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Calibration of Central Catadioptric Cameras Using a DLTLike Approach
"... the date of receipt and acceptance should be inserted later Since their introduction to the computer vision community, catadioptric omnidirectional cameras have been utilized in many application areas such as surveillance [1], telepresence [2], robot navigation [3] and 3D reconstruction [4]. Omnidi ..."
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the date of receipt and acceptance should be inserted later Since their introduction to the computer vision community, catadioptric omnidirectional cameras have been utilized in many application areas such as surveillance [1], telepresence [2], robot navigation [3] and 3D reconstruction [4]. Omnidirectional cameras being singleviewpoint are searched, since it is an important property. If singleviewpoint cameras are used, directions of the light rays coming into the camera can easily be calculated and combined in a multiview geometric framework [5]. Catadioptric systems, combinations of camera lenses and mirrors were extensively studied by Baker and Nayar [6]. They showed which of these systems are able to provide the singleviewpoint property, i.e., if the mirror has a focal point which can behave like an effective pinhole. Among those systems the most useful ones are the paracatadioptric and the hypercatadioptric models, using a mirror of parabolic/hyperbolic shape, coupled with an orthographic/perspective camera. Swaminathan et al. [7] conducted a detailed study on the geometry of nonsingleviewpoint systems. There also exist studies for approximating a viewpoint in nonsingleviewpoint systems as Derrien and Konolige proposed for spherical mirrors [8]. Camera calibration is essential when we want to extract metric information from images. It establishes a relationship between the 3D rays and their corresponding pixels in the image. This relationship makes possible to measure distances in a real world from their projections on the images [9]. Camera calibration is bainria00590268,
Multibody Motion Estimation and Segmentation from Multiple Central Panoramic Views
 In IEEE International Conference on Robotics and Automation
, 2003
"... We present an algorithm for infinitesimal motion estimation and segmentation from multiple central panoramic views. We first show that the central panoramic optical flows corresponding to independent motions lie in orthogonal tendimensional subspaces of a higherdimensional linear space. We then pr ..."
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Cited by 8 (7 self)
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We present an algorithm for infinitesimal motion estimation and segmentation from multiple central panoramic views. We first show that the central panoramic optical flows corresponding to independent motions lie in orthogonal tendimensional subspaces of a higherdimensional linear space. We then propose a factorizationbased technique that estimates the number of independent motions, the segmentation of the image measurements and the motion of each object relative to the camera from a set of image points and their optical flows in multiple frames. Finally, we present experimental results on motion estimation and segmentation for a real image sequence with two independently moving mobile robots, and evaluate the performance of our algorithm by comparing the vision estimates with GPS measurements gathered by the mobile robots.
Visual Servoing from 3D Straight Lines with Central Catadioptric Cameras
 in Fifth Workshop on Omnidirectional Vision, Omnivis’2004
, 2004
"... In this paper we consider the problem of controlling the six degrees of freedom of a manipulator using the projection of 3D lines in the image plane of central catadioptric systems. Most of the e#ort in visual servoing are devoted to points, only few works have investigated the use of lines in v ..."
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In this paper we consider the problem of controlling the six degrees of freedom of a manipulator using the projection of 3D lines in the image plane of central catadioptric systems. Most of the e#ort in visual servoing are devoted to points, only few works have investigated the use of lines in visual servoing with traditional cameras and none has explored the case of omnidirectional cameras. First a generic interaction matrix for the projection of 3D straight lines is derived from the projection model of the entire class of central catadioptric cameras. Then an imagebased control law is designed and validated through simulation results.
Omnidirectional vision applied to unmanned aerial vehicles (uavs) attitude and heading estimation
 Robot. Autonom. Syst
"... Aerial Vehicles (UAVs) attitude and heading ..."
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Uav attitude estimation by vanishing points in catadioptric images
 In ICRA
, 2008
"... Abstract — Unmanned Aerial Vehicles (UAV) are the subject of an increasing interest in many applications and a key requirement is the stabilization of the vehicle. Some previous works have suggested using catadioptric vision, instead of traditional perspective cameras, in order to gather much more i ..."
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Abstract — Unmanned Aerial Vehicles (UAV) are the subject of an increasing interest in many applications and a key requirement is the stabilization of the vehicle. Some previous works have suggested using catadioptric vision, instead of traditional perspective cameras, in order to gather much more information from the environment and therefore improve the robustness of the UAV attitude estimation. This paper belongs to a series of recent publications of our research group concerning catadioptric vision for UAVs. Currently, we focus on the estimation of the complete attitude of a UAV flying in urban environment. In order to avoid the limitations of horizonbased approaches, the difficulties of traditional epipolar methods (such as rotationtranslation ambiguity, lack of features, retrieving motion parameters from matrix decomposition, etc...) and improve UAV dynamic control, we suggest computing infinite homography. We show how catadioptric vision plays a key role to: first, extract a large number of lines, second robustly estimate the associated vanishing points and third, track them even during long video sequences. Therefore it is not only possible to estimate the relative rotation between consecutive frames but also compute the absolute rotation between two distant frames without error accumulation. Finally, we present some experimental results with ground truth data to demonstrate the accuracy and the robustness of our method. I.
Geometric invariants and applications under catadioptric camera model
 in Tenth IEEE International Conference on Computer Vision, 2005. ICCV 2005
, 2005
"... This paper presents geometric invariants of points and their applications under central catadioptric camera model. Although the image has severe distortions under the model, we establish some accurate projective geometric invariants of scene points and their image points. These invariants, being fun ..."
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This paper presents geometric invariants of points and their applications under central catadioptric camera model. Although the image has severe distortions under the model, we establish some accurate projective geometric invariants of scene points and their image points. These invariants, being functions of principal point, are useful, from which a method for calibrating the camera principal point and a method for recovering planar scene structures are proposed. The main advantage of using these invariants for plane reconstruction is that neither camera motion nor the intrinsic parameters, except for the principal point, is needed. The theoretical correctness of the established invariants and robustness of the proposed methods are demonstrated by experiments. In addition, our results are found to be applicable to some more general camera models other than the catadioptric one.
Simultaneously calibrating catadioptric camera and detecting line features using Hough transform
 in 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005. (IROS
, 2005
"... Abstract A line in space is projected to a conic in a central catadioptric image, and such a conic is called a line image. This paper proposes a novel approach to calibrating catadioptric camera and detecting line images simultaneously by using Hough transform. Previous approaches to catadioptric c ..."
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Abstract A line in space is projected to a conic in a central catadioptric image, and such a conic is called a line image. This paper proposes a novel approach to calibrating catadioptric camera and detecting line images simultaneously by using Hough transform. Previous approaches to catadioptric cameras calibration employ the traditional conic detecting or fitting methods for line images, and then use these recovered conics to estimate the intrinsic parameters based on some properties of line images. However, the type of a line image can be line, circle, ellipse, hyperbola or parabola, and in general only a small arc of the conic is visible in the image, which brings novel challenges for conic detection and fitting where traditional conic detecting and fitting methods may fail. As we know, the accuracy of the estimated intrinsic parameters highly depends on the accuracy of the extracted conics. The main contribution of this work is we show that all line images from catadioptric cameras with the same intrinsic parameters must belong to a family of conics with only two degreeoffreedom, and such a family is called a line image family. Therefore, we present a novel special Hough transform for line images detection which ensures that all detected conics must belong to a line image family related to certain intrinsic parameters. For all possible values of the unknown intrinsic parameters, the line image special Hough transform are performed. The one with the highest confidence is chosen as the estimated values for these unknown intrinsic parameters, and the corresponding results of line image detection are chosen as the estimated values for line images. In order to make the searching process more efficient, the hierarchical approaches are employed in this paper. The validity of our proposed approach is illustrated by experiments. Index Terms – Camera calibration, omnidirectional camera, Hough transform, feature extraction, line features.
Line extraction in central hypercatadioptric systems
"... Abstract — In central hypercatadioptric systems the 3D lines are projected into conics in the image plane. The general representation of conics considers five parameters. These conics can be represented by two parameters if the hypercatadioptric camera calibration is known. In this paper we presen ..."
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Abstract — In central hypercatadioptric systems the 3D lines are projected into conics in the image plane. The general representation of conics considers five parameters. These conics can be represented by two parameters if the hypercatadioptric camera calibration is known. In this paper we present a new approach to extract these projected lines that we name catadioptric image lines (CILs). We propose an approximation to the geometric distance from point to conic that combined with the two point representation inside a RANSAC approach allows us to extract the CILs present in a hypercatadioptric image. We also perform an exhaustive analysis on the elements that can affect the CILs extraction accuracy. Particularly we analyze the effect of calibration errors of the omnidirectional system and the effect of the distribution of the image points on the projected line, i. e. the conic in the image and its length. We present simulations with different hypercatadioptric systems, and experiments with real images. I.
Catadioptric Visual Servoing From 3D Straight Lines
"... Abstract—In this paper, we consider the problem of controlling a6DOFholonomic robot and a nonholonomic mobile robot from the projection of 3D straight lines in the image plane of central catadioptric systems. A generic central catadioptric interaction matrix for the projection of 3D straight lines ..."
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Abstract—In this paper, we consider the problem of controlling a6DOFholonomic robot and a nonholonomic mobile robot from the projection of 3D straight lines in the image plane of central catadioptric systems. A generic central catadioptric interaction matrix for the projection of 3D straight lines is derived using an unifying imaging model valid for an entire class of cameras. This result is exploited to design an imagebased control law that allows us to control the 6 DOF of a robotic arm. Then, the projected lines are exploited to control a nonholonomic robot. We show that as when considering a robotic arm, the control objectives are mainly based on catadioptric image feature and that local asymptotic convergence is guaranteed. Simulation results and real experiments with a 6 DOF eyetohand system and a mobile robot illustrate the control strategy. Index Terms—3D straight lines, omnidirectional vision, visual servoing. I.