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18
Multi-perspective stereo matching and volumetric reconstruction
- In ICCV
, 2009
"... Stereo matching and volumetric reconstruction are the most explored 3D scene recovery techniques in computer vision. Many existing approaches assume perspective input images and use the epipolar constraint to reduce the search space and improve the accuracy. In this paper we present a novel framewor ..."
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Cited by 18 (1 self)
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Stereo matching and volumetric reconstruction are the most explored 3D scene recovery techniques in computer vision. Many existing approaches assume perspective input images and use the epipolar constraint to reduce the search space and improve the accuracy. In this paper we present a novel framework that uses multi-perspective cameras for stereo matching and volumetric reconstruction. Our approach first decomposes a multi-perspective camera into piecewise primitive General Linear Cameras or GLCs [32]. A pair of GLCs in general do not satisfy the epipolar constraint. However, they still form a nearly stereo pair. We develop a new Graph-Cut-based algorithm to account for the slight vertical parallax using the GLC ray geometry. We show that the recovered pseudo disparity map conveys important depth cues analogous to perspective stereo matching. To more accurately reconstruct a 3D scene, we develop a new multi-perspective volumetric reconstruction method. We discretize the scene into voxels and apply the GLC back-projections to map the voxel onto each input multi-perspective camera. Finally, we apply the graph-cut algorithm to optimize the 3D embedded voxel graph. We demonstrate our algorithms on both synthetic and real multi-perspective cameras. Experimental results show that our methods are robust and reliable. 1.
Analytical Forward Projection for Axial Non-Central Dioptric & Catadioptric Cameras
"... Abstract. Wepresentatechniqueformodelingnon-centralcatadioptric cameras consisting of a perspective camera and a rotationally symmetric conic reflector. While previous approaches use a central approximation and/or iterative methods for forward projection, we present an analytical solution. This allo ..."
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Cited by 18 (8 self)
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Abstract. Wepresentatechniqueformodelingnon-centralcatadioptric cameras consisting of a perspective camera and a rotationally symmetric conic reflector. While previous approaches use a central approximation and/or iterative methods for forward projection, we present an analytical solution. This allows computation of the optical path from a given 3D point to the given viewpoint by solving a 6 th degree forward projection equation for general conic mirrors. For a spherical mirror, the forward projection reduces to a 4 th degree equation, resulting in a closed form solution. We also derive the forward projection equation for imaging through a refractive sphere (non-central dioptric camera) and show that it is a 10 th degree equation. While central catadioptric cameras lead to conic epipolar curves, we show the existence of a quartic epipolar curve for catadioptric systems using a spherical mirror. The analytical forward projection leads to accurate and fast 3D reconstruction via bundle adjustment. Simulations and real results on single image sparse 3D reconstruction are presented. We demonstrate ∼ 100 times speed up using the analytical solution over iterative forward projection for 3D reconstruction using spherical mirrors. 1
Axial-cones: Modeling spherical catadioptric cameras for wide-angle light field rendering
- ACM Trans. Graph
, 2010
"... Catadioptric imaging systems are commonly used for wide-angle imaging, but lead to multiperspective images which do not allow algorithms designed for perspective cameras to be used. Efficient use of such systems requires accurate geometric ray modeling as well as fast algorithms. We present accurate ..."
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Cited by 12 (4 self)
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Catadioptric imaging systems are commonly used for wide-angle imaging, but lead to multiperspective images which do not allow algorithms designed for perspective cameras to be used. Efficient use of such systems requires accurate geometric ray modeling as well as fast algorithms. We present accurate geometric modeling of the multi-perspective photo captured with a spherical catadioptric imaging system using axial-cone cameras: multiple perspective cameras lying on an axis each with a different viewpoint and a different cone of rays. This modeling avoids geometric approximations and allows several algorithms developed for perspective cameras to be applied to multi-perspective catadioptric cameras. We demonstrate axial-cone modeling in the context of rendering wide-angle light fields, captured using a spherical mirror array. We present several applications such as spherical distortion correction, digital refocusing for artistic depth of field effects in wide-angle scenes, and wide-angle dense depth estimation. Our GPU implementation using axial-cone modeling achieves up to three orders of magnitude speed up over ray tracing for these applications.
Multiperspective Modeling, Rendering, and Imaging
- EUROGRAPHICS 2008
, 2008
"... A perspective image represents the spatial relationships of objects in a scene as they appear from a single viewpoint. In contrast, a multiperspective image combines what is seen from several viewpoints into a single image. Despite their incongruity of view, effective multiperspective images are abl ..."
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Cited by 12 (6 self)
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A perspective image represents the spatial relationships of objects in a scene as they appear from a single viewpoint. In contrast, a multiperspective image combines what is seen from several viewpoints into a single image. Despite their incongruity of view, effective multiperspective images are able to preserve spatial coherence and can depict, within a single context, details of a scene that are simultaneously inaccessible from a single view, yet easily interpretable by a viewer. In computer vision, multiperspective images have been used for analyzing structure revealed via motion and generating panoramic images with a wide field-of-view using mirrors. In this STAR, we provide a practical guide on topics in multiperspective modeling and rendering methods and multiperspective imaging systems. We start with a brief review of multiperspective image techniques frequently employed by artists such as the visual paradoxes of Escher, the Cubism of Picasso and Braque, and multiperspective panoramas in cel animations. We then characterize existing multiperspective camera models, with an emphasis on their underlying geometry and image properties. We demonstrate how to use these camera models for creating specific multiperspective rendering effects. Furthermore, we show that many of these cameras satisfy the multiperspective stereo constraints and we demonstrate several multiperspective imaging systems for extracting 3D geometry for computer vision. The
Reconstructing a 3d line from a single catadioptric image
- In Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission
, 2006
"... This paper demonstrates that, for axial non-central optical systems, the equation of a 3D line can be estimated using only four points extracted from a single image of the line. This result, which is a direct consequence of the lack of vantage point, follows from a classic result in enumerative geom ..."
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Cited by 9 (0 self)
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This paper demonstrates that, for axial non-central optical systems, the equation of a 3D line can be estimated using only four points extracted from a single image of the line. This result, which is a direct consequence of the lack of vantage point, follows from a classic result in enumerative geometry: there are exactly two lines in 3-space which intersect four given lines in general position. We present a simple algorithm to reconstruct the equation of a 3D line from four image points. This algorithm is based on computing the Singular Value Decomposition (SVD) of the matrix of Plücker coordinates of the four corresponding rays. We evaluate the conditions for which the reconstruction fails, such as when the four rays are nearly coplanar. Preliminary experimental results using a spherical catadioptric camera are presented. We conclude by discussing the limitations imposed by poor calibration and numerical errors on the proposed reconstruction algorithm. 1
Single Image Calibration of Multi-Axial Imaging Systems
"... Imaging systems consisting of a camera looking at mul-tiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wide-angle imaging applications. We describe such setups as multi-axial imag-ing systems, since a single sphere results in an axial sys-tem. Assum ..."
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Cited by 6 (1 self)
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Imaging systems consisting of a camera looking at mul-tiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wide-angle imaging applications. We describe such setups as multi-axial imag-ing systems, since a single sphere results in an axial sys-tem. Assuming an internally calibrated camera, calibration of such multi-axial systems involves estimating the sphere radii and locations in the camera coordinate system. How-ever, previous calibration approaches require manual inter-vention 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 cal-ibration 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 lo-cation. This leads to an interesting result that 6-DOF pose estimation of a multi-axial camera can be done without the knowledge of full calibration. Simulations and real experi-ments demonstrate the applicability of our algorithm. 1.
Beyond Alhazen’s Problem: Analytical Projection Model for Non-Central 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, non-central 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, non-central 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 non-central 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 non-central catadioptric cameras primarily use an axial configuration where the camera is placed on the axis of a rotationally symmetric mirror, we allow off-axis (any) camera placement. Using this analytical model, a non-central catadioptric camera can be used for sparse as well as dense 3D reconstruction similar to perspective cameras, using well-known algorithms such as bundle adjustment and plane sweeping. Our paper is the first to show such results for off-axis placement of camera with multiple quadric mirrors. Simulation and real results using parabolic mirrors and an off-axis perspective camera are demonstrated. 1.
Extrinsic camera calibration without a direct view using spherical mirror
- in ICCV
, 2013
"... agrawal at merl dot com We consider the problem of estimating the extrinsic pa-rameters (pose) of a camera with respect to a reference 3D object without a direct view. Since the camera does not view the object directly, previous approaches have utilized reflec-tions in a planar mirror to solve this ..."
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Cited by 2 (0 self)
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agrawal at merl dot com We consider the problem of estimating the extrinsic pa-rameters (pose) of a camera with respect to a reference 3D object without a direct view. Since the camera does not view the object directly, previous approaches have utilized reflec-tions in a planar mirror to solve this problem. However, a planar mirror based approach requires a minimum of three reflections and has degenerate configurations where esti-mation fails. In this paper, we show that the pose can be obtained using a single reflection in a spherical mirror of known radius. This makes our approach simpler and easier in practice. In addition, unlike planar mirrors, the spher-ical mirror based approach does not have any degenerate configurations, leading to a robust algorithm. While a planar mirror reflection results in a virtual per-spective camera, a spherical mirror reflection results in a non-perspective axial camera. The axial nature of rays al-lows us to compute the axis (direction of sphere center) and few pose parameters in a linear fashion. We then derive an analytical solution to obtain the distance to the sphere cen-ter and remaining pose parameters and show that it corre-sponds to solving a 16th degree equation. We present com-parisons with a recent method that use planar mirrors and show that our approach recovers more accurate pose in the presence of noise. Extensive simulations and results on real data validate our algorithm. 1.
Single Image Calibration of Multi-Axial Imaging Systems
, 2013
"... Imaging systems consisting of a camera looking at multiple spherical mirrors (reflection) or multiple refractive spheres (refraction) have been used for wide-angle imaging applications. We describe such setups as multi-axial imaging systems, since a single sphere results in an axial system. Assuming ..."
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Cited by 1 (0 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 wide-angle imaging applications. We describe such setups as multi-axial imaging systems, since a single sphere results in an axial system. Assuming an internally calibrated camera, calibration of such multi-axial 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 6-DOF pose estimation of a multi-axial camera can be done without the knowledge of full calibration. Simulations and real experiments demonstrate the applicability of our algorithm.
Polygonal Light Source Estimation
"... Abstract. This paper studies the problem of light estimation using a specular sphere. Most existing work on light estimation assumes distant point light sources, while this work considers an area light source which is estimated in 3D space by reconstructing its edges. An empirical analysis on existi ..."
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Cited by 1 (1 self)
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Abstract. This paper studies the problem of light estimation using a specular sphere. Most existing work on light estimation assumes distant point light sources, while this work considers an area light source which is estimated in 3D space by reconstructing its edges. An empirical analysis on existing methods for line estimation from a single view is carried out, and it is shown that line estimation for a single view of a sphere is an ill-conditioned configuration. By considering a second identical sphere, a closed form solution for single view polygonal light estimation is proposed. In addition, this paper also proposes an iterative approach based on two unknown views of just a single sphere. Experimental results on both synthetic and real data are presented. 1
