize is the leitmotiv of the results in this thesis. Three problems are studied in the field of computer vision and computational geometry. In the first one, we extend all the machinery of the pinhole model for classical cameras to a whole set of cameras (two-slit, pushbroom, oblique, pencil), which were separately studied with different approaches. In the second one, we generalize to convex bodies in $\R^3$ the work on pinning lines by lines or balls, which had so far been tackled by techniques intimately linked to the geometry of the objects. In the third one, we attempt to work out a systematic approach in place of problem-specific methods in order to build polynomial evaluation trees for geometric predicates. Such goals could not be reached without a mathematical investigation in the study of linear line congruences, differential properties of sets of tangent lines to a convex and classical invariant theory respectively. These tools or their uses are mostly based on line geometry in $\p^3(\R)$. This geometry was designed in the second half of the 19th century but its full power has not yet been used by the computational geometry community. This thesis therefore also serves as an extended tutorial.
Mots-clés :
Document type :
Theses
Géométrie algorithmique [cs.CG]. Université Nancy II, 2011. Français
Domain :

https://tel.archives-ouvertes.fr/tel-00653043
Contributor : Guillaume Batog <>
Submitted on : Friday, November 9, 2012 - 2:19:10 PM
Last modification on : Wednesday, October 7, 2015 - 1:09:11 AM

### Identifiers

• HAL Id : tel-00653043, version 2

### Citation

Guillaume Batog. Problèmes classiques en vision par ordinateur et en géométrie algorithmique revisités via la géométrie des droites. Géométrie algorithmique [cs.CG]. Université Nancy II, 2011. Français. <tel-00653043v2>

Record views