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96
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 ..."
Abstract

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.
A Factorization Based Algorithm for MultiImage Projective Structure and Motion
, 1996
"... . 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 ..."
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Cited by 212 (15 self)
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. 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. 1 Introduction In the last few years, the geometric and algebraic relations between uncalibrated views have found lively interest in the computer vision community. A first key result states that, from two uncalibrated views, one can recover the 3D structure of a scene up to an unknown projective transformation [Fau92, HGC92]. The information one needs to do so is entirely contained in the fundam...
A SpaceSweep Approach to True MultiImage Matching
, 1996
"... The problem of determining feature correspondences across multiple views is considered. The term "true multiimage" matching is introduced to describe techniques that make full and efficient use of the geometric relationships between multiple images and the scene. A true multiimage technique must ge ..."
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Cited by 184 (4 self)
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The problem of determining feature correspondences across multiple views is considered. The term "true multiimage" matching is introduced to describe techniques that make full and efficient use of the geometric relationships between multiple images and the scene. A true multiimage technique must generalize to any number of images, be of linear algorithmic complexity in the number of images, and use all the images in an equal manner. A new spacesweep approach to true multiimage matching is presented that simultaneously determines 2D feature correspondences and the 3D positions of feature points in the scene. The method is based on the premise that areas of space where several viewing rays intersect are the likely locations of observed 3D scene features. It is shown that the intersections of viewing rays with a plane sweeping through space can be determined very efficiently, and a statistical model is developed to tell how likely it is that a given number of viewing rays will pass th...
Factorization methods for projective structure and motion
 In IEEE Conf. Computer Vision & Pattern Recognition
, 1996
"... This paper describes a family of factorizationbased algorithms that recover 3D projective structure and motion from multiple uncalibrated perspective images of 3D points and lines. They can be viewed as generalizations of the TomasiKanade algorithm from affine to fully perspective cameras, and fro ..."
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Cited by 106 (5 self)
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This paper describes a family of factorizationbased algorithms that recover 3D projective structure and motion from multiple uncalibrated perspective images of 3D points and lines. They can be viewed as generalizations of the TomasiKanade algorithm from affine to fully perspective cameras, and from points to lines. They make no restrictive assumptions about scene or camera geometry, and unlike most existing reconstruction methods they do not rely on ‘privileged’ points or images. All of the available image data is used, and each feature in each image is treated uniformly. The key to projective factorization is the recovery of a consistent set of projective depths (scale factors) for the image points: this is done using fundamental matrices and epipoles estimated from the image data. We compare the performance of the new techniques with several existing ones, and also describe an approximate factorization method that gives similar results to SVDbased factorization, but runs much more quickly for large problems.
Novel View Synthesis in Tensor Space
 In Proc. of IEEE Conference on Computer Vision and Pattern Recognition
, 1997
"... We present a new method for synthesizing novel views of a 3D scene from few model images in full correspondence. The core of this work is the derivation of a tensorial operator that describes the transformation from a given tensor of three views to a novel tensor of a new configuration of three view ..."
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Cited by 96 (8 self)
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We present a new method for synthesizing novel views of a 3D scene from few model images in full correspondence. The core of this work is the derivation of a tensorial operator that describes the transformation from a given tensor of three views to a novel tensor of a new configuration of three views. By repeated application of the operator on a seed tensor with a sequence of desired virtual camera positions we obtain a chain of warping functions (tensors) from the set of model images to create the desired virtual views. 1. Introduction This paper addresses the problem of synthesizing a novel image, from an arbitrary viewing position, given a small number of model images (registered by means of an opticflow engine) of the 3D scene. The most significant aspect of our approach is the ability to synthesize images that are far away from the viewing positions of the sample model images without ever computing explicitly any 3D information about the scene. This property provides a multiimag...
Lines and Point in Three Views and the Trifocal Tensor
, 1997
"... This paper disc#274# the basic role of the trifoc al tensor insc#37 rec# nstr uc#r# n from three views. This 3 3 tensor plays a role in the analysis of sc#422 from three views analogous to the role played by the fundamental matrix in the twoviewc ase. In partic ular, the trifoc al tensor may ..."
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Cited by 74 (3 self)
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This paper disc#274# the basic role of the trifoc al tensor insc#37 rec# nstr uc#r# n from three views. This 3 3 tensor plays a role in the analysis of sc#422 from three views analogous to the role played by the fundamental matrix in the twoviewc ase. In partic ular, the trifoc al tensor may bec omputed by a linear algorithm from a set of 13 linec orrespondenc#3 in three views. It is further shown in this paper, that the trifoc al tensor is essentially identic## to a set ofc oe#c#99 ts introduc#5 by Shashua toe#ec# point transfer in the three viewc##22 This observation means that the 13line algorithm may be extended to allow for thec omputation of the trifoc al tensor given any mixture of su#c#36 tly many line and pointc orrespondenc#9# From the trifoc al tensor thec amera matric## of the images may be c#25371# and the sc#35 may berec#31#41562# For unrelatedunc# libratedc ameras, this rec# nstr uc#r# n will be unique up to projec#939# y. Thus, projec#61 e rec#376#39162 of a set of lines and points may bec#40940 out linearly from three views.
Affine Structure from Line Correspondences with Uncalibrated Affine Cameras
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1997
"... This paper presents a linear algorithm for recovering 3D affine shape and motion from line correspondences with uncalibrated affine cameras. The algorithm requires a minimum of seven line correspondences over three views. The key idea is the introduction of a onedimensional projective camera. This ..."
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Cited by 74 (9 self)
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This paper presents a linear algorithm for recovering 3D affine shape and motion from line correspondences with uncalibrated affine cameras. The algorithm requires a minimum of seven line correspondences over three views. The key idea is the introduction of a onedimensional projective camera. This converts 3D affine reconstruction of "line directions" into 2D projective reconstruction of "points". In addition, a linebased factorisation method is also proposed to handle redundant views. Experimental results both on simulated and real image sequences validate the robustness and the accuracy of the algorithm.
Trilinear Tensor: The Fundamental Construct of Multipleview Geometry and its Applications
 INT. WORSKSHOP ON AFPAC
, 1997
"... The topic of representation, recovery and manipulation of threedimensional (3D) scenes from twodimensional (2D) images thereof, provides a fertile ground for both intellectual theoretically inclined questions related to the algebra and geometry of the problem and to practical applications such ..."
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Cited by 40 (8 self)
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The topic of representation, recovery and manipulation of threedimensional (3D) scenes from twodimensional (2D) images thereof, provides a fertile ground for both intellectual theoretically inclined questions related to the algebra and geometry of the problem and to practical applications such as Visual Recognition, Animation and View Synthesis, recovery of scene structure and camera egomotion, object detection and tracking, multisensor alignment, etc. The basic materials have been known since the turn of the century, but the full scope of the problem has been under intensive study since 1992, first on the algebra of two views and then on the algebra of multiple views leading to a relatively mature understanding of what is known as "multilinear matching constraints", and the "trilinear tensor" of three or more views. The purpose of this paper is, first and foremost, to provide a coherent framework for expressing the ideas behind the analysis of multiple views. Seco...
Mixing catadioptric and perspective cameras
 in: Workshop on Omnidirectional Vision
, 2002
"... We analyze relations that exist between multiple views of a static scene, where the views can be taken by any mixture of paracatadioptric, perspective or affine cameras. Concretely, we introduce the notion of fundamental matrix, trifocal and quadrifocal tensors for the different possible combinatio ..."
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Cited by 33 (14 self)
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We analyze relations that exist between multiple views of a static scene, where the views can be taken by any mixture of paracatadioptric, perspective or affine cameras. Concretely, we introduce the notion of fundamental matrix, trifocal and quadrifocal tensors for the different possible combinations of these camera types. We also introduce the notion of plane homography for mixed image pairs. Generally speaking, these novel multiview relations may form the basis for the typical geometric computations like motion estimation, 3D reconstruction or (self) calibration. A few novel algorithms illustrating some of these aspects, are described, especially concerning what we call calibration transfer, using fundamental matrices, and selfcalibration from plane homographies. 1.
Algebraic Properties of Multilinear Constraints
, 1996
"... In this paper the dioeerent algebraic varieties that can be generated from multiple view geometry with uncalibrated cameras have been investigated. The natural descriptor, Vn , to work with is the image of IP 3 in IP 2 \Theta IP 2 \Theta \Delta \Delta \Delta \Theta IP 2 under a corresponding product ..."
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Cited by 32 (4 self)
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In this paper the dioeerent algebraic varieties that can be generated from multiple view geometry with uncalibrated cameras have been investigated. The natural descriptor, Vn , to work with is the image of IP 3 in IP 2 \Theta IP 2 \Theta \Delta \Delta \Delta \Theta IP 2 under a corresponding product of projections, (A1 \Theta A2 \Theta : : : \Theta Am). Another descriptor, the variety Vb , is the one generated by all bilinear forms between pairs of views, which consists of all points in IP 2 \Theta IP 2 \Theta \Delta \Delta \Delta \Theta IP 2 where all bilinear forms vanish. Yet another descriptor, the variety V t , is the variety generated by all trilinear forms between triplets of views. It has been shown that when m = 3, Vb is a reducible variety with one component corresponding to V t and another corresponding to the trifocal plane. Furthermore, when m = 3, V t is generated by the three bilinearities and one trilinearity, when m = 4, V t is generated by the six bil...