## Estimating Motion and Structure from Correspondences of Line Segments Between Two Perspective Images (1994)

Citations: | 30 - 1 self |

### BibTeX

@MISC{Zhang94estimatingmotion,

author = {Zhengyou Zhang},

title = {Estimating Motion and Structure from Correspondences of Line Segments Between Two Perspective Images},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present in this paper an algorithm for determining 3D motion and structure from correspondences of line segments between two perspective images. To our knowledge, this paper is the first investigation on use of line segments in motion and structure from motion. Classical methods use their geometric abstraction, namely straight lines, but then three images are necessary. We show in this paper that two views are in general sufficient when using line segments. The assumption we use is that two matched line segments contain the projection of a common part of the corresponding line segment in space. Indeed, this is what we use to match line segments between different views. Both synthetic and real data have been used to test the proposed algorithm, and excellent results have been obtained with real data containing about one hundred line segments. The results are comparable with those obtained with calibrated stereo.

### Citations

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Citation Context ...nction F = n X i=1 i (1 \Gamma L i =l i ) 2 + (1 \Gamma L 0 i =l 0 i ) 2 j : (7) 3.4 Implementation details The minimization of the objective function (7) is conducted using a downhill simplex method =-=[17]-=-. The rotation R is represented by a 3D vector r = [r 1 ; r 2 ; r 3 ] T , whose direction is that of the rotation axis and whose norm is the equal to the rotation angle. The vector r is related to the... |

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Citation Context ... sufficient to recover the motion and structure of the scene. When straight lines are used, three perspective views are necessary. Closed-form solutions are available either for point correspondences =-=[13, 18]-=- or for line correspondences [17, 12]. Algorithms using both points and lines are also available [16]. However, another important type of geometric primitives, namely that of line segments , has been ... |

504 |
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Citation Context ...y, 50). To alleviate this requirement, we can use points in combination, and this is what we are doing. Recently, many researchers are working with uncalibrated images using points and straight lines =-=[5, 10, 14, 20]-=-. The proposed algorithm in this paper can be easily extended to estimate the epipolar geometry between two uncalibrated images using line segments. The only problem is that we need to sample a higher... |

467 |
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Citation Context ... Introduction The problem of estimating motion and structure from two or three images has been studied for a while in the computer vision community. We can trace it back to the late seventies: Ullman =-=[19]-=- assumed a orthographic camera projection model and showed that three views are necessary to recover the motion and structure from point correspondences; Roach and Aggarwal [15] used a full perspectiv... |

313 |
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(Show Context)
Citation Context ... sufficient to recover the motion and structure of the scene. When straight lines are used, three perspective views are necessary. Closed-form solutions are available either for point correspondences =-=[13, 18]-=- or for line correspondences [17, 12]. Algorithms using both points and lines are also available [16]. However, another important type of geometric primitives, namely that of line segments , has been ... |

242 |
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Citation Context ...y, 50). To alleviate this requirement, we can use points in combination, and this is what we are doing. Recently, many researchers are working with uncalibrated images using points and straight lines =-=[5, 10, 14, 20]-=-. The proposed algorithm in this paper can be easily extended to estimate the epipolar geometry between two uncalibrated images using line segments. The only problem is that we need to sample a higher... |

157 |
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Citation Context ...om point correspondences. Since then, many approaches have been proposed to solve the problem using either linear or nonlinear methods. The reader is referred to [1, 12] for a complete review, and to =-=[16]-=- for a theoretical study. Essentially, two types of geometric primitives have been used in solving motion and struc ture problem, namely points and straight lines. When points are used, two perspectiv... |

153 |
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Citation Context ...l and thus two views are sufficient from point correspondences. Since then, many approaches have been proposed to solve the problem using either linear or nonlinear methods. The reader is referred to =-=[11]-=- for a complete review. Essentially, two types of geometric primitives have been used in solving motion and structure problem, namely points and straight lines. When points are used, two perspective v... |

147 |
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Citation Context ...el and thus two views are suOEcient from point correspondences. Since then, many approaches have been proposed to solve the problem using either linear or nonlinear methods. The reader is referred to =-=[1, 12]-=- for a complete review, and to [16] for a theoretical study. Essentially, two types of geometric primitives have been used in solving motion and struc ture problem, namely points and straight lines. W... |

142 |
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Citation Context ...ithm with three sets of real data which were extracted from a trinocular stereo system [1]. We have chosen the stereo data because the stereo system has been calibrated which serves as a ground truth =-=[7]-=-. The first set of real data is an image pair of an Office scene (see Fig. 20). 98 line segments have been matched by our trinocular stereo system, as shown in Fig. 21. One can notice quite a few fals... |

109 |
Structure from Motion Using Line Correspondences
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Citation Context ... structure of the scene. When straight lines are used, three perspective views are necessary. Closed-form solutions are available either for point correspondences [13, 18] or for line correspondences =-=[17, 12]-=-. Algorithms using both points and lines are also available [16]. However, another important type of geometric primitives, namely that of line segments , has been since long ignored in motion and stru... |

96 |
Tracking Line Segments
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(Show Context)
Citation Context ...lap). Indeed, this assumption is minimal, and is what we use to match line segments between different views. We do not address the problem of matching line segments here. This can be done by tracking =-=[4, 8]-=- or other techniques [3]. This paper is organized as follows. Section 2 describes the problem we want to solve and shows why we can determine 3D motion and structure from corresponding line segments b... |

57 |
Matrice Fondamentale et Calibration Visuelle sur l’Environment
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(Show Context)
Citation Context ...y, 50). To alleviate this requirement, we can use points in combination, and this is what we are doing. Recently, many researchers are working with uncalibrated images using points and straight lines =-=[5, 10, 14, 20]-=-. The proposed algorithm in this paper can be easily extended to estimate the epipolar geometry between two uncalibrated images using line segments. The only problem is that we need to sample a higher... |

51 |
A unified theory of structure from motion
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(Show Context)
Citation Context ...tive views are necessary. Closed-form solutions are available either for point correspondences [13, 18] or for line correspondences [17, 12]. Algorithms using both points and lines are also available =-=[16]-=-. However, another important type of geometric primitives, namely that of line segments , has been since long ignored in motion and structure from motion 1 . The importance of line segments in compute... |

49 |
Determining the movement of objects from a sequence of images
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(Show Context)
Citation Context ...late seventies: Ullman [19] assumed a orthographic camera projection model and showed that three views are necessary to recover the motion and structure from point correspondences; Roach and Aggarwal =-=[15]-=- used a full perspective projection model and thus two views are sufficient from point correspondences. Since then, many approaches have been proposed to solve the problem using either linear or nonli... |

39 |
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Citation Context ...els: Data Car, 17 segments : : : : : : : 19 12 Motion errors versus different noise levels: Data All, 32 segments : : : : : : : 20 13 Motion errors versus different initial rotations: r true + is0:02s=-=[0; 1; 0]-=- T : : : 21 14 Motion errors versus different initial rotations: r true + is0:02s[1; 0; 0] T : : : 21 15 Motion errors versus different initial rotations: r true + is0:02s[1; 1; 1] T : : : 22 16 Motio... |

39 |
3D Dynamic Scene Analysis,: A stereo based approach
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(Show Context)
Citation Context ...ts of lines segments. Section 4 addresses the issue of 3D reconstruction of line segments 1 3D line segments, reconstructed by a stereo system, have been used in motion analysis by Zhang and Faugeras =-=[21]-=-, but the problem there is different from the one addressed here. RR n2340 4 Zhengyou Zhang provided the motion is estimated. Section 5 provides the experimental results with both synthetic and real d... |

25 | Motion of points and lines in the uncalibrated case
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Citation Context |

24 |
Image registration by matching relational structures
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(Show Context)
Citation Context ...on is minimal, and is what we use to match line segments between different views. We do not address the problem of matching line segments here. This can be done by tracking [4, 8] or other techniques =-=[3]-=-. This paper is organized as follows. Section 2 describes the problem we want to solve and shows why we can determine 3D motion and structure from corresponding line segments between two images. Secti... |

8 |
A linear algorithm for determining motion and structure from line correspondences
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(Show Context)
Citation Context ... structure of the scene. When straight lines are used, three perspective views are necessary. Closed-form solutions are available either for point correspondences [13, 18] or for line correspondences =-=[17, 12]-=-. Algorithms using both points and lines are also available [16]. However, another important type of geometric primitives, namely that of line segments , has been since long ignored in motion and stru... |

4 |
Motion of points and lines in the uncalibrated case
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(Show Context)
Citation Context ...tion to this would be just to discard the line segments that form a small angle with the epipolar lines. Recently, many researchers have worked with uncalibrated images using points or straight lines =-=[6, 11, 15, 23]-=-. The algorithm proposed in this paper can easily be extended to estimate the epipolar geometry between two uncalibrated images using line segments. The only problem is that we need to sample a higher... |

2 |
Suivi de segments dans une s'equence d'images monoculaire
- Giai-Checa, Deriche, et al.
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(Show Context)
Citation Context ...lap). Indeed, this assumption is minimal, and is what we use to match line segments between different views. We do not address the problem of matching line segments here. This can be done by tracking =-=[4, 8]-=- or other techniques [3]. This paper is organized as follows. Section 2 describes the problem we want to solve and shows why we can determine 3D motion and structure from corresponding line segments b... |

2 |
Chainage efficace contour. Rapport de Recherche 605
- Giraudon
- 1987
(Show Context)
Citation Context ...ion and Structure from Correspondences of Line Segments 7 However, the location and orientation of a line segment can generally be reliably determined by fitting a line to a set of linked edge points =-=[9]-=-. Now, the problem to be solved in this paper can be stated as follows: Given two sets of line segments, f(l i ; l 0 i ) j i = 1; : : : ; ng, which are in correspondence, Estimate the camera motion pa... |

1 |
Suivi de segments dans une s#quence d'images monoculaire
- Giai-Checa, Deriche, et al.
- 1993
(Show Context)
Citation Context ...lap). Indeed, this assumption is minimal, and is what we use to match line segments between dioeerent views. We do not address the problem of matching line segments here. This can be done by tracking =-=[5, 9]-=- or other techniques [4]. This paper is organized as follows. Section 2 describes the problem we want to solve and shows why we can recover 3D motion and structure from corresponding line segments bet... |

1 |
Cha#nage eOEcace contour. Rapport de Recherche 605
- Giraudon
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(Show Context)
Citation Context ...ges, the segments endpoints may vary from frame to frame. However, the location and orientation of a line segment can generally be reliably determined by ��tting a line to a set of linked edge poi=-=nts [10]-=-. Now, the problem to be solved in this paper can be stated as follows: Given two sets of line segments, f(l i ; l 0 i ) j i = 1; : : : ; ng, which are in correspondence, Estimate the camera motion pa... |