Problèmes classiques en vision par ordinateur et engéométrie algorythmique revisités via la géométrie des droites

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 R3 the work on pinning lines by 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 P3 (R). This geometry was designed in the second half of the 19th century but its full power hos not yet been used by the computational geometry community. This thesis therefore also serves as an extended tutorial.
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Guillaume Batog. Problèmes classiques en vision par ordinateur et engéométrie algorythmique revisités via la géométrie des droites. Autre [cs.OH]. Université Nancy 2, 2011. Français. ⟨NNT : 2011NAN23001⟩. ⟨tel-01749781⟩

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