Topic
Real projective line
About: Real projective line is a research topic. Over the lifetime, 856 publications have been published within this topic receiving 12419 citations.
Papers published on a yearly basis
1 / 2
Papers
15 Apr 1996
TL;DR: A practical method for the recovery of projective shape and motion from multiple images of a scene by the factorization of a matrix containing the images of all points in all views, using only fundamental matrices and epipoles estimated from the image data.
Abstract: We propose a method for the recovery of projective shape and motion from multiple images of a scene by the factorization of a matrix containing the images of all points in all views. This factorization is only possible when the image points are correctly scaled. The major technical contribution of this paper is a practical method for the recovery of these scalings, using only fundamental matrices and epipoles estimated from the image data. The resulting projective reconstruction algorithm runs quickly and provides accurate reconstructions. Results are presented for simulated and real images.
719 citations
TL;DR: In this paper, a general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces, then applied to gauge theories to carry out integration over the non-linear, infinite-dimensional spaces of connections modulo gauge transformations.
Abstract: A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non‐linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used either in the Euclidean path integral approach or the Lorentzian canonical approach. A number of measures discussed are diffeomorphism invariant and therefore of interest to (the connection dynamics version of) quantum general relativity. The account is pedagogical; in particular, prior knowledge of projective techniques is not assumed.
506 citations
TL;DR: A new method for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of “matched epipolar projections”, based on an examination of the fundamental matrix of Longuet-Higgins which describes the epipolar geometry of the image pair.
Abstract: This paper gives a new method for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of “matched epipolar projections”. These are projections in which the epipolar lines run parallel with the x-axis and consequently, disparities between the images are in the x-direction only. The method is based on an examination of the fundamental matrix of Longuet-Higgins which describes the epipolar geometry of the image pair. The approach taken is consistent with that advocated by Faugeras (1992) of avoiding camera calibration. The paper uses methods of projective geometry to determine a pair of 2D projective transformations to be applied to the two images in order to match the epipolar lines. The advantages include the simplicity of the 2D projective transformation which allows very fast resampling as well as subsequent simplification in the identification of matched points and scene reconstruction.
482 citations
TL;DR: The space of inequivalent representations of a compact surface S with χ(S) < 0 as a quotient of a convex domain in RP by a properly discontinuous group of projective transformations is a cell of dimension as discussed by the authors.
Abstract: The space of inequivalent representations of a compact surface S with χ(S) < 0 as a quotient of a convex domain in RP by a properly discontinuous group of projective transformations is a cell of dimension
305 citations
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| Year | Papers |
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| 2024 | 1 |
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| 2022 | 4 |
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| 2019 | 3 |