Projective reconstruction from line correspondences
21 Jun 1994-pp 903-907
TL;DR: A practical rapid algorithm for doing projective reconstruction of a scene consisting of a set of lines seen in three or more images with uncalibrated cameras, which can be applied to images from different cameras or the same camera.
Abstract: The paper gives a practical rapid algorithm for doing projective reconstruction of a scene consisting of a set of lines seen in three or more images with uncalibrated cameras. The algorithm is evaluated on real and ideal data to determine its performance in the presence of varying degrees of noise. By carefully consideration of sources of error, it is possible to get accurate reconstruction with realistic levels of noise. The algorithm can be applied to images from different cameras or the same camera. For images with the same camera with unknown calibration, it is possible to do a complete Euclidean reconstruction of the image. This extends to the case of uncalibrated cameras previous results on scene reconstruction from lines,. >
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07 Jun 2015
TL;DR: Inception as mentioned in this paper is a deep convolutional neural network architecture that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14).
Abstract: We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.
40,257 citations
TL;DR: This paper shows that by preceding the eight-point 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.
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.
1,722 citations
Cites background from "Projective reconstruction from line..."
...This same approach can be applied to many different linear algorithms, such as camera pose and calibration estimation [22], projective reconstruction from lines [23], and reconstruction of point positions in space [24]....
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20 Jun 1995
TL;DR: By preceding the 8 point 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.
Abstract: The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the 8 point algorithm is a frequently cited method for computing the fundamental matrix from a set of 8 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. The 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. >
760 citations
Cites background from "Projective reconstruction from line..."
...This same approach can be applied to many different linear algorithms, such as camera pose and calibration estimation ([22]), projective reconstruction from lines ([23]) and reconstruction of point positions in space ([24])....
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TL;DR: This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3×3 matrix of rank 2 which is proposed to call the Fundamental matrix, a task which is of practical importance.
Abstract: In this paper we analyze in some detail the geometry of a pair of cameras, i.e., a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of the principal points, pixels aspect ratio and focal lengths). This is important for two reasons. First, it is more realistic in applications where these parameters may vary according to the task (active vision). Second, the general case considered here, captures all the relevant information that is necessary for establishing correspondences between two pairs of images. This information is fundamentally projective and is hidden in a confusing manner in the commonly used formalism of the Essential matrix introduced by Longuet-Higgins (1981). This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3×3 matrix of rank 2 which we propose to call the Fundamental matrix. After this theoretical analysis, we embark on the task of estimating the Fundamental matrix from point correspondences, a task which is of practical importance. We analyze theoretically, and compare experimentally using synthetic and real data, several methods of estimation. The problem of the stability of the estimation is studied from two complementary viewpoints. First we show that there is an interesting relationship between the Fundamental matrix and three-dimensional planes which induce homographies between the images and create unstabilities in the estimation procedures. Second, we point to a deep relation between the unstability of the estimation procedure and the presence in the scene of so-called critical surfaces which have been studied in the context of motion analysis. Finally we conclude by stressing the fact that we believe that the Fundamental matrix will play a crucial role in future applications of three-dimensional Computer Vision by greatly increasing its versatility, robustness and hence applicability to real difficult problems.
707 citations
TL;DR: It is shown in this paper, that the trifocal tensor is essentially identical to a set of coefficients introduced by Shashua to effect point transfer in the three view case, which means that the 13-line algorithm may be extended to allow for the computation of the Trifocal Tensor given any mixture of sufficiently many line and point correspondences.
Abstract: This paper discusses the basic role of the trifocal tensor in scene reconstruction from three views. This 3\times 3\times 3 tensor plays a role in the analysis of scenes from three views analogous to the role played by the fundamental matrix in the two-view case. In particular, the trifocal tensor may be computed by a linear algorithm from a set of 13 line correspondences in three views. It is further shown in this paper, that the trifocal tensor is essentially identical to a set of coefficients introduced by Shashua to effect point transfer in the three view case. This observation means that the 13-line algorithm may be extended to allow for the computation of the trifocal tensor given any mixture of sufficiently many line and point correspondences. From the trifocal tensor the camera matrices of the images may be computed, and the scene may be reconstructed. For unrelated uncalibrated cameras, this reconstruction will be unique up to projectivity. Thus, projective reconstruction of a set of lines and points may be carried out linearly from three views.
303 citations
Cites background or methods from "Projective reconstruction from line..."
...It was later shown by the present author in Hartley (1993, 1994b) to be equally applicable to projective scene reconstruction from 13 lines in the uncalibrated case....
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...This tensor may be computed linearly from a set of line correspondences in three images, and as shown previously in Hartley (1993, 1994b), leads to an algorithm for projective reconstruction from line correspondences in three views....
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...These fundamental matrices have a very simple expression in terms of the camera matrices, as follows Hartley (1994): F12 = a4 × A; F13 = b4 × B (14) where notation such as a4 × A means the matrix made up by forming the vector product of a4 with each of the columns of A separately....
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...The importance of this result is that it allows an amalgamation of the linear algorithms for points (Shashua, 1995) and for lines (Hartley, 1994b)....
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...The previous algorithm published in Hartley (1994b) for retrieving the camera matrices, and hence projective structure, from the trifocal tensor was not very stable numerically....
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References
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Book•
31 Jan 1986TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Abstract: From the Publisher:
This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, this book is more than ever the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, with many new topics presented at the same accessible level. In addition, some sections of more advanced material have been introduced, set off in small type from the main body of the text. Numerical Recipes is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests. All this is in addition to material on such basic top
12,662 citations
11,285 citations
"Projective reconstruction from line..." refers background or methods in this paper
...This is a straight-forward parameter minimization problem, solved simply using the LevenbergMarquardt algorithm ([10])....
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...Let the singular value decomposition ([10]) be X = UDV , where D is a diagonal matrix diag(α, β, 0, 0)....
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...Furthermore, each iteration is very fast, since construction of the normal equations ([10]) requires time linear in the number of points, and the normal equations are only of size 24× 24....
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01 Jan 1989
TL;DR: This paper presents a list of recommended recipes for making CDRom decks and some examples of how these recipes can be modified to suit theommelier's needs.
Abstract: Keywords: informatique ; numerical recipes Note: contient un CDRom Reference Record created on 2004-09-07, modified on 2016-08-08
4,920 citations
"Projective reconstruction from line..." refers background or methods in this paper
...This is a straight-forward parameter minimization problem, solved simply using the LevenbergMarquardt algorithm ([10])....
[...]
...Let the singular value decomposition ([10]) be X = UDV , where D is a diagonal matrix diag(α, β, 0, 0)....
[...]
...Furthermore, each iteration is very fast, since construction of the normal equations ([10]) requires time linear in the number of points, and the normal equations are only of size 24× 24....
[...]
4,036 citations
TL;DR: A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two projections is unknown.
Abstract: A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two projections is unknown. This problem is relevant not only to photographic surveying1 but also to binocular vision2, where the non-visual information available to the observer about the orientation and focal length of each eye is much less accurate than the optical information supplied by the retinal images themselves. The problem also arises in monocular perception of motion3, where the two projections represent views which are separated in time as well as space. As Marr and Poggio4 have noted, the fusing of two images to produce a three-dimensional percept involves two distinct processes: the establishment of a 1:1 correspondence between image points in the two views—the ‘correspondence problem’—and the use of the associated disparities for determining the distances of visible elements in the scene. I shall assume that the correspondence problem has been solved; the problem of reconstructing the scene then reduces to that of finding the relative orientation of the two viewpoints.
2,671 citations
"Projective reconstruction from line..." refers background or methods in this paper
...The fundamental matrix defined by LonguetHiggins ([7]) (originally for calibrated cameras) contains all the information available about relative camera placements that can be derived from image point correspondences....
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...Methods have been given for the computation of the fundamental matrix from point correspondences [7, 8, 6]....
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...It is at the heart of algorithms for camera calibration [9, 4, 2], image rectification [5], scene reconstruction [6, 3, 7] and transfer [1]....
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