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Keywords
(5)
Closed Form Solution
Eigenvectors
Linear System
Shape Estimation
Weighted Sums
Related Publications
(5)
Semidefinite Programming Heuristics for Surface Reconstruction Ambiguities
Convex Optimization for Deformable Surface 3D Tracking
Fast NonRigid Surface Detection, Registration and Realistic Augmentation
Monocular Templatebased Reconstruction of Inextensible Surfaces
Distinctive Image Features from ScaleInvariant Keypoints
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ClosedForm Solution to Nonrigid 3D Surface Registration
ClosedForm Solution to Nonrigid 3D Surface Registration,10.1007/9783540886938_43,Mathieu Salzmann,Francesc Morenonoguer,Vincent Lepetit,Pascal
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ClosedForm Solution to Nonrigid 3D Surface Registration
(
Citations: 20
)
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Mathieu Salzmann
,
Francesc Morenonoguer
,
Vincent Lepetit
,
Pascal Fua
We present a closedform solution to the problem of recovering the 3D shape of a nonrigid inelastic surface from 3Dto2D correspondences. This lets us detect and reconstruct such a surface by matching individual images against a reference configuration, which is in contrast to all existing approaches that require initial shape estimates and track deformations from image to image. We represent the surface as a mesh, and write the constraints provided by the correspondences as a
linear system
whose solution we express as a weighted sum of eigenvectors. Obtaining the weights then amounts to solving a set of quadratic equations accounting for inextensibility constraints between neighboring mesh vertices. Since available closedform solutions to quadratic systems fail when there are too many variables, we reduce the number of unknowns by expressing the deformations as a linear combination of modes. The overall closedform solution then becomes tractable even for complex deformations that require many modes.
Conference:
European Conference on Computer Vision  ECCV
, pp. 581594, 2008
DOI:
10.1007/9783540886938_43
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Citation Context
(19)
...We make two basic assumptions, shared with many stateoftheart approaches [16, 19, 21,
22
]...
...Several recent methods have been proposed to recover nonrigid shape from single images, by using deformation modes in conjunction with local rigidity constraints to reconstruct inextensible surfaces [9, 19, 21,
22
], and in conjunction with shading constraints to reconstruct stretchable surfaces [16]...
...In particular, as part of future work, we pretend to investigate the use of length constraints on the edges of the mesh, as has been done in previous literature [19,
22
]...
Francesc MorenoNoguer
,
et al.
Probabilistic simultaneous pose and nonrigid shape recovery
...The nonrigid surface is usually modeled by a collection of triangles [18], [
19
]...
Sandy Martedi
,
et al.
Foldable augmented papers with a relaxed constraint
...An efficient approximation consists in saying that the geodesic distance between two points is an upper bound to the Euclidean distance [3,
16
]...
...Other methods use more complex surface models such as triangular meshes [1,
16
] or smooth surfaces such as ThinPlate Splines [3, 5]. In this latter case, the 3D surface is represented as a parametric 2D3D map between the template image space and the 3D space...
...Such an approach has been used for instance in [2, 12,
16
, 20]...
...Another sort of implementation is given by [1,
16
]...
...The approaches of [1, 2,
16
] use a triangular mesh as surface model, and the inextensibility constraints are applied to the vertices of the mesh...
...We can express this in terms of imageplane measurements. As in [1,
16
], 56 F. Brunet et al...
...However, contrary to [1,
16
], our approach is a pointwise method that does not require us to tune the relative influence of minimizing the reprojection error and maximizing the depths...
Florent Brunet
,
et al.
Monocular TemplateBased Reconstruction of Smooth and Inextensible Sur...
...When 3Dto2D correspondences between an input image and another one for which the shape is known can be established, monocular 3D nonrigid reconstruction is a well understood problem effectively addressed by many recent works [7, 19, 21, 22,
23
]...
...Several approaches have shown that shape may be recovered from a set of 3Dto2D correspondences, between the 3D points of a reference shape and the 2D points on the input image [7, 19, 21, 22,
23
]...
...This lets us to retrieve the shape without imposing the additional constraints that these methods consider, based on local inextensibility [7, 21, 22,
23
] or shading information [19]...
...Given the set of 3D points and their potential 2D candidates, we could now follow a RANSACbased approach and hypothesize sets of 3Dto2D correspondences and validate them with any of the current techniques to retrieve shape from such correspondences [7, 19, 21, 22,
23
]...
Jordi SanchezRiera
,
et al.
Simultaneous pose, correspondence and nonrigid shape
...We use the data made available by the EPFL computer vision group for that purpose [
13
]...
...Figure 3. Results on the cloth dataset [
13
]...
...As in [
13
] we plot this error as a function of the average curvature over the ground truth mesh...
...In a way similar to [
13
] we synthesized 2D3D correspondences and added centered 2DGaussian noises to evaluate the behavior of our framework in the presence of noise...
...Following [
13
], we do not plot the temporal evolution of the error but sort the frames using the average curvature over the ground truth mesh and plot the error in respect to it...
Cedric Cagniart
,
et al.
Freeform mesh tracking: A patchbased approach
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Citations
(20)
Probabilistic simultaneous pose and nonrigid shape recovery
Francesc MorenoNoguer
,
Josep M. Porta
Conference:
Computer Vision and Pattern Recognition  CVPR
, pp. 12891296, 2011
Foldable augmented papers with a relaxed constraint
Sandy Martedi
,
Hideo Saito
Conference:
International Symposium on Access Spaces  ISAS
, 2011
Monocular 3D Tracking of Inextensible Deformable Surfaces Under L2 Norm
(
Citations: 3
)
Shuhan Shen
,
Wenhuan Shi
,
Yuncai Liu
Journal:
IEEE Transactions on Image Processing
, vol. 19, no. 2, pp. 512521, 2010
Monocular TemplateBased Reconstruction of Smooth and Inextensible Surfaces
(
Citations: 2
)
Florent Brunet
,
Richard I. Hartley
,
Adrien Bartoli
,
Nassir Navab
,
Rémy Malgouyres
Conference:
Asian Conference on Computer Vision  ACCV
, pp. 5266, 2010
Simultaneous pose, correspondence and nonrigid shape
(
Citations: 2
)
Jordi SanchezRiera
,
Jonas Ostlund
,
Pascal Fua
,
Francesc MorenoNoguer
Conference:
Computer Vision and Pattern Recognition  CVPR
, pp. 11891196, 2010