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Closed-Form Solution to Non-rigid 3D Surface Registration

Closed-Form Solution to Non-rigid 3D Surface Registration,10.1007/978-3-540-88693-8_43,Mathieu Salzmann,Francesc Moreno-noguer,Vincent Lepetit,Pascal

Closed-Form Solution to Non-rigid 3D Surface Registration   (Citations: 20)
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We present a closed-form solution to the problem of recovering the 3D shape of a non-rigid inelastic surface from 3D-to-2D 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 closed-form 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 closed-form solution then becomes tractable even for complex deformations that require many modes.
Conference: European Conference on Computer Vision - ECCV , pp. 581-594, 2008
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    • ...We make two basic assumptions, shared with many state-of-the-art approaches [16, 19, 21, 22]...
    • ...Several recent methods have been proposed to recover non-rigid 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 Moreno-Nogueret al. Probabilistic simultaneous pose and non-rigid shape recovery

    • ...The non-rigid surface is usually modeled by a collection of triangles [18], [19]...

    Sandy Martediet 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 Thin-Plate Splines [3, 5]. In this latter case, the 3D surface is represented as a parametric 2D-3D 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 image-plane measurements. As in [1, 16], 56 F. Brunet et al...
    • ...However, contrary to [1, 16], our approach is a point-wise method that does not require us to tune the relative influence of minimizing the reprojection error and maximizing the depths...

    Florent Brunetet al. Monocular Template-Based Reconstruction of Smooth and Inextensible Sur...

    • ...When 3D-to-2D correspondences between an input image and another one for which the shape is known can be established, monocular 3D non-rigid 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 3D-to-2D 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 RANSAC-based approach and hypothesize sets of 3D-to-2D correspondences and validate them with any of the current techniques to retrieve shape from such correspondences [7, 19, 21, 22, 23]...

    Jordi Sanchez-Rieraet al. Simultaneous pose, correspondence and non-rigid 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 2D-3D correspondences and added centered 2D-Gaussian 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 Cagniartet al. Free-form mesh tracking: A patch-based approach

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