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Recovering specular surfaces using curved line images
 In CVPR ’09. 2
"... We present a new shapefromdistortion framework for recovering specular (reflective/refractive) surfaces. While most existing approaches rely on accurate correspondences between 2D pixels and 3D points, we focus on analyzing the curved images of 3D lines which we call curved line images or CLIs. Ou ..."
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Cited by 8 (3 self)
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We present a new shapefromdistortion framework for recovering specular (reflective/refractive) surfaces. While most existing approaches rely on accurate correspondences between 2D pixels and 3D points, we focus on analyzing the curved images of 3D lines which we call curved line images or CLIs. Our approach models CLIs of local reflections or refractions using the recently proposed general linear cameras (GLCs)[23]. We first characterize all possible CLIs in a GLC. We show that a 3D line will appear as a conic in any GLC. For a fixed GLC, the conic type is invariant to the position and orientation of the line and is determined by the GLC parameters. Furthermore, CLIs under single reflection/refraction can only be lines or hyperbolas. Based on our new theory, we develop efficient algorithms to use multiple CLIs to recover the GLC camera parameters. We then apply the curvatureGLC theory to derive the Gaussian and mean curvatures from the GLC intrinsics. This leads to a complete distortionbased reconstruction framework. Unlike conventional correspondencebased approaches that are sensitive to image distortions, our approach benefits from the CLI distortions. Finally, we demonstrate applying our framework for recovering curvature fields on both synthetic and real specular surfaces. 1.
Single Image Calibration of MultiAxial Imaging Systems
"... Imaging systems consisting of a camera looking at multiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wideangle imaging applications. We describe such setups as multiaxial imaging systems, since a single sphere results in an axial system. Assum ..."
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Cited by 6 (1 self)
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Imaging systems consisting of a camera looking at multiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wideangle imaging applications. We describe such setups as multiaxial imaging systems, since a single sphere results in an axial system. Assuming an internally calibrated camera, calibration of such multiaxial systems involves estimating the sphere radii and locations in the camera coordinate system. However, previous calibration approaches require manual intervention or constrained setups. We present a fully automatic approach using a single photo of a 2D calibration grid. The pose of the calibration grid is assumed to be unknown and is also recovered. Our approach can handle unconstrained setups, where the mirrors/refractive balls can be arranged in any fashion, not necessarily on a grid. The axial nature of rays allows us to compute the axis of each sphere separately. We then show that by choosing rays from two or more spheres, the unknown pose of the calibration grid can be obtained linearly and independently of sphere radii and locations. Knowing the pose, we derive analytical solutions for obtaining the sphere radius and location. This leads to an interesting result that 6DOF pose estimation of a multiaxial camera can be done without the knowledge of full calibration. Simulations and real experiments demonstrate the applicability of our algorithm. 1.
Beyond Alhazen’s Problem: Analytical Projection Model for NonCentral Catadioptric Cameras with Quadric Mirrors
"... Catadioptric cameras are widely used to increase the field of view using mirrors. Central catadioptric systems having an effective single viewpoint are easy to model and use, but severely constraint the camera positioning with respect to the mirror. On the other hand, noncentral catadioptric system ..."
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Cited by 4 (0 self)
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Catadioptric cameras are widely used to increase the field of view using mirrors. Central catadioptric systems having an effective single viewpoint are easy to model and use, but severely constraint the camera positioning with respect to the mirror. On the other hand, noncentral catadioptric systems allow greater flexibility in camera placement, but are often approximated using central or linear models due to the lack of an exact model. We bridge this gap and describe an exact projection model for noncentral catadioptric systems. We derive an analytical ‘forward projection’ equation for the projection of a 3D point reflected by a quadric mirror on the imaging plane of a perspective camera, with no restrictions on the camera placement, and show that it is an 8 th degree equation in a single unknown. While previous noncentral catadioptric cameras primarily use an axial configuration where the camera is placed on the axis of a rotationally symmetric mirror, we allow offaxis (any) camera placement. Using this analytical model, a noncentral catadioptric camera can be used for sparse as well as dense 3D reconstruction similar to perspective cameras, using wellknown algorithms such as bundle adjustment and plane sweeping. Our paper is the first to show such results for offaxis placement of camera with multiple quadric mirrors. Simulation and real results using parabolic mirrors and an offaxis perspective camera are demonstrated. 1.
Single Image Calibration of MultiAxial Imaging Systems
, 2013
"... Imaging systems consisting of a camera looking at multiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wideangle imaging applications. We describe such setups as multiaxial imaging systems, since a single sphere results in an axial system. Assuming ..."
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Imaging systems consisting of a camera looking at multiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wideangle imaging applications. We describe such setups as multiaxial imaging systems, since a single sphere results in an axial system. Assuming an internally calibrated camera, calibration of such multiaxial systems involves estimating the sphere radii and locations in the camera coordinate system. However, previous calibration approaches require manual intervention or constrained setups. We present a fully automatic approach using a single photo of a 2D calibration grid. The pose of the calibration grid is assumed to be unknown and is also recovered. Our approach can handle unconstrained setups, where the mirrors/refractive balls can be arranged in any fashion, not necessarily on a grid. The axial nature of rays allows us to compute the axis of each sphere separately. We then show that by choosing rays from two or more spheres, the unknown pose of the calibration grid can be obtained linearly and independently of sphere radii and locations. Knowing the pose, we derive analytical solutions for obtaining the sphere radius and location. This leads to an interesting result that 6DOF pose estimation of a multiaxial camera can be done without the knowledge of full calibration. Simulations and real experiments demonstrate the applicability of our algorithm.
The Camera Itself as a Calibration Pattern: A Novel SelfCalibration Method for NonCentral Catadioptric Cameras
, 2012
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Abstract Reflective Array
"... Imaging systems consisting of a camera looking at multiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wideangle imaging applications. We describe such setups as multiaxial imaging systems, since a single sphere results in an axial system. Assuming ..."
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Imaging systems consisting of a camera looking at multiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wideangle imaging applications. We describe such setups as multiaxial imaging systems, since a single sphere results in an axial system. Assuming an internally calibrated camera, calibration of such multiaxial systems involves estimating the sphere radii and locations in the camera coordinate system. However, previous calibration approaches require manual intervention or constrained setups. We present a fully automatic approach using a single photo of a 2D calibration grid. The pose of the calibration grid is assumed to be unknown and is also recovered. Our approach can handle unconstrained setups, where the mirrors/refractive balls can be arranged in any fashion, not necessarily on a grid. The axial nature of rays allows us to compute the axis of each sphere separately. We then show that by choosing rays from two or more spheres, the unknown pose of the calibration grid can be obtained linearly and independently of sphere radii and locations. Knowing the pose, we derive analytical solutions for obtaining the sphere radius and location. This leads to an interesting result that 6DOF pose estimation of a multiaxial camera can be done without the knowledge of full calibration. Simulations and real experiments demonstrate the applicability of our algorithm. 1.
Lineimages in Cone Mirror Catadioptric Systems J. BermudezCameo, G. LopezNicolas and J.J. Guerrero Instituto de Investigación en Ingenierı́a de Aragón (I3A)
"... Abstract—The projection surface of a 3D line in a noncentral camera is a ruled surface, containing the complete information of the 3D line. The resulting lineimage is a curve which contains the 4 degrees of freedom of the 3D line. In this paper we investigate the properties of the lineimage in co ..."
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Abstract—The projection surface of a 3D line in a noncentral camera is a ruled surface, containing the complete information of the 3D line. The resulting lineimage is a curve which contains the 4 degrees of freedom of the 3D line. In this paper we investigate the properties of the lineimage in conical catadioptric systems. This curve is a particular quartic that can be described by only six homogeneous parameters. We present the relation between the lineimage description and the geometry of the mirror. This result reveals the coupling between the depth of the line and the distance from the camera to the mirror. If this distance is unknown the 3D information of a projected line can be recovered up to scale. Knowing this distance allows obtaining the 3D metric reconstruction. The proposed parametrization also allows to simultaneously reconstruct the 3D line and computing the aperture angle of the mirror from five projected points on the lineimage. We analytically solve the metric distance from a point to a lineimage and we evaluate the proposal with real images. I.
Lineimages in Cone Mirror Catadioptric Systems J. BermudezCameo, G. LopezNicolas and J.J. Guerrero Instituto de Investigación en Ingenierı́a de Aragón (I3A)
"... Abstract—The projection surface of a 3D line in a noncentral camera is a ruled surface, containing the complete information of the 3D line. The resulting lineimage is a curve which contains the 4 degrees of freedom of the 3D line. In this paper we investigate the properties of the lineimage in co ..."
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Abstract—The projection surface of a 3D line in a noncentral camera is a ruled surface, containing the complete information of the 3D line. The resulting lineimage is a curve which contains the 4 degrees of freedom of the 3D line. In this paper we investigate the properties of the lineimage in conical catadioptric systems. This curve is a particular quartic that can be described by only six homogeneous parameters. We present the relation between the lineimage description and the geometry of the mirror. This result reveals the coupling between the depth of the line and the distance from the camera to the mirror. If this distance is unknown the 3D information of a projected line can be recovered up to scale. Knowing this distance allows obtaining the 3D metric reconstruction. The proposed parametrization also allows to simultaneously reconstruct the 3D line and computing the aperture angle of the mirror from five projected points on the lineimage. We analytically solve the metric distance from a point to a lineimage and we evaluate the proposal with real images. I.
EyeFull Tower: AGPUbasedVariableMultibaseline Omnidirectional Stereovision Systemwith Automatic Baseline Selection for OutdoorMobile Robot Navigation
"... In recent years, it can be observed that there is a gradual increase in the number of researchers and projects involved with the development of omnidirectional vision systems for various applications. The primary factors, which contributed towards this positive trend, are the availability of inexpen ..."
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In recent years, it can be observed that there is a gradual increase in the number of researchers and projects involved with the development of omnidirectional vision systems for various applications. The primary factors, which contributed towards this positive trend, are the availability of inexpensive and high resolution vision sensors, robust and fast computers and the advantages of using such systems over perspective vision systems. In this paper, a novel variable multibaseline omnidirectional stereovision system is presented. The proposed algorithm is implemented on the GPU based on the Nvidia CUDA libraries and subsequently, this paper will provide details of the automatic baseline selection process. Finally, results of the multibaseline stereovision algorithm based on voxel voting will be illustrated and discussed. In addition, possible research directions suggested by this approach will also be discussed.