## A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry (1994)

Citations: | 486 - 32 self |

### BibTeX

@MISC{Zhang94arobust,

author = {Zhengyou Zhang and Rachid Deriche and Olivier Faugeras and Quang-Tuan Luong},

title = { A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

1923 |
Robust Statistics
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Citation Context ... the robustness of vision algorithms because the data are unavoidably error prone [17, 60]. Many the so-called robust regression methods have been proposed that are not so easily affected by outliers =-=[25, 48]-=-. The reader is referred to [48, Chap. 1] for a review of different robust methods. The two most popular robust methods are the M-estimators and the least-median-of-squares (LMedS) method (see Sect. 6... |

1813 | A Combined Corner and Edge Detector
- Harris, Stephens
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(Show Context)
Citation Context ...ve been proposed within this group are generally based on the measurement of the gradients and of the curvatures of the surface (see [11] for a review). In our application, we use the corner detector =-=[19]-=-, which is a slightly modified version of the Plessey corner detector [20, 41]. It is based on the following operator: R(x; y) = det[sC] \Gamma k trace 2 [sC] ; (3) INRIA A Robust Technique for Matchi... |

1158 |
Robust regression and outlier detection
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Citation Context ... the robustness of vision algorithms because the data are unavoidably error prone [17, 60]. Many the so-called robust regression methods have been proposed that are not so easily affected by outliers =-=[25, 48]-=-. The reader is referred to [48, Chap. 1] for a review of different robust methods. The two most popular robust methods are the M-estimators and the least-median-of-squares (LMedS) method (see Sect. 6... |

852 |
Computer Vision
- Ballard, Brown
- 1982
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Citation Context ... two categories: 1. Template matching. In this category, the algorithms attempt to correlate the grey levels of image patches in the views being considered, assuming that they present some similarity =-=[4, 15, 16, 7, 14]-=-. The underlying assumption appears to be a valid one for relatively textured areas and for image pairs with small difference; however it may be wrong at occlusion boundaries and within featureless re... |

650 |
A computer algorithm for reconstructing a scene from two projections
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Citation Context ... lie in a single plane. This is the well-known co-planarity constraint or epipolar equation in solving motion and structure from motion problems when the intrinsic parameters of the cameras are known =-=[29]-=-. Let the displacement from the first camera to the second be (R; t). Let m 1 and m 2 be the images of a 3-D point M on the cameras. Without loss of generality, we assume that M is expressed in the co... |

484 |
The interpretation of visual motion
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(Show Context)
Citation Context ... because only a small subset of the image pixels are used, but may fail if the chosen primitives cannot be reliably detected in the images. The following list of references is by no means exhaustive: =-=[54, 50, 5, 6, 45, 35, 22, 55]-=- The approach we propose in this paper aims at exploiting the only geometric constraint, i.e., the epipolar constraint, to establish robustly correspondences between two perspective images of a single... |

356 |
Scene labeling by relaxation operations
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Citation Context ...hus saving half of the computation. There are several strategies for updating the matching in order to minimize the total energy. The first is the "winner-take-all ", as exploited by Rosenfe=-=ld et al. [47]-=-, Zucker et al. [61], and Pollard et al. [44]. The method works as follows. At each iteration, any matches which have the highest matching strengths for both of the two image points that formed them a... |

319 | Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces
- Tsai, Huang
- 1984
(Show Context)
Citation Context ... to the essential matrix E = t \Theta R [29, 23] by F = A \GammaT 2 EA \Gamma1 1 : It is thus clear that if the cameras are calibrated, the problem becomes the one of motion and structure from motion =-=[29, 53, 39, 13, 1, 56, 24]-=-. 4 Finding Candidate Matches by Correlation Before recovering the epipolar geometry, we must establish a few correspondences between images. To this end, a corner detector is first applied to each im... |

295 |
Faugeras. A theory of selfcalibration of a moving camera
- Maybank, D
- 1992
(Show Context)
Citation Context ....e., the vertexes of the two pencils of epipolar lines) and the 3 parameters of the homography between these two pencils. This is the only geometric information available from two uncalibrated images =-=[36, 31]-=-. This implies that the fundamental matrix has only seven degrees of freedom. Indeed, it is only defined up to a scale factor and its determinant is zero. Geometrically, F ~ m 1 defines the epipolar l... |

283 | Robust multiresolution estimation of parametric motion models
- Odobez, Bouthemy
- 1995
(Show Context)
Citation Context ... applied the LMedS estimator to detect moving objects using point correspondences between orthographic views. Other recent works on the application of robust techniques to motion segmentation include =-=[52, 42, 3]-=-. Regarding the robust recovery of the epipolar geometry, our work is closely related to that of Olsen [43] and that of Shapiro and Brady [49]. Olsen uses a linear method to estimate the epipolar geom... |

228 |
Robust regression methods for computer vision: A review, Int
- Meer, Mintz, et al.
- 1991
(Show Context)
Citation Context ...timators and the least-median-of-squares (LMedS) method (see Sect. 6.3). Kumar and Hanson [26] compared different robust methods for pose refinement from 3D-2D line correspondences, while Meer et al. =-=[38]-=-, for image smoothing. Haralick et al. [18] applied M-estimators to solve the pose problem from point correspondences. Thompson et al. [51] applied the LMedS estimator to detect moving objects using p... |

196 | The curvature primal sketch
- Asada, Brady
- 1986
(Show Context)
Citation Context ...iterature in the last few years. They can be broadly divided into two groups: The first group consists in first extracting edges as a chain code, and then searching for points having maxima curvature =-=[10, 2, 37]-=- or performing a polygonal approximation on the chains and then searching for the line segment intersections [21]. The second group works directly on a grey-level image. The large number of techniques... |

181 |
Motion and structure from two perspective views: algorithms, error analysis and error estimation
- Weng, Huang, et al.
- 1989
(Show Context)
Citation Context ... to the essential matrix E = t \Theta R [29, 23] by F = A \GammaT 2 EA \Gamma1 1 : It is thus clear that if the cameras are calibrated, the problem becomes the one of motion and structure from motion =-=[29, 53, 39, 13, 1, 56, 24]-=-. 4 Finding Candidate Matches by Correlation Before recovering the epipolar geometry, we must establish a few correspondences between images. To this end, a corner detector is first applied to each im... |

180 |
Structural descriptions and inexact matching
- Shapiro, Haralick
- 1981
(Show Context)
Citation Context ... because only a small subset of the image pixels are used, but may fail if the chosen primitives cannot be reliably detected in the images. The following list of references is by no means exhaustive: =-=[54, 50, 5, 6, 45, 35, 22, 55]-=- The approach we propose in this paper aims at exploiting the only geometric constraint, i.e., the epipolar constraint, to establish robustly correspondences between two perspective images of a single... |

159 |
A.N.: Motion and Structure from Feature Correspondences: A Review
- Huang, Netravali
- 1994
(Show Context)
Citation Context ... to the essential matrix E = t \Theta R [29, 23] by F = A \GammaT 2 EA \Gamma1 1 : It is thus clear that if the cameras are calibrated, the problem becomes the one of motion and structure from motion =-=[29, 53, 39, 13, 1, 56, 24]-=-. 4 Finding Candidate Matches by Correlation Before recovering the epipolar geometry, we must establish a few correspondences between images. To this end, a corner detector is first applied to each im... |

158 |
PMF: A stereo correspondence algorithm using a disparity gradient limit", Perception 14
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- 1985
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Citation Context ...m 1i ; m 2j ; n 1k ; n 2l ) and " r is a threshold on the relative distance difference. The above definition of the strength of a match is similar in the form to that used in the PMF stereo algor=-=ithm [44]-=-. Several remarks can be made regarding our measure of matching support. ffl Firstly, the strength of a match actually counts the number of candidate matches found in the neighborhoods, but only those... |

149 |
On the computation of motion from sequences of images - a review
- Aggarwal
- 1988
(Show Context)
Citation Context |

133 | Disparity Analysis of Images
- Barnard, Thompson
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Citation Context ... because only a small subset of the image pixels are used, but may fail if the chosen primitives cannot be reliably detected in the images. The following list of references is by no means exhaustive: =-=[54, 50, 5, 6, 45, 35, 22, 55]-=- The approach we propose in this paper aims at exploiting the only geometric constraint, i.e., the epipolar constraint, to establish robustly correspondences between two perspective images of a single... |

118 |
A parallel stereo algorithm that produces dense depth maps and preserve iamge features
- Fua
- 1993
(Show Context)
Citation Context ... two categories: 1. Template matching. In this category, the algorithms attempt to correlate the grey levels of image patches in the views being considered, assuming that they present some similarity =-=[4, 15, 16, 7, 14]-=-. The underlying assumption appears to be a valid one for relatively textured areas and for image pairs with small difference; however it may be wrong at occlusion boundaries and within featureless re... |

110 | A computational approach for corner and vertex detection
- Deriche, Giraudon
- 1993
(Show Context)
Citation Context ...ectly on a grey-level image. The large number of techniques that have been proposed within this group are generally based on the measurement of the gradients and of the curvatures of the surface (see =-=[11]-=- for a review). In our application, we use the corner detector [19], which is a slightly modified version of the Plessey corner detector [20, 41]. It is based on the following operator: R(x; y) = det[... |

103 | Outlier detection and motion segmentation
- Torr, Murray
- 1993
(Show Context)
Citation Context ... applied the LMedS estimator to detect moving objects using point correspondences between orthographic views. Other recent works on the application of robust techniques to motion segmentation include =-=[52, 42, 3]-=-. Regarding the robust recovery of the epipolar geometry, our work is closely related to that of Olsen [43] and that of Shapiro and Brady [49]. Olsen uses a linear method to estimate the epipolar geom... |

99 |
Faugeras, Tracking line segments
- Deriche, O
- 1990
(Show Context)
Citation Context ...istics in one form or another, for example, intensity similarity, which are not applicable to most cases. The difficulty is partly bypassed by taking long sequences of images over short time interval =-=[9, 58]-=-. Indeed, as the time interval is small and object velocity is constrained by physical laws, the interframe displacements of objects are bounded, i.e., the correspondence of a token at the subsequent ... |

95 | Stereo correspondence through feature grouping and maximal cliques
- Skordas
- 1989
(Show Context)
Citation Context |

92 | On Determining the Fundamental Matrix: Analysis of Different Methods and Experimental Result,” technical report
- Luong, Deriche, et al.
- 1993
(Show Context)
Citation Context ...ork is closely related to that of Olsen [43] and that of Shapiro and Brady [49]. Olsen uses a linear method to estimate the epipolar geometry, which has already been shown in one of our previous work =-=[32]-=- to be insufficiently accurate. He further assumes that knowledge of the epipolar geometry, as in many practical cases, is available. In particular, he assumes the epipolar lines are almost aligned ho... |

90 | Faugeras. Robust recovery of the epipolar geometry for an uncalibrated stereo rig
- Deriche, Luong
- 1994
(Show Context)
Citation Context ...lar geometry, and then describe in detail the three steps of the proposed approach. A preliminary version of this paper appeared in the proceedings of the third European Conference on Computer Vision =-=[12]-=-. A similar idea has been independently exploited by Xu et al. [57, 40], who also searched for image correspondences through the recovery of the epipolar geometry. There are however two main differenc... |

66 | Finding Corners
- Noble
- 1988
(Show Context)
Citation Context ...of the gradients and of the curvatures of the surface (see [11] for a review). In our application, we use the corner detector [19], which is a slightly modified version of the Plessey corner detector =-=[20, 41]. It -=-is based on the following operator: R(x; y) = det[sC] \Gamma k trace 2 [sC] ; (3) INRIA A Robust Technique for Matching Two Uncalibrated Images 9 wheresC is the following matrix:sC = " I 2 x d I ... |

60 |
Some properties of the E matrix in two-view motion estimation
- Huang, Faugeras
- 1989
(Show Context)
Citation Context ...ar line. Transposing equation 2 yields the symmetric relation from the second image to the first image. It can be shown that the fundamental matrix F is related to the essential matrix E = t \Theta R =-=[29, 23]-=- by F = A \GammaT 2 EA \Gamma1 1 : It is thus clear that if the cameras are calibrated, the problem becomes the one of motion and structure from motion [29, 53, 39, 13, 1, 56, 24]. 4 Finding Candidate... |

58 |
Matching two perspective views
- Weng, Ahuja, et al.
- 1992
(Show Context)
Citation Context |

57 |
Matrice Fondamentale et Calibration Visuelle sur l’Environment
- Luong
- 1992
(Show Context)
Citation Context ...damental constraint underlying any two images if they are perspective projections of one and the same scene. Let F = A \GammaT 2 TRA \Gamma1 1 , F is known as the fundamental matrix of the two images =-=[31]-=-. Without considering 3-D metric entities, we can think of the fundamental matrix as providing the two epipoles (i.e., the vertexes of the two pencils of epipolar lines) and the 3 parameters of the ho... |

49 |
Corner detection and curve representation using cubic B-splines
- Medioni, Yasumoto
(Show Context)
Citation Context ...iterature in the last few years. They can be broadly divided into two groups: The first group consists in first extracting edges as a chain code, and then searching for points having maxima curvature =-=[10, 2, 37]-=- or performing a polygonal approximation on the chains and then searching for the line segment intersections [21]. The second group works directly on a grey-level image. The large number of techniques... |

45 |
Finding Geometric and Relational Structures in an Image
- Horaud, Skordas
- 1990
(Show Context)
Citation Context ...ng edges as a chain code, and then searching for points having maxima curvature [10, 2, 37] or performing a polygonal approximation on the chains and then searching for the line segment intersections =-=[21]-=-. The second group works directly on a grey-level image. The large number of techniques that have been proposed within this group are generally based on the measurement of the gradients and of the cur... |

44 |
Motion and structure from motion from point and line matching
- Faugeras, Lustman, et al.
- 1987
(Show Context)
Citation Context |

39 | Recovering and characterizing image features using an efficient model based approach
- Deriche, Blaszka
- 1993
(Show Context)
Citation Context ...s us to recover a corner position up to pixel precision. In order to recover the corner position up to sub-pixel position, one uses the model based approach we have already developed and presented in =-=[8]-=-, where corners are extracted directly from the image by searching the parameters of the parametric model that best approximate the observed grey level image intensities around the corner position det... |

39 | Determination of ego-motion from matched points
- Harris
- 1987
(Show Context)
Citation Context ...of the gradients and of the curvatures of the surface (see [11] for a review). In our application, we use the corner detector [19], which is a slightly modified version of the Plessey corner detector =-=[20, 41]. It -=-is based on the following operator: R(x; y) = det[sC] \Gamma k trace 2 [sC] ; (3) INRIA A Robust Technique for Matching Two Uncalibrated Images 9 wheresC is the following matrix:sC = " I 2 x d I ... |

37 |
Segmentation of moving objects by robust motion parameter estimation over multiple frames
- Ayer, Schroeter, et al.
- 1994
(Show Context)
Citation Context ... applied the LMedS estimator to detect moving objects using point correspondences between orthographic views. Other recent works on the application of robust techniques to motion segmentation include =-=[52, 42, 3]-=-. Regarding the robust recovery of the epipolar geometry, our work is closely related to that of Olsen [43] and that of Shapiro and Brady [49]. Olsen uses a linear method to estimate the epipolar geom... |

35 |
Estimation of displacements from two 3D frames obtained from stereo
- Zhang, Faugeras
- 1992
(Show Context)
Citation Context ...n initial set of correspondences. We could apply the same strategy as that of Xu et al. [57, 40]. In fact, it has been applied to solve the correspondence problem between two sets of 3D line segments =-=[59]-=-. When applying it to the problem addressed in this paper, we need 8 point correspondences in order to estimate the epipolar geometry. The complexity is then O(m 8 n 8 ). Suppose both m and n are 100,... |

31 |
The reconstruction of a scene from two projections – configurations that defeat the 8-point algorithm
- Longuet-Higgins
- 1984
(Show Context)
Citation Context ... This approach, known as the eight point algorithm, was introduced by Longuet-Higgins [29] for solving the motion and structure from motion problem, and has been extensively studied in the literature =-=[30, 53, 56, 27]-=- for the computation of the Essential matrix E (see Sect. 3). It has proven to be very sensitive to noise. In practice, we are given many more than 8 matches and we use a least-squares method to solve... |

29 |
Rejecting outliers and estimating errors in an orthogonal regression framework
- Shapiro, Brady
- 1995
(Show Context)
Citation Context ...f robust techniques to motion segmentation include [52, 42, 3]. Regarding the robust recovery of the epipolar geometry, our work is closely related to that of Olsen [43] and that of Shapiro and Brady =-=[49]-=-. Olsen uses a linear method to estimate the epipolar geometry, which has already been shown in one of our previous work [32] to be insufficiently accurate. He further assumes that knowledge of the ep... |

24 |
Image registration by matching relational structures
- Cheng, Huang
- 1984
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Citation Context |

23 |
Modeling and identification of characteristic intensity variations. Image and Vision Computing
- Rohr
- 1992
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Citation Context ...accuracy of matched points. One possibility is to use subpixelprecision corner detector whenever possible. For example, if we are working in an indoor environment, we may use corner detectors such as =-=[11, 46, 8]-=-. Another possibility is to apply subpixel-precision correlation techniques. The idea is to compute the correlation RR n2273 34 Zhang, Deriche, Faugeras, Luong score for each point in the neighborhood... |

22 |
A twestage cross correlation approach to template matching
- Gage, Bartholic
- 1984
(Show Context)
Citation Context ... two categories: 1. Template matching. In this category, the algorithms attempt to correlate the grey levels of image patches in the views being considered, assuming that they present some similarity =-=[4, 15, 16, 7, 14]-=-. The underlying assumption appears to be a valid one for relatively textured areas and for image pairs with small difference; however it may be wrong at occlusion boundaries and within featureless re... |

21 |
2D curve matching using high curvature points: Applications to stereo vision
- Deriche, Faugeras
- 1990
(Show Context)
Citation Context ...iterature in the last few years. They can be broadly divided into two groups: The first group consists in first extracting edges as a chain code, and then searching for points having maxima curvature =-=[10, 2, 37]-=- or performing a polygonal approximation on the chains and then searching for the line segment intersections [21]. The second group works directly on a grey-level image. The large number of techniques... |

21 |
Computer Vision Theory: The Lack Thereof
- Haralick
- 1985
(Show Context)
Citation Context ...ar constraint, which is not addressed in this paper. Recently, computer vision researchers have paid much attention to the robustness of vision algorithms because the data are unavoidably error prone =-=[17, 60]-=-. Many the so-called robust regression methods have been proposed that are not so easily affected by outliers [25, 48]. The reader is referred to [48, Chap. 1] for a review of different robust methods... |

20 | and O.D.Faugeras. A stability analysis for the fundamental matrix
- Luong
- 1994
(Show Context)
Citation Context ...es, and eventually compute the position with the largest correlation score. Stability The stability of our algorithm is directly related to that of finding the fundamental matrix, which is studied in =-=[33]-=-. One of the most stringent situations is that all points are located close to a critical surface, for example, a plane. If the points are almost on a plane, it is better to describe their relation be... |

20 |
Detecting moving objects using the rigidity constraint
- Thompson, Lechleider, et al.
- 1993
(Show Context)
Citation Context ...efinement from 3D-2D line correspondences, while Meer et al. [38], for image smoothing. Haralick et al. [18] applied M-estimators to solve the pose problem from point correspondences. Thompson et al. =-=[51]-=- applied the LMedS estimator to detect moving objects using point correspondences between orthographic views. Other recent works on the application of robust techniques to motion segmentation include ... |

18 |
Epipolar Line Estimation
- Olsen
- 1992
(Show Context)
Citation Context ...r recent works on the application of robust techniques to motion segmentation include [52, 42, 3]. Regarding the robust recovery of the epipolar geometry, our work is closely related to that of Olsen =-=[43]-=- and that of Shapiro and Brady [49]. Olsen uses a linear method to estimate the epipolar geometry, which has already been shown in one of our previous work [32] to be insufficiently accurate. He furth... |

17 |
Image sequence analysis using relational structures
- Radig
- 1984
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Citation Context |

16 |
Image sequences - ten (octal) years - from phenomenology towards a theoretical foundation
- Nagel
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Citation Context |

16 |
A Highly Robust Estimator Through Partially Likelihood Function Modeling and
- Zhuang, Wang, et al.
- 1992
(Show Context)
Citation Context ...ar constraint, which is not addressed in this paper. Recently, computer vision researchers have paid much attention to the robustness of vision algorithms because the data are unavoidably error prone =-=[17, 60]-=-. Many the so-called robust regression methods have been proposed that are not so easily affected by outliers [25, 48]. The reader is referred to [48, Chap. 1] for a review of different robust methods... |

10 |
Analysis of different robust methods for pose refinement
- Kumar, Hanson
- 1990
(Show Context)
Citation Context ...ed to [48, Chap. 1] for a review of different robust methods. The two most popular robust methods are the M-estimators and the least-median-of-squares (LMedS) method (see Sect. 6.3). Kumar and Hanson =-=[26]-=- compared different robust methods for pose refinement from 3D-2D line correspondences, while Meer et al. [38], for image smoothing. Haralick et al. [18] applied M-estimators to solve the pose problem... |