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Sylvie Chambon - One of the best experts on this subject based on the ideXlab platform.

  • Generalized Thin-Plate Spline Warps
    International Journal of Computer Vision, 2009
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    The Thin-Plate Spline warp has been shown to be a very effective parameterized model of the optic flow field between images of various types of deformable surfaces, such as a paper sheet being bent. Recent work has also used such warps for images of a smooth and rigid surface. Standard Thin-Plate Spline warps are however not rigid, in the sense that they do not comply with the epipolar geometry. They are also intrinsically affine, in the sense of the affine camera model, since they are not able to simply model the effect of perspective projection. We propose three types of warps based on the Thin-Plate Spline. The first one is a rigid flexible warp. It describes the optic flow field induced by a smooth and rigid surface, and satisfies the affine epipolar geometry constraint. The second and third proposed warps extend the standard Thin-Plate Spline warp and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details and a hierarchy is defined. Experimental results on simulated and real data are reported.

  • Generalized Thin-Plate Spline Warps
    International Journal of Computer Vision, 2009
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    The Thin-Plate Spline warp has been shown to be a very effective parameterized model of the optic flow field between images of various types of deformable surfaces, such as a paper sheet being bent. Recent work has also used such warps for images of a smooth and rigid surface. Standard Thin-Plate Spline warps are however not rigid, in the sense that they do not comply with the epipolar geometry. They are also intrinsically affine, in the sense of the affine camera model, since they are not able to simply model the effect of perspective projection. We propose three types of warps based on the Thin-Plate Spline. The first one is a rigid flexible warp. It describes the optic flow field induced by a smooth and rigid surface, and satisfies the affine epipolar geometry constraint. The second and third proposed warps extend the standard Thin-Plate Spline warp and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details and a hierarchy is defined. Experimental results on simulated and real data are reported.

  • Generalized Thin-Plate Spline Warps
    2007
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    Thin-Plate Spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard Thin-Plate Spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the Thin-Plate Spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard Thin-Plate Spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.

  • CVPR - Generalized Thin-Plate SplineWarps
    2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    Thin-Plate spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard Thin-Plate spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the Thin-Plate spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard Thin-Plate spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.

Adrien Bartoli - One of the best experts on this subject based on the ideXlab platform.

  • Generalized Thin-Plate Spline Warps
    International Journal of Computer Vision, 2009
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    The Thin-Plate Spline warp has been shown to be a very effective parameterized model of the optic flow field between images of various types of deformable surfaces, such as a paper sheet being bent. Recent work has also used such warps for images of a smooth and rigid surface. Standard Thin-Plate Spline warps are however not rigid, in the sense that they do not comply with the epipolar geometry. They are also intrinsically affine, in the sense of the affine camera model, since they are not able to simply model the effect of perspective projection. We propose three types of warps based on the Thin-Plate Spline. The first one is a rigid flexible warp. It describes the optic flow field induced by a smooth and rigid surface, and satisfies the affine epipolar geometry constraint. The second and third proposed warps extend the standard Thin-Plate Spline warp and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details and a hierarchy is defined. Experimental results on simulated and real data are reported.

  • Generalized Thin-Plate Spline Warps
    International Journal of Computer Vision, 2009
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    The Thin-Plate Spline warp has been shown to be a very effective parameterized model of the optic flow field between images of various types of deformable surfaces, such as a paper sheet being bent. Recent work has also used such warps for images of a smooth and rigid surface. Standard Thin-Plate Spline warps are however not rigid, in the sense that they do not comply with the epipolar geometry. They are also intrinsically affine, in the sense of the affine camera model, since they are not able to simply model the effect of perspective projection. We propose three types of warps based on the Thin-Plate Spline. The first one is a rigid flexible warp. It describes the optic flow field induced by a smooth and rigid surface, and satisfies the affine epipolar geometry constraint. The second and third proposed warps extend the standard Thin-Plate Spline warp and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details and a hierarchy is defined. Experimental results on simulated and real data are reported.

  • Generalized Thin-Plate Spline Warps
    2007
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    Thin-Plate Spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard Thin-Plate Spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the Thin-Plate Spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard Thin-Plate Spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.

  • CVPR - Generalized Thin-Plate SplineWarps
    2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    Thin-Plate spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard Thin-Plate spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the Thin-Plate spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard Thin-Plate spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.

  • Image Registration by Combining Thin-Plate Splines with a 3D Morphable Model
    2006 International Conference on Image Processing, 2006
    Co-Authors: Vincent Gay-bellile, Mathieu Perriollat, Adrien Bartoli, Patrick Sayd
    Abstract:

    Registering images of a deforming surface is a well-studied problem. It is common practice to describe the image deformation fields with Thin-Plate splines. This has the advantage to involve small numbers of parameters, but has the drawback that the 3D surface is not explicitly reconstructed. We propose an image deformation model combining Thin-Plate splines with 3D entities-a 3D control mesh and a camera-overcoming the above mentioned drawback. An original solution to the non-rigid image registration problem using this model is proposed and demonstrated on simulated and real data.

Mathieu Perriollat - One of the best experts on this subject based on the ideXlab platform.

  • Generalized Thin-Plate Spline Warps
    International Journal of Computer Vision, 2009
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    The Thin-Plate Spline warp has been shown to be a very effective parameterized model of the optic flow field between images of various types of deformable surfaces, such as a paper sheet being bent. Recent work has also used such warps for images of a smooth and rigid surface. Standard Thin-Plate Spline warps are however not rigid, in the sense that they do not comply with the epipolar geometry. They are also intrinsically affine, in the sense of the affine camera model, since they are not able to simply model the effect of perspective projection. We propose three types of warps based on the Thin-Plate Spline. The first one is a rigid flexible warp. It describes the optic flow field induced by a smooth and rigid surface, and satisfies the affine epipolar geometry constraint. The second and third proposed warps extend the standard Thin-Plate Spline warp and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details and a hierarchy is defined. Experimental results on simulated and real data are reported.

  • Generalized Thin-Plate Spline Warps
    International Journal of Computer Vision, 2009
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    The Thin-Plate Spline warp has been shown to be a very effective parameterized model of the optic flow field between images of various types of deformable surfaces, such as a paper sheet being bent. Recent work has also used such warps for images of a smooth and rigid surface. Standard Thin-Plate Spline warps are however not rigid, in the sense that they do not comply with the epipolar geometry. They are also intrinsically affine, in the sense of the affine camera model, since they are not able to simply model the effect of perspective projection. We propose three types of warps based on the Thin-Plate Spline. The first one is a rigid flexible warp. It describes the optic flow field induced by a smooth and rigid surface, and satisfies the affine epipolar geometry constraint. The second and third proposed warps extend the standard Thin-Plate Spline warp and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details and a hierarchy is defined. Experimental results on simulated and real data are reported.

  • Generalized Thin-Plate Spline Warps
    2007
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    Thin-Plate Spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard Thin-Plate Spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the Thin-Plate Spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard Thin-Plate Spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.

  • CVPR - Generalized Thin-Plate SplineWarps
    2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007
    Co-Authors: Adrien Bartoli, Mathieu Perriollat, Sylvie Chambon
    Abstract:

    Thin-Plate spline warps have been shown to be very effective as a parameterized model of the optic flow field between images of various deforming surfaces. Examples include a sheet of paper being manually handled. Recent work has used such warps for images of smooth rigid surfaces. Standard Thin-Plate spline warps are not rigid, in the sense that they do not satisfy the epipolar geometry constraint, and are intrinsically affine, in the sense of the affine camera model. We propose three types of warps based on the Thin-Plate spline. The first one is a flexible rigid warp. It describes the optic flow field induced by a smooth rigid surface, and satisfies the affine epipolar geometry constraint. The second and third ones extend the standard Thin-Plate spline and the proposed rigid flexible warp to the perspective camera model. The properties of these warps are studied in details, and a hierarchy is defined. Experimental results on simulated and real data are reported, showing that the proposed warps outperform the standard one in several cases of interest.

  • Image Registration by Combining Thin-Plate Splines with a 3D Morphable Model
    2006 International Conference on Image Processing, 2006
    Co-Authors: Vincent Gay-bellile, Mathieu Perriollat, Adrien Bartoli, Patrick Sayd
    Abstract:

    Registering images of a deforming surface is a well-studied problem. It is common practice to describe the image deformation fields with Thin-Plate splines. This has the advantage to involve small numbers of parameters, but has the drawback that the 3D surface is not explicitly reconstructed. We propose an image deformation model combining Thin-Plate splines with 3D entities-a 3D control mesh and a camera-overcoming the above mentioned drawback. An original solution to the non-rigid image registration problem using this model is proposed and demonstrated on simulated and real data.

Andrzej Borkowski - One of the best experts on this subject based on the ideXlab platform.

  • Thin Plate spline interpolation
    Journal of Geodesy, 2019
    Co-Authors: Wolfgang Keller, Andrzej Borkowski
    Abstract:

    The Thin Plate spline (TPS) is an interpolation approach that has been developed to investigate a frequently occurring problem in geosciences: the modelling of scattered data. In this paper, we carry over the concept of the Thin Plate spline from the plane to the sphere. To develop the spherical TPS, we utilize the idea of an elastic shell that is attributed with the bending energy and the external energy. The bending energy describes the shape of the membrane, while the external energy reflects deviations between the shell and the data to be modelled. Minimizing both energy terms leads to the variational problem with the solution in the form of the Euler–Lagrange equations. We provide the solution of the variational problem for two cases: (1) total energy minimization over the whole sphere and (2) total energy minimization over a closed region of the sphere. In case (1) we found a closed analytical solution in the form of collocation in a reproducing kernel Hilbert space. The local case (2) solution is based on a discretization of the corresponding Euler–Lagrange equation using the spherical Laplace operator. The performance of the introduced spherical TPS is demonstrated on two real world data sets. It is shown quantitative that the Thin Plate approach is significantly more effective than Gaussian filter in terms of the GRACE data de-striping. We also show that the TPS can be used effectively for the modelling of the vertical total electron content. It allows the reduction of the computational effort in comparison with well-established planar TPS approximation. Moreover, the harmonicity property of the TPS can be utilized to solve various issues related to Earth gravity modelling.

R. Poeckert - One of the best experts on this subject based on the ideXlab platform.

  • Warping digital images using Thin Plate splines
    Pattern Recognition, 1993
    Co-Authors: Ian Barrodale, D. Skea, M. Berkley, R Kuwahara, R. Poeckert
    Abstract:

    This note is to direct attention brack to Thin Plate spline, because evaluation algorithms which became generaly available early in 1992 have dramatically reduced their computational complexity. Thin Plate splines make very effective warping functions, but special attention must be paid when, calculating their coefficients and when evaluating them many times