Relating vanishing points to catadioptric camera calibration

This paper presents the analysis and derivation of the geometric relation between vanishing points and camera parameters of central catadioptric camera systems. These vanishing points correspond to the three mutually orthogonal directions of 3D real world coordinate system (i.e. X, Y and Z axes). Compared to vanishing points (VPs) in the perspective projection, the advantages of VPs under central catadioptric projection are that there are normally two vanishing points for each set of parallel lines, since lines are projected to conics in the catadioptric image plane. Also, their vanishing points are usually located inside the image frame. We show that knowledge of the VPs corresponding to XYZ axes from a single image can lead to simple derivation of both intrinsic and extrinsic parameters of the central catadioptric system. This derived novel theory is demonstrated and tested on both synthetic and real data with respect to noise sensitivity

Adaptative Markov Random Fields for Omnidirectional Vision

International audienceImages obtained with catadioptric sensors contain significant deformations which prevent the direct use of classical image treatments. Thus, Markov Random Fields (MRF) whose usefulness is now obvious for projective image processing , can not be used directly on catadioptric images because of the inadequacy of the neighborhood. In this paper, we propose to define a new neighborhood for MRF by using the equivalence theorem developed for central catadioptric sensors. We show the importance of this adaptation for a motion detection application

Geometric Properties of Central Catadioptric Line Images and Their Application in Calibration

In central catadioptric systems, lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective invariant properties. From these properties, it follows that any central catadioptric system can be fully calibrated from an image of three or more lines. The image of the absolute conic, the relative pose between the camera and the mirror, and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected. This result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors. Moreover, it is proven that systems with a hyperbolic/elliptical mirror can be calibrated from the image of two lines. If both the shape and the pose of the mirror are known, then two line images are enough to determine the image of the absolute conic encoding the camera’s intrinsic parameters. The sensitivity to errors is evaluated and the approach is used to calibrate a real camer

Markov Random Fields for Catadioptric Image Processing

Images obtained with catadioptric sensors contain significant deformations which prevent the direct use of classical image treatments. Thus, Markov Random Fields (MRF) whose usefulness is now obvious for projective image processing, can not be used directly on catadioptric images because of the inadequacy of the neighborhood. In this article, we propose to define a new neighborhood for MRF by using the equivalence theorem developed for central catadioptric sensors. We show the importance of this adaptation for segmentation and motion detection.Les images produites par les capteurs catadioptriques présentent des distorsions importantes qui empêchent l’utilisation systématique de traitements conventionnels. Ainsi les champs de Markov dont l’utilité n’est plus à démontrer en traitement d’images perspectives, ne sont pas utilisables directement sur les images omnidirectionnelles. Dans cet article, nous proposons une adaptation des Champs de Markov aux images catadioptriques. La méthode consiste alors à redéfinir la notion de voisinage en utilisant le théorème de l’équivalence des capteurs catadioptriques centraux. Nous montrons l’intérêt de cette adaptation dans le cas de la segmentation supervisée en niveau de gris et de la détection de mouvement