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Articulated Structure

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Stefan Carlsson – One of the best experts on this subject based on the ideXlab platform.

  • Uncalibrated Motion Capture Exploiting Articulated Structure Constraints
    International Journal of Computer Vision, 2003
    Co-Authors: D Liebowitz, Stefan Carlsson

    Abstract:

    We present an algorithm for 3D reconstruction of dynamic Articulated Structures, such as humans, from uncalibrated multiple views. The reconstruction exploits constraints associated with a dynamic Articulated Structure, specifically the conservation over time of length between rotational joints. These constraints admit reconstruction of metric Structure from at least two different images in each of two uncalibrated parallel projection cameras. As a by product, the calibration of the cameras can also be computed. The algorithm is based on a stratified approach, starting with affine reconstruction from factorization, followed by rectification to metric Structure using the Articulated Structure constraints. The exploitation of these specific constraints admits reconstruction and self-calibration with fewer feature points and views compared to standard self-calibration. The method is extended to pairs of cameras that are zooming, where calibration of the cameras allows compensation for the changing scale factor in a scaled orthographic camera. Results are presented in the form of stick figures and animated 3D reconstructions using pairs of sequences from broadcast television. The technique shows promise as a means of creating 3D animations of dynamic activities such as sports events.

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  • ICCV – Uncalibrated motion capture exploiting Articulated Structure constraints
    International Journal of Computer Vision, 2003
    Co-Authors: D Liebowitz, Stefan Carlsson

    Abstract:

    We present an algorithm for 3D reconstruction of dynamic Articulated Structures, such as humans, from uncalibrated multiple views. The reconstruction exploits constraints associated with a dynamic Articulated Structure, specifically the conservation over time of length between rotational joints. These constraints admit metric reconstruction from at least two different images in each of two uncalibrated parallel projection cameras. The algorithm is based on a stratified approach, starting with affine reconstruction from factorization, followed by rectification to metric Structure using the Articulated Structure constraints. The exploitation of these specific constraints allows reconstruction and self-calibration with fewer feature paints and views compared to standard self-calibration. The method is extended to pairs of cameras that are zooming, Where calibration of the cameras allows compensation for the changing scale factor in a scaled orthographic camera. Results are presented in the form of stick figures and animated 3D reconstructions using pairs of sequences from broadcast television. The technique shows promise as a means of creating 3D animations of dynamic activities such as sports events.

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  • uncalibrated motion capture exploiting Articulated Structure constraints
    International Conference on Computer Vision, 2001
    Co-Authors: D Liebowitz, Stefan Carlsson

    Abstract:

    We present an algorithm for 3D reconstruction of dynamic Articulated Structures, such as humans, from uncalibrated multiple views. The reconstruction exploits constraints associated with a dynamic Articulated Structure, specifically the conservation over time of length between rotational joints. These constraints admit metric reconstruction from at least two different images in each of two uncalibrated parallel projection cameras. The algorithm is based on a stratified approach, starting with affine reconstruction from factorization, followed by rectification to metric Structure using the Articulated Structure constraints. The exploitation of these specific constraints allows reconstruction and self-calibration with fewer feature paints and views compared to standard self-calibration. The method is extended to pairs of cameras that are zooming, Where calibration of the cameras allows compensation for the changing scale factor in a scaled orthographic camera. Results are presented in the form of stick figures and animated 3D reconstructions using pairs of sequences from broadcast television. The technique shows promise as a means of creating 3D animations of dynamic activities such as sports events.

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David Cowburn – One of the best experts on this subject based on the ideXlab platform.

  • Integrating NOE and RDC using sum-of-squares relaxation for protein Structure determination
    Journal of Biomolecular NMR, 2017
    Co-Authors: Yuehaw Khoo, Amit Singer, David Cowburn

    Abstract:

    We revisit the problem of protein Structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate Structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an Articulated Structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein Structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms—RDC-SOS and RDC–NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér–Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein Structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the Structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

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  • Integrating NOE and RDC using sum-of-squares relaxation for protein Structure determination.
    Journal of Biomolecular NMR, 2017
    Co-Authors: Yuehaw Khoo, Amit Singer, David Cowburn

    Abstract:

    We revisit the problem of protein Structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate Structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an Articulated Structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein Structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms—RDC-SOS and RDC–NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramer–Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein Structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the Structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

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  • Integrating NOE and RDC using semidefinite programming for protein Structure determination
    arXiv: Computational Engineering Finance and Science, 2016
    Co-Authors: Yuehaw Khoo, Amit Singer, David Cowburn

    Abstract:

    We revisit the established problem of protein Structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, in practice the distance restraints are imprecise, and sometimes sparse, for accurate Structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an Articulated Structure composed of rigid units. We estimate the rotation of each rigid unit using SDP relaxation that incorporates chirality constraints. The two SDP based methods we propose – RDC-SDP and RDC-NOE-SDP have polynomial time complexity in the number of amino-acids and run efficiently on a regular PC.
    We further introduce a statistical tool, the Cram\’er-Rao bound (CRB) to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein Structure from noisy measurements. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise, for realistic noise magnitude our SDP algorithm attains the CRB. Through such comparison, the utility of CRB for benchmarking other procedures for Structure determination in NMR is demonstrated.
    Finally, we apply our proposed method in a divide-and-conquer fashion to determine the Structure of ubiquitin from experimental distance restraints and RDC measurements obtained in two alignment media.

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D Liebowitz – One of the best experts on this subject based on the ideXlab platform.

  • Uncalibrated Motion Capture Exploiting Articulated Structure Constraints
    International Journal of Computer Vision, 2003
    Co-Authors: D Liebowitz, Stefan Carlsson

    Abstract:

    We present an algorithm for 3D reconstruction of dynamic Articulated Structures, such as humans, from uncalibrated multiple views. The reconstruction exploits constraints associated with a dynamic Articulated Structure, specifically the conservation over time of length between rotational joints. These constraints admit reconstruction of metric Structure from at least two different images in each of two uncalibrated parallel projection cameras. As a by product, the calibration of the cameras can also be computed. The algorithm is based on a stratified approach, starting with affine reconstruction from factorization, followed by rectification to metric Structure using the Articulated Structure constraints. The exploitation of these specific constraints admits reconstruction and self-calibration with fewer feature points and views compared to standard self-calibration. The method is extended to pairs of cameras that are zooming, where calibration of the cameras allows compensation for the changing scale factor in a scaled orthographic camera. Results are presented in the form of stick figures and animated 3D reconstructions using pairs of sequences from broadcast television. The technique shows promise as a means of creating 3D animations of dynamic activities such as sports events.

    Free Register to Access Article

  • ICCV – Uncalibrated motion capture exploiting Articulated Structure constraints
    International Journal of Computer Vision, 2003
    Co-Authors: D Liebowitz, Stefan Carlsson

    Abstract:

    We present an algorithm for 3D reconstruction of dynamic Articulated Structures, such as humans, from uncalibrated multiple views. The reconstruction exploits constraints associated with a dynamic Articulated Structure, specifically the conservation over time of length between rotational joints. These constraints admit metric reconstruction from at least two different images in each of two uncalibrated parallel projection cameras. The algorithm is based on a stratified approach, starting with affine reconstruction from factorization, followed by rectification to metric Structure using the Articulated Structure constraints. The exploitation of these specific constraints allows reconstruction and self-calibration with fewer feature paints and views compared to standard self-calibration. The method is extended to pairs of cameras that are zooming, Where calibration of the cameras allows compensation for the changing scale factor in a scaled orthographic camera. Results are presented in the form of stick figures and animated 3D reconstructions using pairs of sequences from broadcast television. The technique shows promise as a means of creating 3D animations of dynamic activities such as sports events.

    Free Register to Access Article

  • uncalibrated motion capture exploiting Articulated Structure constraints
    International Conference on Computer Vision, 2001
    Co-Authors: D Liebowitz, Stefan Carlsson

    Abstract:

    We present an algorithm for 3D reconstruction of dynamic Articulated Structures, such as humans, from uncalibrated multiple views. The reconstruction exploits constraints associated with a dynamic Articulated Structure, specifically the conservation over time of length between rotational joints. These constraints admit metric reconstruction from at least two different images in each of two uncalibrated parallel projection cameras. The algorithm is based on a stratified approach, starting with affine reconstruction from factorization, followed by rectification to metric Structure using the Articulated Structure constraints. The exploitation of these specific constraints allows reconstruction and self-calibration with fewer feature paints and views compared to standard self-calibration. The method is extended to pairs of cameras that are zooming, Where calibration of the cameras allows compensation for the changing scale factor in a scaled orthographic camera. Results are presented in the form of stick figures and animated 3D reconstructions using pairs of sequences from broadcast television. The technique shows promise as a means of creating 3D animations of dynamic activities such as sports events.

    Free Register to Access Article