The Experts below are selected from a list of 18645 Experts worldwide ranked by ideXlab platform
Stefan Carlsson - One of the best experts on this subject based on the ideXlab platform.
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Uncalibrated Motion Capture Exploiting Articulated Structure Constraints
International Journal of Computer Vision, 2003Co-Authors: D Liebowitz, Stefan CarlssonAbstract: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, 2003Co-Authors: D Liebowitz, Stefan CarlssonAbstract: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, 2001Co-Authors: D Liebowitz, Stefan CarlssonAbstract: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.
David Cowburn - One of the best experts on this subject based on the ideXlab platform.
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Integrating NOE and RDC using sum-of-squares relaxation for protein Structure determination
Journal of Biomolecular NMR, 2017Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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, 2017Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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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Integrating NOE and RDC using sum-of-squares relaxation for protein Structure determination
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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. 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. The two algorithms - RDC-SOS and RDC-NOE-SOS, 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. We 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 methodology. 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, achieving more accurate and faster reconstructions compared to the current state of the art.
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Residual Dipolar Coupling, Protein Backbone Conformation and Semidefinite Programming.
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract:We investigate the classical problem of protein Structure determination in NMR spectroscopy from geometrical restraints 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 semidefinite program (SDP). However, in practice there are often too few distance restraints for accurate Structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between bond directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires good initializations. 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 quaternion algebra. The two SDP based methods we propose - RDC-SDP and RDC-NOE-SDP have polynomial time complexity in the number of amino-acids, with average running time being 25 seconds and 3 minutes respectively for calculating protein fragments of typical size on a personal laptop. We further introduce 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 RDC measurements. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise, for realistic noise magnitude our SDP attains the CRB. 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 medium. Comparing to the X-ray Structure, the ubiquitin fragments considered are determined to 0.6 \AA\ resolution and the full protein Structure formed from the fragments has 1 \AA\ error.
D Liebowitz - One of the best experts on this subject based on the ideXlab platform.
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Uncalibrated Motion Capture Exploiting Articulated Structure Constraints
International Journal of Computer Vision, 2003Co-Authors: D Liebowitz, Stefan CarlssonAbstract: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, 2003Co-Authors: D Liebowitz, Stefan CarlssonAbstract: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, 2001Co-Authors: D Liebowitz, Stefan CarlssonAbstract: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.
Yuehaw Khoo - One of the best experts on this subject based on the ideXlab platform.
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Integrating NOE and RDC using sum-of-squares relaxation for protein Structure determination
Journal of Biomolecular NMR, 2017Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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, 2017Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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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Integrating NOE and RDC using sum-of-squares relaxation for protein Structure determination
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract: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. 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. The two algorithms - RDC-SOS and RDC-NOE-SOS, 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. We 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 methodology. 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, achieving more accurate and faster reconstructions compared to the current state of the art.
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Residual Dipolar Coupling, Protein Backbone Conformation and Semidefinite Programming.
arXiv: Computational Engineering Finance and Science, 2016Co-Authors: Yuehaw Khoo, Amit Singer, David CowburnAbstract:We investigate the classical problem of protein Structure determination in NMR spectroscopy from geometrical restraints 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 semidefinite program (SDP). However, in practice there are often too few distance restraints for accurate Structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between bond directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires good initializations. 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 quaternion algebra. The two SDP based methods we propose - RDC-SDP and RDC-NOE-SDP have polynomial time complexity in the number of amino-acids, with average running time being 25 seconds and 3 minutes respectively for calculating protein fragments of typical size on a personal laptop. We further introduce 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 RDC measurements. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise, for realistic noise magnitude our SDP attains the CRB. 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 medium. Comparing to the X-ray Structure, the ubiquitin fragments considered are determined to 0.6 \AA\ resolution and the full protein Structure formed from the fragments has 1 \AA\ error.
Lourdes Agapito - One of the best experts on this subject based on the ideXlab platform.
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automated Articulated Structure and 3d shape recovery from point correspondences
International Conference on Computer Vision, 2011Co-Authors: Joao Fayad, Chris Russell, Lourdes AgapitoAbstract:In this paper we propose a new method for the simultaneous segmentation and 3D reconstruction of interest point based Articulated motion. We decompose a set of point tracks into rigid-bodied overlapping regions which are associated with skeletal links, while joint centres can be derived from the regions of overlap. This allows us to formulate the problem of 3D reconstruction as one of model assignment, where each model corresponds to the motion and shape parameters of an Articulated body part. We show how this labelling can be optimised using a combination of pre-existing graph-cut based inference, and robust Structure from motion factorization techniques. The strength of our approach comes from viewing both the decomposition into parts, and the 3D reconstruction as the optimisation of a single cost function, namely the image re-projection error. We show results of full 3D shape recovery on challenging real-world sequences with one or more Articulated bodies, in the presence of outliers and missing data.
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Optimal Metric Projections for Deformable and Articulated Structure-from-Motion
International Journal of Computer Vision, 2011Co-Authors: Marco Paladini, Alessio Del Bue, Joao Xavier, Lourdes Agapito, Marko Stošić, Marija DodigAbstract:This paper describes novel algorithms for recovering the 3D shape and motion of deformable and Articulated objects purely from uncalibrated 2D image measurements using a factorisation approach. Most approaches to deformable and Articulated Structure from motion require to upgrade an initial affine solution to Euclidean space by imposing metric constraints on the motion matrix. While in the case of rigid Structure the metric upgrade step is simple since the constraints can be formulated as linear, deformability in the shape introduces non-linearities. In this paper we propose an alternating bilinear approach to solve for non-rigid 3D shape and motion, associated with a globally optimal projection step of the motion matrices onto the manifold of metric constraints. Our novel optimal projection step combines into a single optimisation the computation of the orthographic projection matrix and the configuration weights that give the closest motion matrix that satisfies the correct block Structure with the additional constraint that the projection matrix is guaranteed to have orthonormal rows (i.e. its transpose lies on the Stiefel manifold). This constraint turns out to be non-convex. The key contribution of this work is to introduce an efficient convex relaxation for the non-convex projection step. Efficient in the sense that, for both the cases of deformable and Articulated motion, the proposed relaxations turned out to be exact (i.e. tight) in all our numerical experiments. The convex relaxations are semi-definite (SDP) or second-order cone (SOCP) programs which can be readily tackled by popular solvers. An important advantage of these new algorithms is their ability to handle missing data which becomes crucial when dealing with real video sequences with self-occlusions. We show successful results of our algorithms on synthetic and real sequences of both deformable and Articulated data. We also show comparative results with state of the art algorithms which reveal that our new methods outperform existing ones.
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ICCV - Automated Articulated Structure and 3D shape recovery from point correspondences
2011 International Conference on Computer Vision, 2011Co-Authors: Joao Fayad, Chris Russell, Lourdes AgapitoAbstract:In this paper we propose a new method for the simultaneous segmentation and 3D reconstruction of interest point based Articulated motion. We decompose a set of point tracks into rigid-bodied overlapping regions which are associated with skeletal links, while joint centres can be derived from the regions of overlap. This allows us to formulate the problem of 3D reconstruction as one of model assignment, where each model corresponds to the motion and shape parameters of an Articulated body part. We show how this labelling can be optimised using a combination of pre-existing graph-cut based inference, and robust Structure from motion factorization techniques. The strength of our approach comes from viewing both the decomposition into parts, and the 3D reconstruction as the optimisation of a single cost function, namely the image re-projection error. We show results of full 3D shape recovery on challenging real-world sequences with one or more Articulated bodies, in the presence of outliers and missing data.
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factorization for non rigid and Articulated Structure using metric projections
Computer Vision and Pattern Recognition, 2009Co-Authors: Marco Paladini, Alessio Del Bue, Marko Stosic, Marija Dodig, Joao Xavier, Lourdes AgapitoAbstract:This paper describes a new algorithm for recovering the 3D shape and motion of deformable and Articulated objects purely from uncalibrated 2D image measurements using an iterative factorization approach. Most solutions to non-rigid and Articulated Structure from motion require metric constraints to be enforced on the motion matrix to solve for the transformation that upgrades the solution to metric space. While in the case of rigid Structure the metric upgrade step is simple since the motion constraints are linear, deformability in the shape introduces non-linearities. In this paper we propose an alternating least-squares approach associated with a globally optimal projection step onto the manifold of metric constraints. An important advantage of this new algorithm is its ability to handle missing data which becomes crucial when dealing with real video sequences with self-occlusions. We show successful results of our algorithms on synthetic and real sequences of both deformable and Articulated data.
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CVPR - Factorization for non-rigid and Articulated Structure using metric projections
2009 IEEE Conference on Computer Vision and Pattern Recognition, 2009Co-Authors: Marco Paladini, Alessio Del Bue, Marija Dodig, Joao Xavier, Marko Stošić, Lourdes AgapitoAbstract:This paper describes a new algorithm for recovering the 3D shape and motion of deformable and Articulated objects purely from uncalibrated 2D image measurements using an iterative factorization approach. Most solutions to non-rigid and Articulated Structure from motion require metric constraints to be enforced on the motion matrix to solve for the transformation that upgrades the solution to metric space. While in the case of rigid Structure the metric upgrade step is simple since the motion constraints are linear, deformability in the shape introduces non-linearities. In this paper we propose an alternating least-squares approach associated with a globally optimal projection step onto the manifold of metric constraints. An important advantage of this new algorithm is its ability to handle missing data which becomes crucial when dealing with real video sequences with self-occlusions. We show successful results of our algorithms on synthetic and real sequences of both deformable and Articulated data.
