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131
Determining the Epipolar Geometry and its Uncertainty: A Review
 International Journal of Computer Vision
, 1998
"... Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, an ..."
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Cited by 320 (7 self)
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Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, and its determination is very important in many applications such as scene modeling and vehicle navigation. This paper gives an introduction to the epipolar geometry, and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty. A wellfounded measure is proposed to compare these techniques. Projective reconstruction is also reviewed. The software which we have developed for this review is available on the Internet.
An Efficient Solution to the FivePoint Relative Pose Problem
, 2004
"... An efficient algorithmic solution to the classical fivepoint relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degre ..."
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Cited by 303 (11 self)
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An efficient algorithmic solution to the classical fivepoint relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and subsequently finding its roots. It is the first algorithm well suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well known 8 and 7point methods and a 6point scheme. The algorithm is used in a robust hypothesizeandtest framework to estimate structure and motion in realtime with low delay. The realtime system uses solely visual input and has been demonstrated at major conferences.
Sequential updating of projective and affine structure from motion
 International Journal of Computer Vision
, 1997
"... A structure from motion algorithm is described which recovers structure and camera position, modulo a projective ambiguity. Camera calibration is not required, and camera parameters such as focal length can be altered freely during motion. The structure is updated sequentially over an image sequenc ..."
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Cited by 141 (4 self)
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A structure from motion algorithm is described which recovers structure and camera position, modulo a projective ambiguity. Camera calibration is not required, and camera parameters such as focal length can be altered freely during motion. The structure is updated sequentially over an image sequence, in contrast to schemes which employ a batch process. A specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described, together with a method to periodically update the affine coordinate frame to prevent drift over time. We describe the constraint used to obtain this specialisation. Structure is recovered from image corners detected and matched automatically and reliably in real image sequences. Results are shown for reference objects and indoor environments, and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes. A specific application of the work is demonstrated  affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles. The path planning involves only affine constructions.
SelfCalibration from Image Triplets
, 1996
"... We describe a method for determining affine and metric calibration of a camera with unchanging internal parameters undergoing planar motion. It is shown that affine calibration is recovered uniquely, and metric calibration up to a two fold ambiguity. The novel ..."
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Cited by 105 (18 self)
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We describe a method for determining affine and metric calibration of a camera with unchanging internal parameters undergoing planar motion. It is shown that affine calibration is recovered uniquely, and metric calibration up to a two fold ambiguity. The novel
Critical motion sequences for monocular selfcalibration and uncalibrated euclidean reconstruction
, 1997
"... Abstract. In this paper, sequences of camera motions that lead to inherent ambiguities in uncalibrated Euclidean reconstruction or selfcalibration are studied. Our main contribution is a complete, detailed classification of these critical motion sequences (CMS). The practically important classes ar ..."
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Cited by 102 (5 self)
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Abstract. In this paper, sequences of camera motions that lead to inherent ambiguities in uncalibrated Euclidean reconstruction or selfcalibration are studied. Our main contribution is a complete, detailed classification of these critical motion sequences (CMS). The practically important classes are identified and their degrees of ambiguity are derived. We also discuss some practical issues, especially concerning the reduction of the ambiguity of a reconstruction. 1
Euclidean Reconstruction from Constant Intrinsic Parameters
"... In this paper a new method for Euclidean reconstruction from sequences of images taken by uncalibrated cameras, with constant intrinsic parameters, is described. Our approach leads to a variant of the so called Kruppa equations. It is shown that it is possible to calculate the intrinsic parameters a ..."
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Cited by 69 (5 self)
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In this paper a new method for Euclidean reconstruction from sequences of images taken by uncalibrated cameras, with constant intrinsic parameters, is described. Our approach leads to a variant of the so called Kruppa equations. It is shown that it is possible to calculate the intrinsic parameters as well as the Euclidean reconstruction from at least three images. The novelty of our approach is that we build our calculation on a projective reconstruction, obtained without the assumption on constant intrinsic parameters. This assumption simplifies the analysis, because a projective reconstruction is already obtained and we need ‘only’ to find the correct Euclidean reconstruction among all possible projective reconstructions.
The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image
, 1995
"... This is a paper on the geometry of vision so there will be ‘too many equations, no algorithms and no real images’. However it also represents a powerful new way to think about projective vision and that does have practical consequences. To understand this paper you will need to be comfortable with t ..."
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Cited by 68 (9 self)
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This is a paper on the geometry of vision so there will be ‘too many equations, no algorithms and no real images’. However it also represents a powerful new way to think about projective vision and that does have practical consequences. To understand this paper you will need to be comfortable with the tensorial approach to projective geometry: appendix A sketches the necessary background. This approach will be unfamiliar to many vision researchers, although a matheminria00548382,
Linear pose estimation from points or lines
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... ..."
Recent Developments on Direct Relative Orientation
, 2006
"... This paper presents a novel version of the fivepoint relative orientation algorithm given in Nister (2004). The name of the algorithm arises from the fact that it can operate even on the minimal five point correspondences required for a finite number of solutions to relative orientation. For the mi ..."
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Cited by 61 (0 self)
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This paper presents a novel version of the fivepoint relative orientation algorithm given in Nister (2004). The name of the algorithm arises from the fact that it can operate even on the minimal five point correspondences required for a finite number of solutions to relative orientation. For the minimal five correspondences the algorithm returns up to ten real solutions. The algorithm can also operate on many points. Like the previous version of the fivepoint algorithm, our method can operate correctly even in the face of critical surfaces, including planar and ruled quadric scenes. The paper
Reconstruction from Image Sequences by Means of Relative Depths
 In Proceedings of the International Conference on Computer Vision
, 1995
"... This paper deals with the problem of reconstructing the locations of n points in space from m different images without camera calibration. It shows how these problems can be put into a similar theoretical framework. A new concept, the reduced fundamental matrix, is introduced. It contains just 4 par ..."
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Cited by 57 (19 self)
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This paper deals with the problem of reconstructing the locations of n points in space from m different images without camera calibration. It shows how these problems can be put into a similar theoretical framework. A new concept, the reduced fundamental matrix, is introduced. It contains just 4 parameters and can be used to predict locations of points in the images and to make reconstruction. We also introduce the concept of reduced fundamental tensor, which describes the relations between points in 3 images. It has 15 components and depends on 9 parameters. Necessary and sufficient conditions for a tensor to be a reduced fundamental tensor are derived. This framework can be generalised to a sequence of images. The dependencies between the different representations are investigated. Furthermore a canonical form of the camera matrices in a sequence are presented. 1 Introduction A central problem in scene analysis is the reconstruction of 3Dobjects from 2Dimages, obtained by project...