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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 ..."
Abstract

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
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
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
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
Balanced Exploration and Exploitation Model Search for Efficient Epipolar Geometry Estimation
"... Abstract — The estimation of the epipolar geometry is especially difficult when the putative correspondences include a low percentage of inlier correspondences and/or a large subset of the inliers is consistent with a degenerate configuration of the epipolar geometry that is totally incorrect. This ..."
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Abstract — The estimation of the epipolar geometry is especially difficult when the putative correspondences include a low percentage of inlier correspondences and/or a large subset of the inliers is consistent with a degenerate configuration of the epipolar geometry that is totally incorrect
The Fundamental matrix: theory, algorithms, and stability analysis
 International Journal of Computer Vision
, 1995
"... 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 th ..."
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Cited by 272 (13 self)
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in stereo and shows that the epipolar geometry can be summarized in one 3 \Theta 3 ma...
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
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
Blogs: Balanced local and global search for nondegenerate two view epipolar geometry
, 2009
"... ..."
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
Results 11  20
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