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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 i ..."
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Cited by 401 (9 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
Epipolar Geometry for Panoramic Cameras
, 1998
"... . This paper presents fundamental theory and design of central panoramic cameras. Panoramic cameras combine a convex hyperbolic or parabolic mirror with a perspective camera to obtain a large field of view. We show how to design a panoramic camera with a tractable geometry and we propose a simple ca ..."
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Cited by 74 (10 self)
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calibration method. We derive the image formation function for such a camera. The main contribution of the paper is the derivation of the epipolar geometry between a pair of panoramic cameras. We show that the mathematical model of a central panoramic camera can be decomposed into two central projections
On the probabilistic epipolar geometry
 Image and Vision Computing
, 2008
"... In this paper, we are going to answer the following question: assuming that we have estimates for the epipolar geometry and its uncertainty between two views, how probable it is that a new, independent point pair will satisfy the true epipolar geometry and be, in this sense, a feasible candidate cor ..."
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Cited by 10 (1 self)
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In this paper, we are going to answer the following question: assuming that we have estimates for the epipolar geometry and its uncertainty between two views, how probable it is that a new, independent point pair will satisfy the true epipolar geometry and be, in this sense, a feasible candidate
Cheirality in Epipolar Geometry
, 2000
"... The image points in two images satisfy epipolar constraint. However, not all sets of points satisfying epipolar constraint correspond to any real geometry because there can exist no cameras and scene points projecting to given image points such that all image points have positive depth. Using the ch ..."
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Cited by 14 (3 self)
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The image points in two images satisfy epipolar constraint. However, not all sets of points satisfying epipolar constraint correspond to any real geometry because there can exist no cameras and scene points projecting to given image points such that all image points have positive depth. Using
Epipolar Geometry in Concentric Panoramas
, 2000
"... This work involves a study of the epipolar geometry for the concentric panoramic images. An epipolar curve equation is derived, which enables us to plot the epipolar curve in one of the concentric panoramic images by given an image point in the other image. We also give some analysis on the equation ..."
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Cited by 14 (6 self)
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This work involves a study of the epipolar geometry for the concentric panoramic images. An epipolar curve equation is derived, which enables us to plot the epipolar curve in one of the concentric panoramic images by given an image point in the other image. We also give some analysis
Solving Visibility with Epipolar Geometry
"... In this paper, we use a graphically explaination on how epipolar geometry can be used to solve the visibility. This is paper is prepared mainly for teaching purpose. 1 Introduction Traditional geometrybased computer graphics requires significant amount of time to render complex scenery due to th ..."
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In this paper, we use a graphically explaination on how epipolar geometry can be used to solve the visibility. This is paper is prepared mainly for teaching purpose. 1 Introduction Traditional geometrybased computer graphics requires significant amount of time to render complex scenery due
Epipolar Geometry for Central Catadioptric Cameras
, 2002
"... Central catadioptric cameras are cameras which combine lenses and mirrors to capture a very wide field of view with a central projection. In this paper we extend the classical epipolar geometry of perspective cameras to all central catadioptric cameras. Epipolar geometry is formulated as the geometr ..."
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Cited by 85 (5 self)
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Central catadioptric cameras are cameras which combine lenses and mirrors to capture a very wide field of view with a central projection. In this paper we extend the classical epipolar geometry of perspective cameras to all central catadioptric cameras. Epipolar geometry is formulated
Rectification for any epipolar geometry
 Proc. British Machine Vision Conf
, 2001
"... This paper proposes a new approach to rectification, a process whereby a stereo pair of images is resampled so as to make imposing the two view geometric constraint simple. This is normally performed by applying a single linear transformation per image, a method which has the drawback that some cam ..."
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Cited by 18 (0 self)
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This paper proposes a new approach to rectification, a process whereby a stereo pair of images is resampled so as to make imposing the two view geometric constraint simple. This is normally performed by applying a single linear transformation per image, a method which has the drawback that some camera motions produce rectified images which are heavily distorted or unbounded. More recent attempts have used nonlinear transformations to allow any camera motion, but as a consequence distort images so that matching features no longer look the same in both images. This work provides a hybrid linear/nonlinear method that greatly reduces this problem, and simplifies the technique. The technique also provides further improvements by selecting the rectifying transformation so as to minimise perspective effects between the images. 1
On the Epipolar Geometry in Stereo Vision
"... In this paper we are interested in the calculation of the equation governing pairs of epipolar lines for unregistered images, i.e. when the image acquisition parameters are unknown or no calibration object is available. First we do a thorough analysis of the mathematics required to find the epipolar ..."
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the epipolar line equations in the classical sense. Thereafter we show that for a broad class of stereo images the epipolar line equation can be obtained directly from the images without restrictive assumptions on the stereo geometry and without anyone 3D reference point. Therefore, the estimation
Is Epipolar Geometry Necessary?
"... We examine and co# trast the pro jective pro# ertieso f two simple 3Dco#4366 ratio# s. The first c o# sistso f six po ints, fo# ro f which are c o# lanar. We pro ve that epipo#q1 geo# etry and the essential matrix can bereco vered uniquely fo# this structure and give a c o# structive algo#04 hmfo# t ..."
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We examine and co# trast the pro jective pro# ertieso f two simple 3Dco#4366 ratio# s. The first c o# sistso f six po ints, fo# ro f which are c o# lanar. We pro ve that epipo#q1 geo# etry and the essential matrix can bereco vered uniquely fo# this structure and give a c o# structive algo#04 hmfo# this. The seco# d c figurat io# has fo ur co planar po ints and a singleno nco planar line. In this case it isno t po ssible to determine the epipo#q2 geo# etry. Ho wever, b h structures have two pro jective invariants, and these arereco verable fro# two (uncalibrated) perspective images. We include examples o# the invariants fo# realo# jects. 1
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