This paper introduces a novel imaging system composed of an array of spherical mirrors and a single highresolution digital camera. We describe the mechanical design and construction of a prototype, analyze the geometry of image formation, present a tailored calibration algorithm, and discuss the effect that design decisions had on the calibration routine. This system is presented as a unique platform for the development of efficient multi-view imaging algorithms which exploit the combined properties of camera arrays and non-central projection catadioptric systems. Initial target applications include data acquisition for image-based rendering and 3D scene reconstruction. The main advantages of the proposed system include: a relatively simple calibration procedure, a wide field of view, and a single imaging sensor which eliminates the need for color calibration and guarantees time synchronization. 1.

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

Abstract — This paper presents a method for estimating the six-degrees-of-freedom 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 maximum-likelihood estimate of the camera-to-body 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 real-world experiments. I.

Abstract: This paper presents a method for determining the six degrees-of-freedom 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 camera-to-base 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 high-accuracy estimates of the camera-to-base transformation and the mirror configuration for each image. We validate the accuracy and correctness of our method with simulations and real-world experiments. 1

We present a new method for acquiring data for image-based rendering and 3D reconstruction using an array of spherical mirrors and a single high-resolution digital camera. The main advantages of this system include automatic color calibration and frame synchronization, however the design of calibration and reconstruction algorithms presents a challenge since this system generates non-central projections. In this poster, we describe the mechanical design of a prototype, analyze the geometry of image formation, present a tailored calibration algorithm, and demonstrate preliminary reconstruction results. Mechanical Design The prototype system consists of an aluminum plate with cylindrical stainless steel pins pressed into holes. These pins hold 31 spherical mirrors. The plate is positioned in space to roughly fill the field of view of an Olympus C-8080 8 megapixel digital camera such that a single image captures all 31 mirrors. A structure built out of aluminum extrusions holds the mirror assembly and camera.

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We present a new method for acquiring data for image-based rendering and 3D reconstruction using an array of spherical mirrors and a single high-resolution perspective camera. The main advantage of this setup is a wider field of view, but designing calibration and reconstruction algorithms is challenging because catadioptric systems with spherical mirrors have non-central viewpoints, and do not behave as perspective cameras. A single image from our perspective camera produces sample rays from a very large number of virtual viewpoints. We describe the construction of this system and a new procedure for calibrating it. Mechanical System

Abstract. This paper presents a method for determining the six-degreeof-freedom (DOF) transformation between a camera and a base frame of interest, while concurrently estimating the 3D base-frame coordinates of unknown point features in the scene. The camera observes the reflections of fiducial points, whose base-frame coordinates are known, and reconstruction points, whose base-frame coordinates are unknown. In this paper, we examine the case in which, due to visibility constraints, none of the points are directly viewed by the camera, but instead are seen via reflection in multiple planar mirrors. Exploiting these measurements, we analytically compute the camera-to-base transformation and the 3D base-frame coordinates of the unknown reconstruction points, without a priori knowledge of the mirror sizes, motions, or placements with respect to the camera. Subsequently, we refine the analytical solution using a maximum-likelihood estimator (MLE), to obtain high-accuracy estimates of the camera-to-base transformation, the mirror configurations for each image, and the 3D coordinates of the reconstruction points in the base frame. We validate the accuracy and correctness of our method with simulations and real-world experiments. 1

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.