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594
Signal recovery from random measurements via Orthogonal Matching Pursuit
 IEEE TRANS. INFORM. THEORY
, 2007
"... This technical report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous ..."
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Cited by 802 (9 self)
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This technical report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results for OMP, which require O(m 2) measurements. The new results for OMP are comparable with recent results for another algorithm called Basis Pursuit (BP). The OMP algorithm is faster and easier to implement, which makes it an attractive alternative to BP for signal recovery problems.
Physically based motion transformation
 In Proceedings of ACM SIGGRAPH 99. Computer Graphics Proceedings
, 1999
"... We introduce a novel algorithm for transforming character animation sequences that preserves essential physical properties of the motion. By using the spacetime constraints dynamics formulation our algorithm maintains realism of the original motion sequence without sacrificing full user control of ..."
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Cited by 203 (6 self)
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We introduce a novel algorithm for transforming character animation sequences that preserves essential physical properties of the motion. By using the spacetime constraints dynamics formulation our algorithm maintains realism of the original motion sequence without sacrificing full user control of the editing process. In contrast to most physically based animation techniques that synthesize motion from scratch, we take the approach of motion transformation as the underlying paradigm for generating computer animations. In doing so, we combine the expressive richness of an input animation sequence with the controllability of spacetime optimization to create a wide range of realistic character animations. The spacetime dynamics formulation also allows editing of intuitive, highlevel motion concepts such as the time and placement of footprints, length and mass of various extremities, number of body joints and gravity. Our algorithm is well suited for the reuse of highlydetailed captured motion animations. In addition, we describe a new methodology for mapping a motion between characters with drastically different numbers of degrees of freedom. We use this method to reduce the complexity of the spacetime optimization problems. Furthermore, our approach provides a paradigm for controlling complex dynamic and kinematic systems with simpler ones.
Synthesizing physically realistic human motion in lowdimensional, behaviorspecific spaces
 ACM Transactions on Graphics
, 2004
"... Optimization is an appealing way to compute the motion of an animated character because it allows the user to specify the desired motion in a sparse, intuitive way. The difficulty of solving this problem for complex characters such as humans is due in part to the high dimensionality of the search sp ..."
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Cited by 196 (13 self)
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Optimization is an appealing way to compute the motion of an animated character because it allows the user to specify the desired motion in a sparse, intuitive way. The difficulty of solving this problem for complex characters such as humans is due in part to the high dimensionality of the search space. The dimensionality is an artifact of the problem representation because most dynamic human behaviors are intrinsically low dimensional with, for example, legs and arms operating in a coordinated way. We describe a method that exploits this observation to create an optimization problem that is easier to solve. Our method utilizes an existing motion capture database to find a lowdimensional space that captures the properties of the desired behavior. We show that when the optimization problem is solved within this lowdimensional subspace, a sparse sketch can be used as an initial guess and full physics constraints can be enabled. We demonstrate the power of our approach with examples of forward, vertical, and turning jumps; with running and walking; and with several acrobatic flips.
Articulated Mesh Animation from Multiview Silhouettes
 ACM TRANSACTIONS ON GRAPHICS
, 2008
"... Details in mesh animations are difficult to generate but they have great impact on visual quality. In this work, we demonstrate a practical software system for capturing such details from multiview video recordings. Given a stream of synchronized video images that record a human performance from mu ..."
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Cited by 168 (6 self)
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Details in mesh animations are difficult to generate but they have great impact on visual quality. In this work, we demonstrate a practical software system for capturing such details from multiview video recordings. Given a stream of synchronized video images that record a human performance from multiple viewpoints and an articulated template of the performer, our system captures the motion of both the skeleton and the shape. The output mesh animation is enhanced with the details observed in the image silhouettes. For example, a performance in casual loosefitting clothes will generate mesh animations with flowing garment motions. We accomplish this with a fast pose tracking method followed by nonrigid deformation of the template to fit the silhouettes. The entire process takes less than sixteen seconds per frame and requires no markers or texture cues. Captured meshes are in full correspondence making them readily usable for editing operations including texturing, deformation transfer, and deformation model learning.
Learning PhysicsBased Motion Style with Nonlinear Inverse Optimization
 ACM Trans. Graph
, 2005
"... This paper presents a novel physicsbased representation of realistic character motion. The dynamical model incorporates several factors of locomotion derived from the biomechanical literature, including relative preferences for using some muscles more than others, elastic mechanisms at joints due t ..."
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Cited by 127 (14 self)
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This paper presents a novel physicsbased representation of realistic character motion. The dynamical model incorporates several factors of locomotion derived from the biomechanical literature, including relative preferences for using some muscles more than others, elastic mechanisms at joints due to the mechanical properties of tendons, ligaments, and muscles, and variable stiffness at joints depending on the task. When used in a spacetime optimization framework, the parameters of this model define a wide range of styles of natural human movement.
R.J.: Interiorpoint methods for nonconvex nonlinear programming: orderings and higherorder methods
 Mathematical Programming Ser. B
, 2000
"... Abstract. In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interiorpoint method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear depend ..."
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Cited by 117 (8 self)
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Abstract. In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interiorpoint method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerical results on the MacMPEC test suite of problems.
KNITRO: An integrated package for nonlinear optimization
 Large Scale Nonlinear Optimization, 35–59, 2006
, 2006
"... This paper describes Knitro 5.0, a Cpackage for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving largescale, smooth nonlinear programming problems ..."
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Cited by 111 (3 self)
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This paper describes Knitro 5.0, a Cpackage for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving largescale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming. Various algorithmic options are available, including two interior methods and an activeset method. The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings. 1
User's Guide For SNOPT 5.3: A Fortran Package For LargeScale Nonlinear Programming
, 1999
"... SNOPT is a generalpurpose system for solving optimization problems involving many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming ..."
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Cited by 96 (2 self)
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SNOPT is a generalpurpose system for solving optimization problems involving many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs. SNOPT finds solutions that are locally optimal , and ideally any nonlinear functions should be smooth and users should provide gradients. It is often more widely useful. For example, local optima are often global solutions, and discontinuities in the function gradients can often be tolerated if they are not too close to an optimum. Unknown gradients are estimated by finite differences. SNOPT uses a sequential quadratic programming (SQP) algorithm that obtains search directions from a sequence of quadratic programming subproblems. Each QP subproblem minimizes a quadratic model of a certain Lagrangian function subject to a linearization of the constraints. An augmented Lagrangian merit function is reduced along each search direction to ensure convergence from any starting point. SNOPT is most efficient if only some of the variables enter nonlinearly, or if the number of active constraints (including simple bounds) is nearly as large as the number of variables. SNOPT requires relatively few evaluations of the problem functions. Hence it is especially effective if the objective or constraint functions (and their gradients) are expensive to evaluate. The source code for SNOPT is suitable for any machine with a Fortran compiler. SNOPT may be called from a driver program (typically in Fortran, C or MATLAB). SNOPT can also be used as a standalone package, reading data in the MPS ...