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36
Geometric Properties of Central Catadioptric Line Images and their Application in Calibration
- IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—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 in ..."
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Cited by 80 (8 self)
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Abstract—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 camera. Index Terms—Catadioptric, omnidirectional vision, projective geometry, lines, calibration. 1
Image-based visual servoing for nonholonomic mobile robots using epipolar geometry
- IEEE Transactions on Robotics
, 2007
"... Abstract—We present an image-based visual servoing strategy for driving a nonholonomic mobile robot equipped with a pinhole camera toward a desired configuration. The proposed approach, which exploits the epipolar geometry defined by the current and desired camera views, does not need any knowledge ..."
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Cited by 34 (3 self)
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Abstract—We present an image-based visual servoing strategy for driving a nonholonomic mobile robot equipped with a pinhole camera toward a desired configuration. The proposed approach, which exploits the epipolar geometry defined by the current and desired camera views, does not need any knowledge of the 3-D scene geometry. The control scheme is divided into two steps. In the first, using an approximate input–output linearizing feedback, the epipoles are zeroed so as to align the robot with the goal. Feature points are then used in the second translational step to reach the desired configuration. Asymptotic convergence to the desired configuration is proven, both in the calibrated and partially calibrated case. Simulation and experimental results show the effectiveness of the proposed control scheme. Index Terms—Epipolar geometry, image-based visual servoing (IBVS), input–output feedback linearization, nonholonomic mobile robots. I.
Image-based Visual Servoing with Central Catadioptric Camera
- Int. J. Robot. Res
"... Abstract — This paper presents an epipolar based visual servoing for mobile robots equipped with a panoramic camera. The proposed visual servoing is based on the epipolar geometry and exploits the auto-epipolar property, a special configuration for the epipoles which occurs when the desired and the ..."
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Cited by 22 (3 self)
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Abstract — This paper presents an epipolar based visual servoing for mobile robots equipped with a panoramic camera. The proposed visual servoing is based on the epipolar geometry and exploits the auto-epipolar property, a special configuration for the epipoles which occurs when the desired and the current views undergo a pure translation. This occurrence is detectable observing when the bi-osculating mirror conics co-intersect at the two epipoles. The autoepipolar condition enables our controller to retrieve the equal orientation between target and current camera. Translation is performed by exploiting the epipoles. Simulated experiments and Lyapunov-based stability analysis demonstrate the parametric robustness of the proposed method. I.
Central Catadioptric Visual Servoing from 3D Straight Lines
- Computer Systems Science&Eng.,7
, 2004
"... In this paper we consider the problem of controlling a robotic system using the projection of 3D lines in the image plane of central catadioptric systems. Most of the effort in visual servoing are devoted to points, only few works have investigated the use of lines in visual servoing with traditiona ..."
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Cited by 18 (4 self)
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In this paper we consider the problem of controlling a robotic system using the projection of 3D lines in the image plane of central catadioptric systems. Most of the effort 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 central catadioptric interaction matrix for the projection of 3D straight lines is derived from the projection model of an entire class of camera. Then an image-based control law is designed and validated through simulation results.
Homography-based Tracking for Central Catadioptric Cameras
- IN IROS
, 2006
"... This paper presents a parametric approach for tracking piecewise planar scenes with central catadioptric cameras (including perspective cameras). We extend the standard notion of homography to this wider range of devices through the unified projection model on the sphere. We avoid unwarping the imag ..."
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Cited by 15 (5 self)
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This paper presents a parametric approach for tracking piecewise planar scenes with central catadioptric cameras (including perspective cameras). We extend the standard notion of homography to this wider range of devices through the unified projection model on the sphere. We avoid unwarping the image to a perspective view and take into account the non-uniform pixel resolution specific to non-perspective central catadioptric sensors. The homography is parametrised by the Lie algebra of the special linear group SL(3) to ensure that only eight free parameters are estimated. With this model, we use an efficient second-order minimisation technique leading to a fast tracking algorithm with a complexity similar to a first-order approach. The developed algorithm was tested on the estimation of the displacement of a mobile robot in a real application and proved to be very precise.
Constrained multiple planar template tracking for central catadioptric cameras
- In British Machine Vision Conference
, 2006
"... This paper presents a homography-based approach for tracking multiple planar templates with central catadioptric cameras (which include perspective cameras). We extend the standard notion of homography to this wider range of devices through the unified projection model on the sphere. To enforce the ..."
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Cited by 11 (6 self)
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This paper presents a homography-based approach for tracking multiple planar templates with central catadioptric cameras (which include perspective cameras). We extend the standard notion of homography to this wider range of devices through the unified projection model on the sphere. To enforce the same movement of the camera for the different planes, we parametrise the homography by the Lie algebra of the special euclidean group SE(3) and estimate the normal and depth for each plane. With this model, we use a minimisation technique to obtain a close to second-order convergence rate with a complexity similar to a first-order approach. The proposed method takes into account the non-uniform resolution of the sensor and proved robust to poor initial values for the plane normals. To assess the precision of the approach, the developed algorithm was tested on the estimation of the displacement of a mobile robot in a real application. We compare the results when the planes are tracked independently to the constrained case. We show that the proposed minimisation approach leads to better results in terms of speed and precision than current tracking algorithms. 1
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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Cited by 8 (0 self)
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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 image-based control law is designed and validated through simulation results.
Fast Central Catadioptric Line Extraction, Estimation, Tracking And Structure from Motion
"... In this paper we present an analysis of 3D line projections for central catadioptric cameras from a projective perspective. Most algorithms consider the projection of lines as general conics in the image plane with five degrees of freedom. However, in the calibrated case, only two parameters are nee ..."
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Cited by 8 (2 self)
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In this paper we present an analysis of 3D line projections for central catadioptric cameras from a projective perspective. Most algorithms consider the projection of lines as general conics in the image plane with five degrees of freedom. However, in the calibrated case, only two parameters are needed to represent lines. We describe methods to obtain fast extraction and estimation algorithms. We then explain how classical edgetracking algorithms can be adapted to these sensors. To this avail, we introduce two parametric equations for lines in central catadioptric images. We then propose a minimal representation for the euclidean transformation in the structure from motion problem and introduce possible metrics between a point and a central catadioptric line. These metrics are evaluated on simulated data. The structure from motion algorithm, from the line extraction process to the tracking and the reconstruction is tested on a real sequence.
Improvements on Visual Servoing From Spherical Targets Using a Spherical Projection Model
"... Abstract—This paper is concerned with improvements to visual feature modeling using a spherical projection model. Three spherical targets are considered: a sphere, a sphere marked with a tangent vector to a point on its surface, and a sphere marked with two points on its surface. A new minimal and d ..."
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Cited by 6 (1 self)
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Abstract—This paper is concerned with improvements to visual feature modeling using a spherical projection model. Three spherical targets are considered: a sphere, a sphere marked with a tangent vector to a point on its surface, and a sphere marked with two points on its surface. A new minimal and decoupled set of visual features is proposed for each target using any central catadioptric camera. Using the proposed set for a sphere, a classical control law is proved to be globally asymptotically stable in the presence of modeling errors and locally asymptotically stable in the presence of calibration errors, considering that perspective and paracatadioptric cameras were used. Simulation and experimental results with perspective, paracatadioptric, and fish-eye cameras validate the proposed theoretical results. Index Terms—Central catadioptric systems, spherical projection, visual servoing. I.
Catadioptric Visual Servoing From 3-D Straight Lines
"... Abstract—In this paper, we consider the problem of controlling a6DOFholonomic robot and a nonholonomic mobile robot from the projection of 3-D straight lines in the image plane of central catadioptric systems. A generic central catadioptric interaction matrix for the projection of 3-D straight lines ..."
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Cited by 4 (1 self)
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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 3-D straight lines in the image plane of central catadioptric systems. A generic central catadioptric interaction matrix for the projection of 3-D straight lines is derived using an unifying imaging model valid for an entire class of cameras. This result is exploited to design an image-based 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 eye-to-hand system and a mobile robot illustrate the control strategy. Index Terms—3-D straight lines, omnidirectional vision, visual servoing. I.
