Wachs sg2005

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Wachs sg2005

  1. 1. Calibrating a Catadioptric Light Field Array Megan A. Wachs Daniel Crispell Gabriel Taubin∗ Brown University Brown University Brown UniversityWe present a new method for acquiring data for image-based ren- ing pins. We use an ellipse fitting algorithm to refine the locationdering and 3D reconstruction using an array of spherical mirrors estimates for all the pins, and then we recompute the homographyand a single high-resolution perspective camera. The main advan- and plane equations more precisely from this data in the LS sense.tage of this setup is a wider field of view, but designing calibration This step has to be repeated every time the camera moves with re-and reconstruction algorithms is challenging because catadioptric spect to the plate, or when camera parameters, such as zoom orsystems with spherical mirrors have non-central viewpoints, and focus, are changed. The mirrors are then approximated as spheresdo not behave as perspective cameras. A single image from our with centers on a plane located behind the plane of the pin heads.perspective camera produces sample rays from a very large num- Initial estimates for the sphere center locations with respect to theber of virtual viewpoints. In this sketch we describe the construc- plate coordinate system and sphere radii are available from the me-tion of this system and a new procedure for calibrating it. Pre- chanical design data, but the exact radii and precise center locationsvious methods for acquiring a number of images from different are not known. We propose a method for the third calibration stepviewpoints have included arrays of cameras [Levoy and Hanrahan using a new bundle adjustment formulation. Once the locations of1995] and moving cameras [Gortler et al. 1995]. Another previous the mirror spheres are known, Nayar’s [Nayar 1988] method of con-method was an array of lenses mounted on a flatbed scanner [Yang verting an image point u to a ray Ru = {p = q(u, Λ) + λ v(u, Λ)} in2000]. The literature on catadioptric systems is extensive, but to space is used, where Λ is a set of parameters including the sphereour knowledge systems with large numbers of identical mirrors ar- centers and radii. For every point p j in a calibration target, andranged in regular configurations have not been presented. The main each corresponding image point ui j associated with the i-th mir-advantages of our system are the wide field of view, the single cam- ror, we have one ray equation qi j + λi j vi j = p j . To eliminate theera capture makes the time synchronization issues associated with additional λi j unknowns, the estimates for the sphere centers andmulti-camera systems vanish. On the other hand, frame-rate video radii are estimated by locally minimizing the performance functionprocessing is not possible with these high resolution consumer- E(Λ) = ∑ j ∑i vi j × (p j − qi j ) 2 . This process is computationallygrade digital cameras. Mechanical System Design: The system, expensive, but since the mirrors are not expected to move with re-shown above, consists of a thick aluminum plate with stainless steel spect to the plate it needs to be performed only once in a laboratorycylindrical pins pressed into holes. These pins hold 31 spherical environment.mirrors. They were cut to length and inserted in the plate with highprecision in our machine shop, but the inexpensive plastic mirrorswere glued to the plate using a synthetic silicon rubber adhesive. Asa result, the mirror parameters (location of sphere centers and radii)are not known with high precision. This plate is positioned in spaceto roughly fill the field of view of our Olympus C-8080 8 MegaPixel digital camera. A structure built out of standard aluminum ex-trusions keeps the whole structure in place. A single image capturesall 31 mirrors. The camera’s SDK provided by the manufacturerwas used to automate the capture and calibration processes. Cali-bration: We divide the calibration process into three steps: 1) In-trinsic camera calibration, 2) Extrinsic calibration of the plate withrelation to the camera, and 3) Calibration of the individual mirrors G ORTLER , S., G RZESZCZUK , R., S ZELISKI , R., AND C OHEN ,with respect to the plate. For the intrinsic camera calibration step M. 1995. The lumigraph. In ACM SIGGRAPH.we use well-established techniques and free high-quality software.The second step is carried out from a single input image as follows. L EVOY, M., AND H ANRAHAN , P. 1995. Light-field rendering. InWe use an ellipse detection algorithm to locate the four corner pins ACM SIGGRAPH.close to the four corners of the image. Since we know the preciselocation of these four pins in the plate and their relative distances, NAYAR , S. 1988. Sphereo: Determining Depth using Two Specularfrom the four point correspondences we compute a homography, Spheres and a Single Camera. In Proceedings of SPIE Confer-and from this homography a first estimate of the equation of the ence on Optics, Illumination, and Image Sensing for Machineplane in space. We can now predict the locations of the rest of the Vision III, 245–254.pins in the image. We use these predictions to search for the remain- YANG , J. 2000. Light fields on the cheap. In ACM SIGGRAPH. ∗ e-mail:taubin@brown.edu

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