813,193 research outputs found
Certifying the Existence of Epipolar Matrices
Given a set of point correspondences in two images, the existence of a
fundamental matrix is a necessary condition for the points to be the images of
a 3-dimensional scene imaged with two pinhole cameras. If the camera
calibration is known then one requires the existence of an essential matrix.
We present an efficient algorithm, using exact linear algebra, for testing
the existence of a fundamental matrix. The input is any number of point
correspondences. For essential matrices, we characterize the solvability of the
Demazure polynomials. In both scenarios, we determine which linear subspaces
intersect a fixed set defined by non-linear polynomials. The conditions we
derive are polynomials stated purely in terms of image coordinates. They
represent a new class of two-view invariants, free of fundamental
(resp.~essential)~matrices
Performance characterization of fundamental matrix estimation under image degradation
The fundamental matrix represents the epipolar geometry between two images. We describe an algorithm for simultaneously estimating the fundamental matrix and corresponding points automatically from the two images. The performance of this algorithm is then assessed as the images are degraded by JPEG lossy compression. A number of performance measures are proposed and evaluated over image pairs corresponding to different camera motions and scene types
noRANSAC for fundamental matrix estimation
The estimation of the fundamental matrix from a set of corresponding points is a relevant topic in epipolar stereo geometry [10]. Due to the high amount of outliers between the matches, RANSAC-based approaches [7, 13, 29] have been used to obtain the fundamental matrix. In this paper two new contributes are presented: a new normalized epipolar error measure which takes into account the shape of the features used as matches [17] and a new strategy to compare fundamental matrices. The proposed error measure gives good results and it does not depend on the image scale. Moreover, the new evaluation strategy describes a valid tool to compare different RANSAC-based methods because it does not rely on the inlier ratio, which could not correspond to the best allowable fundamental matrix estimated model, but it makes use of a reference ground truth fundamental matrix obtained by a set of corresponding points given by the use
Robust Self-calibration of Focal Lengths from the Fundamental Matrix
The problem of self-calibration of two cameras from a given fundamental
matrix is one of the basic problems in geometric computer vision. Under the
assumption of known principal points and square pixels, the well-known Bougnoux
formula offers a means to compute the two unknown focal lengths. However, in
many practical situations, the formula yields inaccurate results due to
commonly occurring singularities. Moreover, the estimates are sensitive to
noise in the computed fundamental matrix and to the assumed positions of the
principal points. In this paper, we therefore propose an efficient and robust
iterative method to estimate the focal lengths along with the principal points
of the cameras given a fundamental matrix and priors for the estimated camera
parameters. In addition, we study a computationally efficient check of models
generated within RANSAC that improves the accuracy of the estimated models
while reducing the total computational time. Extensive experiments on real and
synthetic data show that our iterative method brings significant improvements
in terms of the accuracy of the estimated focal lengths over the Bougnoux
formula and other state-of-the-art methods, even when relying on inaccurate
priors
q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
A set of four factorizable non-relativistic S-matrices for a multiplet of
fundamental particles are defined based on the R-matrix of the quantum group
deformation of the centrally extended superalgebra su(2|2). The S-matrices are
a function of two independent couplings g and q=exp(i\pi/k). The main result is
to find the scalar factor, or dressing phase, which ensures that the unitarity
and crossing equations are satisfied. For generic (g,k), the S-matrices are
branched functions on a product of rapidity tori. In the limit k->infinity, one
of them is identified with the S-matrix describing the magnon excitations on
the string world sheet in AdS5 x S5, while another is the mirror S-matrix that
is needed for the TBA. In the g->infinity limit, the rapidity torus
degenerates, the branch points disappear and the S-matrices become meromorphic
functions, as required by relativistic S-matrix theory. However, it is only the
mirror S-matrix which satisfies the correct relativistic crossing equation. The
mirror S-matrix in the relativistic limit is then closely related to that of
the semi-symmetric space sine-Gordon theory obtained from the string theory by
the Pohlmeyer reduction, but has anti-symmetric rather than symmetric bound
states. The interpolating S-matrix realizes at the quantum level the fact that
at the classical level the two theories correspond to different limits of a
one-parameter family of symplectic structures of the same integrable system.Comment: 41 pages, late
In Defense of the Eight-Point Algorithm
Abstract—The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the eight-point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches. It has the advantage of simplicity of implementation. The prevailing view is, however, that it is extremely susceptible to noise and hence virtually useless for most purposes. This paper challenges that view, by showing that by preceding the algorithm with a very simple normalization (translation and scaling) of the coordinates of the matched points, results are obtained comparable with the best iterative algorithms. This improved performance is justified by theory and verified by extensive experiments on real images. Index Terms—Fundamental matrix, eight-point algorithm, condition number, epipolar structure, stereo vision
Probabilistic Sparse Subspace Clustering Using Delayed Association
Discovering and clustering subspaces in high-dimensional data is a
fundamental problem of machine learning with a wide range of applications in
data mining, computer vision, and pattern recognition. Earlier methods divided
the problem into two separate stages of finding the similarity matrix and
finding clusters. Similar to some recent works, we integrate these two steps
using a joint optimization approach. We make the following contributions: (i)
we estimate the reliability of the cluster assignment for each point before
assigning a point to a subspace. We group the data points into two groups of
"certain" and "uncertain", with the assignment of latter group delayed until
their subspace association certainty improves. (ii) We demonstrate that delayed
association is better suited for clustering subspaces that have ambiguities,
i.e. when subspaces intersect or data are contaminated with outliers/noise.
(iii) We demonstrate experimentally that such delayed probabilistic association
leads to a more accurate self-representation and final clusters. The proposed
method has higher accuracy both for points that exclusively lie in one
subspace, and those that are on the intersection of subspaces. (iv) We show
that delayed association leads to huge reduction of computational cost, since
it allows for incremental spectral clustering
Calibration of a wide angle stereoscopic system
This paper was published in OPTICS LETTERS and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OL.36.003064. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.Inaccuracies in the calibration of a stereoscopic system appear with errors in point correspondences between both images and inexact points localization in each image. Errors increase if the stereoscopic system is composed of wide angle lens cameras. We propose a technique where detected points in both images are corrected before estimating the fundamental matrix and the lens distortion models. Since points are corrected first, errors in point correspondences and point localization are avoided. To correct point location in both images, geometrical and epipolar constraints are imposed in a nonlinear minimization problem. Geometrical constraints define the point localization in relation to its neighbors in the same image, and eipolar constraints represent the location of one point referred to its corresponding point in the other image. © 2011 Optical Society of America.Ricolfe Viala, C.; Sánchez SalmerĂłn, AJ.; MartĂnez Berti, E. (2011). Calibration of a wide angle stereoscopic system. Optics Letters. 36(16):3064-3067. doi:10.1364/OL.36.003064S306430673616Zhang, Z., Ma, H., Guo, T., Zhang, S., & Chen, J. (2011). Simple, flexible calibration of phase calculation-based three-dimensional imaging system. Optics Letters, 36(7), 1257. doi:10.1364/ol.36.001257Longuet-Higgins, H. C. (1981). A computer algorithm for reconstructing a scene from two projections. Nature, 293(5828), 133-135. doi:10.1038/293133a0Ricolfe-Viala, C., & Sanchez-Salmeron, A.-J. (2010). Lens distortion models evaluation. Applied Optics, 49(30), 5914. doi:10.1364/ao.49.005914ArmanguĂ©, X., & Salvi, J. (2003). Overall view regarding fundamental matrix estimation. Image and Vision Computing, 21(2), 205-220. doi:10.1016/s0262-8856(02)00154-3Devernay, F., & Faugeras, O. (2001). Straight lines have to be straight. Machine Vision and Applications, 13(1), 14-24. doi:10.1007/pl0001326
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