Geometrical Analysis of the Caustic Surfaces-Application to Catadioptric Sensors. Les Surfaces Caustiques par la Géométrie-Application aux Capteurs Catadioptriques

Geometrical Analysis of the Caustic Surfaces-Application to Catadioptric Sensors

Les Surfaces Caustiques par la Géométrie-Application aux Capteurs Catadioptriques

Siohoï Ieng Ryad Benosman 

LISIF-PARC, Université Pierre et Marie Curie, 3 rue Galilée, 94200 Ivry-sur-Seine. LACSC ECE, 53 rue de Grenelle, 75007 Paris

LISIT-PARC, Université Pierre et Marie Curie, 3 rue Galilée, 94200 Ivry-sur-Seine

Page: 
433-442
|
Received: 
24 January 2005
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

Omnidirectional vision makes use of optical systems that usually simplify the notion of caustic in order to preserve perpectively correct views.Caustic surfaces are in these cases degenerated and reduced to a single point.Such a property is called single view point constraint.

Hence,most of the catadioptric cameras rely on the single viewpoint constraint that is hardly fullfilled since it requires highly precised components placement.There exists many works on non single viewpoint catadioptric sensors fullfilling specific resolutions.In such configurations,the computation of the caustic curve becomes essential.Existing solutions are unfortunately too specific to a class of curves and need heavy computation load.This paper presents a flexible geometric construction of the caustic curve of a 3D surface.This construction is an extension of a geometric construction designed for 2D plane curves.Tests and experimental results illustrate the possibilities of this approach.

Résumé

La vision omnidirectionnelle utilise des systèmes optiques pour lesquels la notion de caustique est souvent occultée par souci de simplification,afin de respecter une reconstruction perspective correcte. La surface caustique est ramenée à un cas de dégénérescence,appelé la contrainte du point focal unique. Une telle hypothèse implique un placement précis des composants la rendant difficile à satisfaire. De plus,afin d’exploiter des propriétés plus générales de résolutions,il est nécessaire d’examiner la surface caustique. Une étude de la caustique par réflexion (dite catacaustique) est abordée ici dans la mesure où les capteurs utilisés sont principalement à base de surfaces réfléchissantes. Les travaux existants sont malheureusement spécifiques à une famille de surfaces et nécessitent un prétraitement lourd en calcul. Nous proposons ici une méthode souple de construction géométrique de la caustique adaptée aux surfaces 3D,basée sur une méthode développée à l’origine pour les courbes planes 2D.

Keywords: 

Omnidirectional vision,catadioptric sensor,calibration,caustic (by reflection).

Mots clés 

Vision omnidirectionelle,capteur catadioptrique,calibrage,caustique (par réflexion).

1. Introduction
2. Courbe Caustique: Définition et Construction
3. Tests et Simulations
4. Conclusion
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