Representing stereo data with the Delaunay triangulation

Faugeras, Olivier; Bras-Mehlman, E. Le; Boissonnat, Jean Daniel

doi:10.1016/0004-3702(90)90098-k

Cited by 99 publications

(49 citation statements)

References 17 publications

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“…We abstract the representation of correspondences using a bipartite graph. Because of its well documented robustness to noise and change of viewpoint, we adopt the Delaunay triangulation as our basic representation of image structure [38], [13]. We establish Delaunay triangulations on the data and the model by seeding Voronoi tessellations from the feature-points [1], [2], [3].…”

Section: Point Correspondencesmentioning

confidence: 99%

Graph matching with a dual-step EM algorithm

Cross

Hancock

1998

IEEE Trans. Pattern Anal. Machine Intell.

170

106

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Abstract-This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data.

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Section: Point Correspondencesmentioning

confidence: 99%

Graph matching with a dual-step EM algorithm

Cross

Hancock

1998

IEEE Trans. Pattern Anal. Machine Intell.

170

106

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“…Several sculpting methods [5,13,15,18,20] use visibility knowledge and sparse point cloud P estimated from images. The manifold constraint on |δV | is not enforced by [13,15,18].…”

Section: Sculpting Methods In a 3d Delaunay Triangulationmentioning

confidence: 99%

“…In [13], a non-incremental method estimates a surface minimizing a cost involving visibility and photoconsistency. The manifold constraint is enforced in [5,20]. Method [5] is limited to genus zero surface.…”

Section: Sculpting Methods In a 3d Delaunay Triangulationmentioning

confidence: 99%

“…The manifold constraint is enforced in [5,20]. Method [5] is limited to genus zero surface. Method [20] is incremental but the time complexity of one iteration can be too large: if the camera trajectory is a loop, this complexity is at least linear to the number of camera poses in the loop.…”

Section: Sculpting Methods In a 3d Delaunay Triangulationmentioning

confidence: 99%

“…extra vertices): the diameter of the circumscribing sphere of a tetrahedron is less than the diagonal length l of the (implicit) grid voxels. Since every tetrahedron created by the addition of a point has this point as vertex [5], the addition of P t+1 is a local update of T included in B r+l (c t+1 ).…”

Section: Assumptions and Consequencesmentioning

confidence: 99%

See 2 more Smart Citations

Incremental Solid Modeling from Sparse and Omnidirectional Structure-from-Motion Data

Литвинов¹,

Lhuillier²

2013

Procedings of the British Machine Vision Conference 2013

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This paper introduces a sparse and incremental 2-manifold surface reconstruction method. It uses a sparse 3D point cloud generated by a Structure-from-Motion algorithm (SfM) as its main input as opposed to the more common dense algorithms. Furthermore, our method is incremental: the surface is updated for every new camera pose computed by SfM, and the update occurs in a small neighborhood of the new camera pose. Compared to the other surface reconstruction methods, our method has the advantage to have all these properties at the same time. The quality and execution time of the proposed algorithm is evaluated on a large scale (2.5 km.) real sequence taken in an urban environment, and the method is quantitatively evaluated on a synthetic urban scene.

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Reconstruction of object surfaces by using occlusion information from active stereo vision

et al. 1997

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With robots moving in an unknown 3D environment, it is necessary to work out a method for reconstruction of surface structures (that is, where a surface is present and where there is a free space). In this paper, a method is proposed to recover surfaces by means of active moving of a stereo camera. First, the surface structure of the environment under consideration is represented by a set of virtual 3D segments (arcs) obtained by connecting edge points that lie on the same epipolar line; then the 3D position information and occlusion information acquired by active moving of the stereo camera are used to decide if a physical surface exists between the arcs. Using surface structures that have been so far recovered, camera location that offers the best results in surface reconstruction is predicted, and the camera is moved to this new location to obtain more precise results. The proposed method offers a way to select viewpoints that ensure efficient surface reconstruction, which has not been discussed in any previous study. Experiments showed that the proposed method offers correct reconstruction of object surfaces with a small number of measurements. © 1997 Scripta Technica, Inc. Syst Comp Jpn, 28(9): 86–97, 1997

show abstract

Representing stereo data with the Delaunay triangulation

Cited by 99 publications

References 17 publications

Graph matching with a dual-step EM algorithm

Graph matching with a dual-step EM algorithm

Incremental Solid Modeling from Sparse and Omnidirectional Structure-from-Motion Data

Reconstruction of object surfaces by using occlusion information from active stereo vision

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