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Axialcones: Modeling spherical catadioptric cameras for wideangle light field rendering
 ACM Trans. Graph
, 2010
"... Catadioptric imaging systems are commonly used for wideangle 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 ..."
Abstract

Cited by 6 (2 self)
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Catadioptric imaging systems are commonly used for wideangle 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 multiperspective photo captured with a spherical catadioptric imaging system using axialcone 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 multiperspective catadioptric cameras. We demonstrate axialcone modeling in the context of rendering wideangle 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 wideangle scenes, and wideangle dense depth estimation. Our GPU implementation using axialcone modeling achieves up to three orders of magnitude speed up over ray tracing for these applications.
Determining the Camera to Robotbody Transformation from Planar Mirror Reflections
"... Abstract — This paper presents a method for estimating the sixdegreesoffreedom transformation between a camera and the body of the robot on which it is rigidly attached. The robot maneuvers in front of a planar mirror, allowing the camera to observe fiducial features on the robot from several van ..."
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Cited by 4 (2 self)
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Abstract — This paper presents a method for estimating the sixdegreesoffreedom transformation between a camera and the body of the robot on which it is rigidly attached. The robot maneuvers in front of a planar mirror, allowing the camera to observe fiducial features on the robot from several vantage points. Exploiting these measurements, we form a maximumlikelihood estimate of the cameratobody transformation, without assuming prior knowledge of the robot motion or of the mirror configuration. Additionally, we estimate the mirror configuration with respect to the camera for each image. We validate the accuracy and correctness of our method with simulations and realworld experiments. I.
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 2 (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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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 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.
MirrorBased Extrinsic Camera Calibration
"... Abstract: This paper presents a method for determining the six degreesoffreedom transformation between a camera and a base frame of interest. A planar mirror is maneuvered so as to allow the camera to observe the environment from several viewing angles. Points, whose coordinates in the base frame ..."
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Cited by 1 (1 self)
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Abstract: This paper presents a method for determining the six degreesoffreedom transformation between a camera and a base frame of interest. A planar mirror is maneuvered so as to allow the camera to observe the environment from several viewing angles. Points, whose coordinates in the base frame are known, are observed by the camera via their reflections in the mirror. Exploiting these measurements, we determine the cameratobase transformation analytically, without assuming prior knowledge of the mirror motion or placement with respect to the camera. The computed solution is refined using a maximum likelihood estimator, to obtain highaccuracy estimates of the cameratobase transformation and the mirror configuration for each image. We validate the accuracy and correctness of our method with simulations and realworld experiments. 1
Focus Back (Aliasing) Depth Map Focus Back (AntiAliased) Setup Focus Ball (AntiAliased) Focus All Foreground Objects
"... Figure 1: Our axialcone modeling enables wideFOV digital refocusing and dense depth estimation using an array of spherical mirrors. We generate 150 ◦ × 150 ◦ FOV refocused images and a dense depth map on a challenging outdoor scene. The estimated depth map is used for aliasing removal, surfacede ..."
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Figure 1: Our axialcone modeling enables wideFOV digital refocusing and dense depth estimation using an array of spherical mirrors. We generate 150 ◦ × 150 ◦ FOV refocused images and a dense depth map on a challenging outdoor scene. The estimated depth map is used for aliasing removal, surfacedependent refocusing, and allinfocus rendering. The results are depicted using Mercator projection. Catadioptric imaging systems are commonly used for wideangle 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 multiperspective photo captured with a spherical catadioptric imaging system using axialcone 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 multiperspective catadioptric cameras. We demonstrate axialcone modeling in the context of rendering wideangle 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 wideangle scenes, and wideangle dense depth estimation. Our GPU implementation using axialcone modeling achieves up to three orders of magnitude speed up over ray tracing for these applications.
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 ..."
Abstract
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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.
Extrinsic Camera Calibration Without a Direct View Using Spherical Mirror
, 2013
"... We consider the problem of estimating the extrinsic parameters (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 reflections in a planar mirror to solve this problem. However, a planar ..."
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We consider the problem of estimating the extrinsic parameters (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 reflections 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 estimation 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 spherical mirror based approach does not have any degenerate configurations, leading to a robust algorithm. While a planar mirror reflection results in a virtual perspective camera, a spherical mirror reflection results in a nonperspective axial camera. The axial nature of rays allows 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 center and remaining pose parameters and show that it corresponds to solving a 16th degree equation. We present comparisons with stateofart method using 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.